|\^/| Maple 18 (X86 64 WINDOWS)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
# End Function number 7
# Begin Function number 8
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number 0
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
> if (years_int > 0) then # if number 1
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 2
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 8
# Begin Function number 9
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 7
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 7;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 7
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 12
# Begin Function number 13
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 6
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 7
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 8
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 9
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 10
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 11
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 12
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 12
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 19
# Begin Function number 20
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 20
# Begin Function number 21
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 21
# Begin Function number 22
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 12
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 12;
> if (errflag) then # if number 12
> quit;
> fi;# end if 12
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 22
# Begin Function number 23
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 12
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 13
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 13
> fi;# end if 12;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 23
# Begin Function number 24
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 12
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 12;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 24
# Begin Function number 25
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 25
# Begin Function number 26
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 26
# Begin Function number 27
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalf(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalf(in_val); ret end proc
# End Function number 27
# Begin Function number 28
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 12
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 28
# Begin Function number 29
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 29
# Begin Function number 30
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 12
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 13
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 15
> if (rcs > glob__0) then # if number 16
> rad_c := sqrt(rcs) * float_abs(glob_h);
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 16
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> fi;# end if 13
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 12;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := sqrt(rcs)*float_abs(glob_h)
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 30
# Begin Function number 31
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 31
# Begin Function number 32
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 32
# Begin Function number 33
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 12
> if (array_fact_1[nnn] = 0) then # if number 13
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 13;
> else
> ret := factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 33
# Begin Function number 34
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 12
> if (array_fact_2[mmm,nnn] = 0) then # if number 13
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 13;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 34
# Begin Function number 35
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 35
# Begin Function number 36
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 36
# Begin Function number 37
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 37
# Begin Function number 38
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 38
# Begin Function number 39
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 39
# Begin Function number 40
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 40
# Begin Function number 41
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 41
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return((c(sin(0.1)) + c(cos(0.05)) - c(tan(0.02))) *c( x)) ;
> end;
exact_soln_y :=
proc(x) return (c(sin(0.1)) + c(cos(0.05)) - c(tan(0.02)))*c(x) end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]);
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if (rad_given < glob_least_given_sing) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])*
(array_x[1] - array_given_rad_poles[1, 1])
+ array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if rad_given < glob_least_given_sing then
glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if array_rad_test_poles[1, 1] < glob_least_ratio_sing then
glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_float(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if array_rad_test_poles[1, 2] < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if array_rad_test_poles[1, 3] < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D05,
> array_const_0D02,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_tmp5_g,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y[1]) < min_size) then # if number 3
> min_size := float_abs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < glob__1) then # if number 3
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D05, array_const_0D02, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
array_tmp5_g, array_tmp5, array_tmp6, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y[1]) < min_size then
min_size := float_abs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D05,
> array_const_0D02,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_tmp5_g,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D05, array_const_0D02, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
array_tmp5_g, array_tmp5, array_tmp6, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := float_abs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D05,
> array_const_0D02,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_tmp5_g,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
> est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
> fi;# end if 3;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 3
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D05, array_const_0D02, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
array_tmp5_g, array_tmp5, array_tmp6, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y[no_terms - 3]))
+ c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D05,
> array_const_0D02,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_tmp5_g,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D05, array_const_0D02, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
array_tmp5_g, array_tmp5, array_tmp6, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D05,
> array_const_0D02,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_tmp5_g,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 3
> if (iter >= 0) then # if number 4
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> closed_form_val_y := evalf(exact_soln_y(ind_var));
> omniout_float(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := float_abs(numeric_val - closed_form_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 5
> relerr := abserr*glob__100/float_abs(closed_form_val_y);
> if (c(relerr) > c(glob_prec)) then # if number 6
> glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 6;
> else
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 5;
> if (glob_good_digits < glob_min_good_digits) then # if number 5
> glob_min_good_digits := glob_good_digits;
> fi;# end if 5;
> if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 5
> glob_min_apfp_est_good_digits := glob_apfp_est_good_digits;
> fi;# end if 5;
> if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 5
> est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*27*ATS_MAX_TERMS/float_abs(numeric_val));
> if (evalf(est_rel_err) > glob_prec) then # if number 6
> glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
> else
> glob_est_digits := Digits;
> fi;# end if 6;
> else
> relerr := glob__m1 ;
> glob_est_digits := -16;
> fi;# end if 5;
> array_est_digits[1] := glob_est_digits;
> if (glob_iter = 1) then # if number 5
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 5;
> array_est_rel_error[1] := est_rel_err;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," ");
> omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," ");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 4;
> #BOTTOM DISPLAY ALOT
> fi;# end if 3;
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D05, array_const_0D02, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
array_tmp5_g, array_tmp5, array_tmp6, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
closed_form_val_y := evalf(exact_soln_y(ind_var));
omniout_float(ALWAYS, "y[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := float_abs(numeric_val - closed_form_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if c(glob_prec) < c(float_abs(closed_form_val_y)) then
relerr := abserr*glob__100/float_abs(closed_form_val_y);
if c(glob_prec) < c(relerr) then
glob_good_digits := -int_trunc(log10(c(relerr))) + 3
else glob_good_digits := Digits
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits
then glob_min_apfp_est_good_digits := glob_apfp_est_good_digits
end if;
if glob_prec < evalf(float_abs(numeric_val)) then
est_rel_err := evalf(array_max_est_error[1]*100.0*
sqrt(glob_iter)*27*ATS_MAX_TERMS/float_abs(numeric_val))
;
if glob_prec < evalf(est_rel_err) then
glob_est_digits := -int_trunc(log10(est_rel_err)) + 3
else glob_est_digits := Digits
end if
else relerr := glob__m1; glob_est_digits := -16
end if;
array_est_digits[1] := glob_est_digits;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
array_est_rel_error[1] := est_rel_err;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Desired digits ", 32,
glob_desired_digits_correct, 4, " ");
omniout_int(INFO, "Estimated correct digits ", 32,
glob_est_digits, 4, " ");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D05,
> array_const_0D02,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_tmp5_g,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr((glob_clock_sec));
> if (c(percent_done) < glob__100) then # if number 3
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 3;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr((left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D05, array_const_0D02, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
array_tmp5_g, array_tmp5, array_tmp6, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(glob_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(left_sec);
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D05,
> array_const_0D02,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_tmp5_g,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 3;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 4
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_rad_test_poles[1,1]) then # if number 6
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,2]) then # if number 8
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 9
> glob_min_pole_est := rad_c;
> fi;# end if 9;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[1,3]) then # if number 10
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 11
> glob_min_pole_est := rad_c;
> fi;# end if 11;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test1
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 10;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 9;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 9
> display_poles();
> fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D05, array_const_0D02, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
array_tmp5_g, array_tmp5, array_tmp6, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4],
array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
if
float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_poles() end if
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D05,
> array_const_0D02,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_tmp5_g,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre sin ID_CONST $eq_no = 1
> array_tmp1[1] := sin(array_const_0D1[1]);
> #emit pre add CONST CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre cos ID_CONST $eq_no = 1
> array_tmp3[1] := cos(array_const_0D05[1]);
> #emit pre add CONST CONST $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp2[1] + array_tmp3[1];
> #emit pre tan ID_CONST $eq_no = 1
> array_tmp5[1] := tan(array_const_0D02[1]);
> #emit pre sub CONST CONST $eq_no = 1 i = 1
> array_tmp6[1] := array_tmp4[1] - array_tmp5[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp6[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp6[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp6[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp6[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp6[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (false) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp6[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D05, array_const_0D02, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
array_tmp5_g, array_tmp5, array_tmp6, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
array_tmp1[1] := sin(array_const_0D1[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
array_tmp3[1] := cos(array_const_0D05[1]);
array_tmp4[1] := array_tmp2[1] + array_tmp3[1];
array_tmp5[1] := tan(array_const_0D02[1]);
array_tmp6[1] := array_tmp4[1] - array_tmp5[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D05,
> array_const_0D02,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_tmp5_g,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 30;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(30),[]);
> array_norms:= Array(0..(30),[]);
> array_fact_1:= Array(0..(30),[]);
> array_1st_rel_error:= Array(0..(2),[]);
> array_last_rel_error:= Array(0..(2),[]);
> array_est_rel_error:= Array(0..(2),[]);
> array_max_est_error:= Array(0..(2),[]);
> array_type_pole:= Array(0..(2),[]);
> array_type_real_pole:= Array(0..(2),[]);
> array_type_complex_pole:= Array(0..(2),[]);
> array_est_digits:= Array(0..(2),[]);
> array_y:= Array(0..(30),[]);
> array_x:= Array(0..(30),[]);
> array_tmp0:= Array(0..(30),[]);
> array_tmp1_g:= Array(0..(30),[]);
> array_tmp1:= Array(0..(30),[]);
> array_tmp2:= Array(0..(30),[]);
> array_tmp3_g:= Array(0..(30),[]);
> array_tmp3:= Array(0..(30),[]);
> array_tmp4:= Array(0..(30),[]);
> array_tmp5_g:= Array(0..(30),[]);
> array_tmp5:= Array(0..(30),[]);
> array_tmp6:= Array(0..(30),[]);
> array_m1:= Array(0..(30),[]);
> array_y_higher := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..30+ 1),[]);
> array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(30) ,(0..30+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 30) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp1_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp3_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp5_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp6[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=30) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1_g);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3_g);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5_g);
> zero_ats_ar(array_tmp5);
> zero_ats_ar(array_tmp6);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_0D1);
> array_const_0D1[1] := c(0.1);
> zero_ats_ar(array_const_0D05);
> array_const_0D05[1] := c(0.05);
> zero_ats_ar(array_const_0D02);
> array_const_0D02[1] := c(0.02);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_h := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 1000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 30;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/add_sub_sin_c_cos_c_tan_cpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( 0.1 ) + cos ( 0.05 ) - tan ( 0.02 ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := c(-5.0);");
> omniout_str(ALWAYS,"x_end := c(5.0) ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 3;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=100000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return((c(sin(0.1)) + c(cos(0.05)) - c(tan(0.02))) *c( x)) ;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := c(-5.0);
> x_end := c(5.0) ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_type_given_pole := 3;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=100000;
> glob_upper_ratio_limit:=c(1.000001);
> glob_lower_ratio_limit:=c(0.999999);
> glob_look_poles:=true;
> glob_h:=c(0.001);
> glob_display_interval:=c(0.01);
> #END OVERRIDE BLOCK
> #END BLOCK 2
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
> # after second input block
> glob_check_sign := c(my_check_sign(x_start,x_end));
> glob__pi := arccos(glob__m1);
> glob_prec = expt(10.0,c(-Digits));
> if (glob_optimize) then # if number 9
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> found_h := false;
> glob_min_pole_est := glob_larger_float;
> last_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> glob_min_h := float_abs(glob_min_h) * glob_check_sign;
> glob_max_h := float_abs(glob_max_h) * glob_check_sign;
> glob_h := float_abs(glob_min_h) * glob_check_sign;
> glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign));
> display_max := c(x_end) - c(x_start)/glob__10;
> if ((glob_display_interval) > (display_max)) then # if number 10
> glob_display_interval := c(display_max);
> fi;# end if 10;
> chk_data();
> min_value := glob_larger_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := glob_small_float;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> atomall();
> if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> glob_h := glob_check_sign * float_abs(glob_min_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
> glob_h_reason := 2;
> glob_h := glob_display_interval;
> found_h := true;
> fi;# end if 10;
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if ( not found_h) then # if number 10
> est_answer := est_size_answer();
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := test_suggested_h();
> omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
> if (estimated_step_error < est_needed_step_err) then # if number 11
> omniout_str(ALWAYS,"Double H and LOOP");
> glob_h := glob_h*glob__2;
> else
> omniout_str(ALWAYS,"Found H for OPTIMAL");
> found_h := true;
> glob_h_reason := 3;
> glob_h := glob_h/glob__2;
> fi;# end if 11;
> fi;# end if 10;
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 10
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 10;
> if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MAX H");
> glob_h := glob_check_sign * float_abs(glob_max_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> else
> found_h := true;
> glob_h := glob_h * glob_check_sign;
> fi;# end if 9;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 9
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 9;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 9
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> glob_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and (glob_check_sign * array_x[1] < glob_check_sign * x_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1
> #left paren 0001C
> if (reached_interval()) then # if number 10
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 10;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> track_estimated_error();
> atomall();
> track_estimated_error();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if (reached_interval()) then # if number 10
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 10;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 10
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 10;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 10;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = sin ( 0.1 ) + cos ( 0.05 ) - tan ( 0.02 ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2015-05-01T21:46:14-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"add_sub_sin_c_cos_c_tan_c")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( 0.1 ) + cos ( 0.05 ) - tan ( 0.02 ) ; ")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 308.maple.seems.ok | ")
> ;
> logitem_str(html_log_file,"add_sub_sin_c_cos_c_tan_c diffeq.mxt")
> ;
> logitem_str(html_log_file,"add_sub_sin_c_cos_c_tan_c maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> fi;# end if 14
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D05, array_const_0D02, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
array_tmp5_g, array_tmp5, array_tmp6, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
ATS_MAX_TERMS := 30;
Digits := 32;
max_terms := 30;
glob_html_log := true;
array_y_init := Array(0 .. 30, []);
array_norms := Array(0 .. 30, []);
array_fact_1 := Array(0 .. 30, []);
array_1st_rel_error := Array(0 .. 2, []);
array_last_rel_error := Array(0 .. 2, []);
array_est_rel_error := Array(0 .. 2, []);
array_max_est_error := Array(0 .. 2, []);
array_type_pole := Array(0 .. 2, []);
array_type_real_pole := Array(0 .. 2, []);
array_type_complex_pole := Array(0 .. 2, []);
array_est_digits := Array(0 .. 2, []);
array_y := Array(0 .. 30, []);
array_x := Array(0 .. 30, []);
array_tmp0 := Array(0 .. 30, []);
array_tmp1_g := Array(0 .. 30, []);
array_tmp1 := Array(0 .. 30, []);
array_tmp2 := Array(0 .. 30, []);
array_tmp3_g := Array(0 .. 30, []);
array_tmp3 := Array(0 .. 30, []);
array_tmp4 := Array(0 .. 30, []);
array_tmp5_g := Array(0 .. 30, []);
array_tmp5 := Array(0 .. 30, []);
array_tmp6 := Array(0 .. 30, []);
array_m1 := Array(0 .. 30, []);
array_y_higher := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []);
array_y_set_initial := Array(0 .. 2, 0 .. 31, []);
array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
array_fact_2 := Array(0 .. 30, 0 .. 31, []);
term := 1;
while term <= 30 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 30 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 30 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp1_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp3_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp5_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp6[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 30 do
term := 1;
while term <= 30 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1_g);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3_g);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5_g);
zero_ats_ar(array_tmp5);
zero_ats_ar(array_tmp6);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_0D1);
array_const_0D1[1] := c(0.1);
zero_ats_ar(array_const_0D05);
array_const_0D05[1] := c(0.05);
zero_ats_ar(array_const_0D02);
array_const_0D02[1] := c(0.02);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_h := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 1000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 30;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS, "##############temp/add_sub_sin_c_cos_c_tan_cpost\
ode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( 0.1 ) + \
cos ( 0.05 ) - tan ( 0.02 ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := c(-5.0);");
omniout_str(ALWAYS, "x_end := c(5.0) ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 3;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=100000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS,
"return((c(sin(0.1)) + c(cos(0.05)) - c(tan(0.02))) *c( x)) ;");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := c(-5.0);
x_end := c(5.0);
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 3;
glob_desired_digits_correct := 8;
glob_max_minutes := 3.0;
glob_subiter_method := 3;
glob_max_iter := 100000;
glob_upper_ratio_limit := c(1.000001);
glob_lower_ratio_limit := c(0.999999);
glob_look_poles := true;
glob_h := c(0.001);
glob_display_interval := c(0.01);
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
glob_check_sign := c(my_check_sign(x_start, x_end));
glob__pi := arccos(glob__m1);
glob_prec = expt(10.0, c(-Digits));
if glob_optimize then
omniout_str(ALWAYS, "START of Optimize");
found_h := false;
glob_min_pole_est := glob_larger_float;
last_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
glob_min_h := float_abs(glob_min_h)*glob_check_sign;
glob_max_h := float_abs(glob_max_h)*glob_check_sign;
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_display_interval :=
c(float_abs(c(glob_display_interval))*glob_check_sign);
display_max := c(x_end) - c(x_start)/glob__10;
if display_max < glob_display_interval then
glob_display_interval := c(display_max)
end if;
chk_data();
min_value := glob_larger_float;
est_answer := est_size_answer();
opt_iter := 1;
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
;
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := glob_small_float;
while opt_iter <= 100 and not found_h do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] :=
array_y_init[it]*expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
atomall();
if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if;
if
glob_check_sign*glob_display_interval <= glob_check_sign*glob_h
then
omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL");
glob_h_reason := 2;
glob_h := glob_display_interval;
found_h := true
end if;
if glob_look_poles then check_for_pole() end if;
if not found_h then
est_answer := est_size_answer();
est_needed_step_err := estimated_needed_step_error(x_start,
x_end, glob_h, est_answer);
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := test_suggested_h();
omniout_float(ALWAYS, "estimated_step_error", 32,
estimated_step_error, 32, "");
if estimated_step_error < est_needed_step_err then
omniout_str(ALWAYS, "Double H and LOOP");
glob_h := glob_h*glob__2
else
omniout_str(ALWAYS, "Found H for OPTIMAL");
found_h := true;
glob_h_reason := 3;
glob_h := glob_h/glob__2
end if
end if;
opt_iter := opt_iter + 1
end do;
if not found_h and opt_iter = 1 then
omniout_str(ALWAYS, "Beginning glob_h too large.");
found_h := false
end if;
if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then
omniout_str(ALWAYS, "SETTING H FOR MAX H");
glob_h := float_abs(glob_max_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if
else found_h := true; glob_h := glob_check_sign*glob_h
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
glob_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
glob_clock_sec - glob_orig_start_sec < glob_max_sec do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
track_estimated_error();
atomall();
track_estimated_error();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = sin ( 0.1 ) +\
cos ( 0.05 ) - tan ( 0.02 ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2015-05-01T21:46:14-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "add_sub_sin_c_cos_c_tan_c");
logitem_str(html_log_file, "diff ( y , x , 1 ) = si\
n ( 0.1 ) + cos ( 0.05 ) - tan ( 0.02 ) ; ");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 308.maple.seems.ok | ");
logitem_str(html_log_file, "add_sub_sin_c_cos_c_tan_c diffeq.mxt\
");
logitem_str(html_log_file, "add_sub_sin_c_cos_c_tan_c maple res\
ults");
logitem_str(html_log_file, "OK");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
##############ECHO OF PROBLEM#################
##############temp/add_sub_sin_c_cos_c_tan_cpostode.ode#################
diff ( y , x , 1 ) = sin ( 0.1 ) + cos ( 0.05 ) - tan ( 0.02 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(-5.0);
x_end := c(5.0) ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 3;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=100000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return((c(sin(0.1)) + c(cos(0.05)) - c(tan(0.02))) *c( x)) ;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
x[1] = -5
y[1] (closed_form) = -5.392905049741959874861393478458
y[1] (numeric) = -5.392905049741959874861393478458
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 14
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4.2MB, alloc=40.3MB, time=0.06
TOP MAIN SOLVE Loop
x[1] = -4.99
y[1] (closed_form) = -5.3821192396424759551116706915011
y[1] (numeric) = -5.382119239642475955111670691501
absolute error = 1e-31
relative error = 1.8580041717292538407038400857301e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.98
y[1] (closed_form) = -5.3713334295429920353619479045442
y[1] (numeric) = -5.371333429542992035361947904544
absolute error = 2e-31
relative error = 3.7234702076019986606876152722061e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.97
y[1] (closed_form) = -5.3605476194435081156122251175873
y[1] (numeric) = -5.360547619443508115612225117587
absolute error = 3e-31
relative error = 5.5964431490516961761240414654687e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.96
y[1] (closed_form) = -5.3497618093440241958625023306303
y[1] (numeric) = -5.34976180934402419586250233063
absolute error = 3e-31
relative error = 5.6077263005618810474468721942298e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.95
y[1] (closed_form) = -5.3389759992445402761127795436734
y[1] (numeric) = -5.338975999244540276112779543673
absolute error = 4e-31
relative error = 7.4920733874173548808987167901360e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.94
y[1] (closed_form) = -5.3281901891450563563630567567165
y[1] (numeric) = -5.328190189145056356363056756716
absolute error = 5e-31
relative error = 9.3840494098471423735953056961471e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.93
y[1] (closed_form) = -5.3174043790455724366133339697596
y[1] (numeric) = -5.317404379045572436613333969759
absolute error = 6e-31
relative error = 1.1283700791394292087357600845185e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.92
y[1] (closed_form) = -5.3066185689460885168636111828027
y[1] (numeric) = -5.306618568946088516863611182802
absolute error = 7e-31
relative error = 1.3191074333029031840606734592389e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.91
y[1] (closed_form) = -5.2958327588466045971138883958458
y[1] (numeric) = -5.295832758846604597113888395845
absolute error = 8e-31
relative error = 1.5106217216992222672280508395590e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.9
y[1] (closed_form) = -5.2850469487471206773641656088888
y[1] (numeric) = -5.285046948747120677364165608888
absolute error = 8e-31
relative error = 1.5137046231720778228754550249459e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.89
y[1] (closed_form) = -5.2742611386476367576144428219319
y[1] (numeric) = -5.274261138647636757614442821931
absolute error = 9e-31
relative error = 1.7064001503550263800819930112503e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.88
y[1] (closed_form) = -5.263475328548152837864720034975
y[1] (numeric) = -5.263475328548152837864720034974
absolute error = 1.0e-30
relative error = 1.8998854133051181690803610712691e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.87
y[1] (closed_form) = -5.2526895184486689181149972480181
y[1] (numeric) = -5.252689518448668918114997248017
absolute error = 1.1e-30
relative error = 2.0941652769244095136803651397480e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.86
y[1] (closed_form) = -5.2419037083491849983652744610612
y[1] (numeric) = -5.24190370834918499836527446106
absolute error = 1.2e-30
relative error = 2.2892446461553028802746079080971e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.85
y[1] (closed_form) = -5.2311178982497010786155516741043
y[1] (numeric) = -5.231117898249701078615551674103
absolute error = 1.3e-30
relative error = 2.4851284663933339514733630177590e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.84
y[1] (closed_form) = -5.2203320881502171588658288871473
y[1] (numeric) = -5.220332088150217158865828887146
absolute error = 1.3e-30
relative error = 2.4902630293404276166623575694486e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.83
y[1] (closed_form) = -5.2095462780507332391161061001904
y[1] (numeric) = -5.209546278050733239116106100189
absolute error = 1.4e-30
relative error = 2.6873741498344859898875831964618e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.82
y[1] (closed_form) = -5.1987604679512493193663833132335
y[1] (numeric) = -5.198760467951249319366383313232
absolute error = 1.5e-30
relative error = 2.8853031587953246883129134941265e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.81
y[1] (closed_form) = -5.1879746578517653996166605262766
y[1] (numeric) = -5.187974657851765399616660526275
absolute error = 1.6e-30
relative error = 3.0840551573984121962951058720310e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.8
y[1] (closed_form) = -5.1771888477522814798669377393197
y[1] (numeric) = -5.177188847752281479866937739318
absolute error = 1.7e-30
relative error = 3.2836352893290125688938907181768e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.79
y[1] (closed_form) = -5.1664030376527975601172149523628
y[1] (numeric) = -5.166403037652797560117214952361
absolute error = 1.8e-30
relative error = 3.4840487412259202499377644363315e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.78
y[1] (closed_form) = -5.1556172275533136403674921654058
y[1] (numeric) = -5.155617227553313640367492165404
absolute error = 1.8e-30
relative error = 3.4913375461238824261928643619306e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.77
y[1] (closed_form) = -5.1448314174538297206177693784489
y[1] (numeric) = -5.144831417453829720617769378447
absolute error = 1.9e-30
relative error = 3.6930267404958187974241316253265e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.76
y[1] (closed_form) = -5.134045607354345800868046591492
y[1] (numeric) = -5.13404560735434580086804659149
absolute error = 2.0e-30
relative error = 3.8955633684575532206353621965518e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.75
y[1] (closed_form) = -5.1232597972548618811183238045351
y[1] (numeric) = -5.123259797254861881118323804533
absolute error = 2.1e-30
relative error = 4.0989527822212317887864295280770e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.74
y[1] (closed_form) = -5.1124739871553779613686010175782
y[1] (numeric) = -5.112473987155377961368601017576
absolute error = 2.2e-30
relative error = 4.3032003791653478192503705614230e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.73
y[1] (closed_form) = -5.1016881770558940416188782306213
y[1] (numeric) = -5.101688177055894041618878230619
absolute error = 2.3e-30
relative error = 4.5083116023121873847268441149946e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=46.8MB, alloc=40.3MB, time=0.58
TOP MAIN SOLVE Loop
x[1] = -4.72
y[1] (closed_form) = -5.0909023669564101218691554436644
y[1] (numeric) = -5.090902366956410121869155443662
absolute error = 2.4e-30
relative error = 4.7142919408113440670061840819287e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.71
y[1] (closed_form) = -5.0801165568569262021194326567074
y[1] (numeric) = -5.080116556856926202119432656705
absolute error = 2.4e-30
relative error = 4.7243010532122174089743500778565e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.7
y[1] (closed_form) = -5.0693307467574422823697098697505
y[1] (numeric) = -5.069330746757442282369709869748
absolute error = 2.5e-30
relative error = 4.9316174558132854601660436318050e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.69
y[1] (closed_form) = -5.0585449366579583626199870827936
y[1] (numeric) = -5.058544936657958362619987082791
absolute error = 2.6e-30
relative error = 5.1398179368902642493159107190325e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.68
y[1] (closed_form) = -5.0477591265584744428702642958367
y[1] (numeric) = -5.047759126558474442870264295834
absolute error = 2.7e-30
relative error = 5.3489081636128711529493242468038e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.67
y[1] (closed_form) = -5.0369733164589905231205415088798
y[1] (numeric) = -5.036973316458990523120541508877
absolute error = 2.8e-30
relative error = 5.5588938516918917906454076397904e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.66
y[1] (closed_form) = -5.0261875063595066033708187219229
y[1] (numeric) = -5.02618750635950660337081872192
absolute error = 2.9e-30
relative error = 5.7697807659000069375161523348928e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.65
y[1] (closed_form) = -5.0154016962600226836210959349659
y[1] (numeric) = -5.015401696260022683621095934963
absolute error = 2.9e-30
relative error = 5.7821888965793617911452193291615e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.64
y[1] (closed_form) = -5.004615886160538763871373148009
y[1] (numeric) = -5.004615886160538763871373148006
absolute error = 3.0e-30
relative error = 5.9944660454282176714087254490043e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.63
y[1] (closed_form) = -4.9938300760610548441216503610521
y[1] (numeric) = -4.993830076061054844121650361049
absolute error = 3.1e-30
relative error = 6.2076601582029865360362207961467e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.62
y[1] (closed_form) = -4.9830442659615709243719275740952
y[1] (numeric) = -4.983044265961570924371927574092
absolute error = 3.2e-30
relative error = 6.4217771892148756121989001058308e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.61
y[1] (closed_form) = -4.9722584558620870046222047871383
y[1] (numeric) = -4.972258455862087004622204787135
absolute error = 3.3e-30
relative error = 6.6368231444393976127700942932143e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.6
y[1] (closed_form) = -4.9614726457626030848724820001814
y[1] (numeric) = -4.961472645762603084872482000178
absolute error = 3.4e-30
relative error = 6.8528040820779392742133371509776e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.59
y[1] (closed_form) = -4.9506868356631191651227592132244
y[1] (numeric) = -4.950686835663119165122759213221
absolute error = 3.4e-30
relative error = 6.8677339384659086408238237242914e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.58
y[1] (closed_form) = -4.9399010255636352453730364262675
y[1] (numeric) = -4.939901025563635245373036426264
absolute error = 3.5e-30
relative error = 7.0851621963431044384044906325932e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.57
y[1] (closed_form) = -4.9291152154641513256233136393106
y[1] (numeric) = -4.929115215464151325623313639307
absolute error = 3.6e-30
relative error = 7.3035420002066336968060794967300e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.56
y[1] (closed_form) = -4.9183294053646674058735908523537
y[1] (numeric) = -4.91832940536466740587359085235
absolute error = 3.7e-30
relative error = 7.5228796102274591361655700664112e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.55
y[1] (closed_form) = -4.9075435952651834861238680653968
y[1] (numeric) = -4.907543595265183486123868065393
absolute error = 3.8e-30
relative error = 7.7431813416110134785552122429922e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.54
y[1] (closed_form) = -4.8967577851656995663741452784399
y[1] (numeric) = -4.896757785165699566374145278436
absolute error = 3.9e-30
relative error = 7.9644535652033059458011964555933e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.53
y[1] (closed_form) = -4.8859719750662156466244224914829
y[1] (numeric) = -4.885971975066215646624422491479
absolute error = 3.9e-30
relative error = 7.9820351404024302414872918120075e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.52
y[1] (closed_form) = -4.875186164966731726874699704526
y[1] (numeric) = -4.875186164966731726874699704522
absolute error = 4.0e-30
relative error = 8.2048148822380324470019132989322e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.51
y[1] (closed_form) = -4.8644003548672478071249769175691
y[1] (numeric) = -4.864400354867247807124976917565
absolute error = 4.1e-30
relative error = 8.4285825608445242410110563889030e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.5
y[1] (closed_form) = -4.8536145447677638873752541306122
y[1] (numeric) = -4.853614544767763887375254130608
absolute error = 4.2e-30
relative error = 8.6533447624670448874380178926071e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.49
y[1] (closed_form) = -4.8428287346682799676255313436553
y[1] (numeric) = -4.842828734668279967625531343651
absolute error = 4.3e-30
relative error = 8.8791081320255233095728945923187e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.48
y[1] (closed_form) = -4.8320429245687960478758085566984
y[1] (numeric) = -4.832042924568796047875808556694
absolute error = 4.4e-30
relative error = 9.1058793737695306532351591344398e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.47
y[1] (closed_form) = -4.8212571144693121281260857697415
y[1] (numeric) = -4.821257114469312128126085769737
absolute error = 4.5e-30
relative error = 9.3336652519419228172270087528119e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.46
y[1] (closed_form) = -4.8104713043698282083763629827845
y[1] (numeric) = -4.81047130436982820837636298278
absolute error = 4.5e-30
relative error = 9.3545927525068150208530782791637e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=89.4MB, alloc=40.3MB, time=1.09
TOP MAIN SOLVE Loop
x[1] = -4.45
y[1] (closed_form) = -4.7996854942703442886266401958276
y[1] (numeric) = -4.799685494270344288626640195823
absolute error = 4.6e-30
relative error = 9.5839612939041107100035832197414e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.44
y[1] (closed_form) = -4.7888996841708603688769174088707
y[1] (numeric) = -4.788899684170860368876917408866
absolute error = 4.7e-30
relative error = 9.8143630269293221455016129573488e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.43
y[1] (closed_form) = -4.7781138740713764491271946219138
y[1] (numeric) = -4.778113874071376449127194621909
absolute error = 4.8e-30
relative error = 1.0045804948365482616825818901446e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.42
y[1] (closed_form) = -4.7673280639718925293774718349569
y[1] (numeric) = -4.767328063971892529377471834952
absolute error = 4.9e-30
relative error = 1.0278294118314928882137917180133e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.41
y[1] (closed_form) = -4.756542253872408609627749048
y[1] (numeric) = -4.756542253872408609627749047995
absolute error = 5.0e-30
relative error = 1.0511837660917207103301771006568e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.4
y[1] (closed_form) = -4.745756443772924689878026261043
y[1] (numeric) = -4.745756443772924689878026261038
absolute error = 5.0e-30
relative error = 1.0535728201055655301263820486129e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.39
y[1] (closed_form) = -4.7349706336734407701283034740861
y[1] (numeric) = -4.734970633673440770128303474081
absolute error = 5.1e-30
relative error = 1.0770922133562136900244197344361e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.38
y[1] (closed_form) = -4.7241848235739568503785806871292
y[1] (numeric) = -4.724184823573956850378580687124
absolute error = 5.2e-30
relative error = 1.1007190010965908369539553092357e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.37
y[1] (closed_form) = -4.7133990134744729306288579001723
y[1] (numeric) = -4.713399013474472930628857900167
absolute error = 5.3e-30
relative error = 1.1244539205886401905055940216774e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.36
y[1] (closed_form) = -4.7026132033749890108791351132154
y[1] (numeric) = -4.70261320337498901087913511321
absolute error = 5.4e-30
relative error = 1.1482977158581760089817815355524e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.35
y[1] (closed_form) = -4.6918273932755050911294123262585
y[1] (numeric) = -4.691827393275505091129412326253
absolute error = 5.5e-30
relative error = 1.1722511377726292335199285322497e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.34
y[1] (closed_form) = -4.6810415831760211713796895393015
y[1] (numeric) = -4.681041583176021171379689539296
absolute error = 5.5e-30
relative error = 1.1749521772605846004174398883148e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.33
y[1] (closed_form) = -4.6702557730765372516299667523446
y[1] (numeric) = -4.670255773076537251629966752339
absolute error = 5.6e-30
relative error = 1.1990777961848099151184320405460e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.32
y[1] (closed_form) = -4.6594699629770533318802439653877
y[1] (numeric) = -4.659469962977053331880243965382
absolute error = 5.7e-30
relative error = 1.2233151077892399766467436008894e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.31
y[1] (closed_form) = -4.6486841528775694121305211784308
y[1] (numeric) = -4.648684152877569412130521178425
absolute error = 5.8e-30
relative error = 1.2476648895171244700150937299583e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.3
y[1] (closed_form) = -4.6378983427780854923807983914739
y[1] (numeric) = -4.637898342778085492380798391468
absolute error = 5.9e-30
relative error = 1.2721279260437433098642268828833e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.29
y[1] (closed_form) = -4.627112532678601572631075604517
y[1] (numeric) = -4.627112532678601572631075604511
absolute error = 6.0e-30
relative error = 1.2967050093606960370786240598312e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.28
y[1] (closed_form) = -4.61632672257911765288135281756
y[1] (numeric) = -4.616326722579117652881352817554
absolute error = 6.0e-30
relative error = 1.2997346939620060745484339291299e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.27
y[1] (closed_form) = -4.6055409124796337331316300306031
y[1] (numeric) = -4.605540912479633733131630030597
absolute error = 6.1e-30
relative error = 1.3244915452755680950160231468276e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.26
y[1] (closed_form) = -4.5947551023801498133819072436462
y[1] (numeric) = -4.59475510238014981338190724364
absolute error = 6.2e-30
relative error = 1.3493646259380200780210188866741e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.25
y[1] (closed_form) = -4.5839692922806658936321844566893
y[1] (numeric) = -4.583969292280665893632184456683
absolute error = 6.3e-30
relative error = 1.3743547563918247762401557829435e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.24
y[1] (closed_form) = -4.5731834821811819738824616697324
y[1] (numeric) = -4.573183482181181973882461669726
absolute error = 6.4e-30
relative error = 1.3994627648194681758659867211763e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.23
y[1] (closed_form) = -4.5623976720816980541327388827755
y[1] (numeric) = -4.562397672081698054132738882769
absolute error = 6.5e-30
relative error = 1.4246894872349491329368570491881e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.22
y[1] (closed_form) = -4.5516118619822141343830160958186
y[1] (numeric) = -4.551611861982214134383016095812
absolute error = 6.6e-30
relative error = 1.4500357675765698101834187057686e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.21
y[1] (closed_form) = -4.5408260518827302146332933088616
y[1] (numeric) = -4.540826051882730214633293308855
absolute error = 6.6e-30
relative error = 1.4534800330577493109201964224094e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.2
y[1] (closed_form) = -4.5300402417832462948835705219047
y[1] (numeric) = -4.530040241783246294883570521898
absolute error = 6.7e-30
relative error = 1.4790155588910510394345591806242e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.19
y[1] (closed_form) = -4.5192544316837623751338477349478
y[1] (numeric) = -4.519254431683762375133847734941
absolute error = 6.8e-30
relative error = 1.5046729726758243752449332169211e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=132.0MB, alloc=40.3MB, time=1.59
TOP MAIN SOLVE Loop
x[1] = -4.18
y[1] (closed_form) = -4.5084686215842784553841249479909
y[1] (numeric) = -4.508468621584278455384124947984
absolute error = 6.9e-30
relative error = 1.5304531492059794016572707653534e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.17
y[1] (closed_form) = -4.497682811484794535634402161034
y[1] (numeric) = -4.497682811484794535634402161027
absolute error = 7.0e-30
relative error = 1.5563569716667346919852550166559e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.16
y[1] (closed_form) = -4.4868970013853106158846793740771
y[1] (numeric) = -4.48689700138531061588467937407
absolute error = 7.1e-30
relative error = 1.5823853317354743827475084230128e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.15
y[1] (closed_form) = -4.4761111912858266961349565871201
y[1] (numeric) = -4.476111191285826696134956587113
absolute error = 7.1e-30
relative error = 1.5861983084384514294529241059598e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.14
y[1] (closed_form) = -4.4653253811863427763852338001632
y[1] (numeric) = -4.465325381186342776385233800156
absolute error = 7.2e-30
relative error = 1.6124244899006915939325499178771e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.13
y[1] (closed_form) = -4.4545395710868588566355110132063
y[1] (numeric) = -4.454539571086858856635511013199
absolute error = 7.3e-30
relative error = 1.6387776746629910328164354189562e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.12
y[1] (closed_form) = -4.4437537609873749368857882262494
y[1] (numeric) = -4.443753760987374936885788226242
absolute error = 7.4e-30
relative error = 1.6652587875066608573259708496522e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.11
y[1] (closed_form) = -4.4329679508878910171360654392925
y[1] (numeric) = -4.432967950887891017136065439285
absolute error = 7.5e-30
relative error = 1.6918687622133169096920003700353e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.1
y[1] (closed_form) = -4.4221821407884070973863426523356
y[1] (numeric) = -4.422182140788407097386342652328
absolute error = 7.6e-30
relative error = 1.7186085416746395769476202783226e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.09
y[1] (closed_form) = -4.4113963306889231776366198653786
y[1] (numeric) = -4.411396330688923177636619865371
absolute error = 7.6e-30
relative error = 1.7228105185491496981626511347489e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.08
y[1] (closed_form) = -4.4006105205894392578868970784217
y[1] (numeric) = -4.400610520589439257886897078414
absolute error = 7.7e-30
relative error = 1.7497572129988509882687168532845e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.07
y[1] (closed_form) = -4.3898247104899553381371742914648
y[1] (numeric) = -4.389824710489955338137174291457
absolute error = 7.8e-30
relative error = 1.7768363236374942994563848603633e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.06
y[1] (closed_form) = -4.3790389003904714183874515045079
y[1] (numeric) = -4.3790389003904714183874515045
absolute error = 7.9e-30
relative error = 1.8040488289098255087287211827480e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.05
y[1] (closed_form) = -4.368253090290987498637728717551
y[1] (numeric) = -4.368253090290987498637728717543
absolute error = 8.0e-30
relative error = 1.8313957169242423042196863264777e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.04
y[1] (closed_form) = -4.3574672801915035788880059305941
y[1] (numeric) = -4.357467280191503578888005930586
absolute error = 8.1e-30
relative error = 1.8588779855723938363219928818100e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.03
y[1] (closed_form) = -4.3466814700920196591382831436371
y[1] (numeric) = -4.346681470092019659138283143629
absolute error = 8.1e-30
relative error = 1.8634905860328712403823452214672e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.02
y[1] (closed_form) = -4.3358956599925357393885603566802
y[1] (numeric) = -4.335895659992535739388560356672
absolute error = 8.2e-30
relative error = 1.8911894203685972301970081748235e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.01
y[1] (closed_form) = -4.3251098498930518196388375697233
y[1] (numeric) = -4.325109849893051819638837569715
absolute error = 8.3e-30
relative error = 1.9190264035040026513823178262016e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4
y[1] (closed_form) = -4.3143240397935678998891147827664
y[1] (numeric) = -4.314324039793567899889114782758
absolute error = 8.4e-30
relative error = 1.9470025715550850996735540258366e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.99
y[1] (closed_form) = -4.3035382296940839801393919958095
y[1] (numeric) = -4.303538229694083980139391995801
absolute error = 8.5e-30
relative error = 1.9751189710249699662519643417605e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.98
y[1] (closed_form) = -4.2927524195946000603896692088526
y[1] (numeric) = -4.292752419594600060389669208844
absolute error = 8.6e-30
relative error = 2.0033766589344019929639345085181e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.97
y[1] (closed_form) = -4.2819666094951161406399464218957
y[1] (numeric) = -4.281966609495116140639946421887
absolute error = 8.7e-30
relative error = 2.0317767029542089921026652302721e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.96
y[1] (closed_form) = -4.2711807993956322208902236349387
y[1] (numeric) = -4.27118079939563222089022363493
absolute error = 8.7e-30
relative error = 2.0369074522040933582443386273182e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.95
y[1] (closed_form) = -4.2603949892961483011405008479818
y[1] (numeric) = -4.260394989296148301140500847973
absolute error = 8.8e-30
relative error = 2.0655361819993669532401778694831e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.94
y[1] (closed_form) = -4.2496091791966643813907780610249
y[1] (numeric) = -4.249609179196664381390778061016
absolute error = 8.9e-30
relative error = 2.0943102352961393989720366001868e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.93
y[1] (closed_form) = -4.238823369097180461641055274068
y[1] (numeric) = -4.238823369097180461641055274059
absolute error = 9.0e-30
relative error = 2.1232307214341167935371363422427e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.92
y[1] (closed_form) = -4.2280375589976965418913324871111
y[1] (numeric) = -4.228037558997696541891332487102
absolute error = 9.1e-30
relative error = 2.1522987610727981544010376135949e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=174.7MB, alloc=40.3MB, time=2.11
TOP MAIN SOLVE Loop
x[1] = -3.91
y[1] (closed_form) = -4.2172517488982126221416097001542
y[1] (numeric) = -4.217251748898212622141609700145
absolute error = 9.2e-30
relative error = 2.1815154863362298035558028300690e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.9
y[1] (closed_form) = -4.2064659387987287023918869131972
y[1] (numeric) = -4.206465938798728702391886913188
absolute error = 9.2e-30
relative error = 2.1871091157883739825392792475820e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.89
y[1] (closed_form) = -4.1956801286992447826421641262403
y[1] (numeric) = -4.195680128699244782642164126231
absolute error = 9.3e-30
relative error = 2.2165655423506293826617765259249e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.88
y[1] (closed_form) = -4.1848943185997608628924413392834
y[1] (numeric) = -4.184894318599760862892441339274
absolute error = 9.4e-30
relative error = 2.2461738061632056869086165737437e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.87
y[1] (closed_form) = -4.1741085085002769431427185523265
y[1] (numeric) = -4.174108508500276943142718552317
absolute error = 9.5e-30
relative error = 2.2759350842590511193427787923524e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.86
y[1] (closed_form) = -4.1633226984007930233929957653696
y[1] (numeric) = -4.16332269840079302339299576536
absolute error = 9.6e-30
relative error = 2.3058505658683465281107967737517e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.85
y[1] (closed_form) = -4.1525368883013091036432729784127
y[1] (numeric) = -4.152536888301309103643272978403
absolute error = 9.7e-30
relative error = 2.3359214525769110039373499134959e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.84
y[1] (closed_form) = -4.1417510782018251838935501914557
y[1] (numeric) = -4.141751078201825183893550191446
absolute error = 9.7e-30
relative error = 2.3420045813596633763434367622291e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.83
y[1] (closed_form) = -4.1309652681023412641438274044988
y[1] (numeric) = -4.130965268102341264143827404489
absolute error = 9.8e-30
relative error = 2.3723268931045423320652529470594e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.82
y[1] (closed_form) = -4.1201794580028573443941046175419
y[1] (numeric) = -4.120179458002857344394104617532
absolute error = 9.9e-30
relative error = 2.4028079604082949995971309967318e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.81
y[1] (closed_form) = -4.109393647903373424644381830585
y[1] (numeric) = -4.109393647903373424644381830575
absolute error = 1.00e-29
relative error = 2.4334490333146920380871816345914e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.8
y[1] (closed_form) = -4.0986078378038895048946590436281
y[1] (numeric) = -4.098607837803889504894659043618
absolute error = 1.01e-29
relative error = 2.4642513750258595873061272758082e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.79
y[1] (closed_form) = -4.0878220277044055851449362566712
y[1] (numeric) = -4.087822027704405585144936256661
absolute error = 1.02e-29
relative error = 2.4952162620758723478665976961343e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.78
y[1] (closed_form) = -4.0770362176049216653952134697142
y[1] (numeric) = -4.077036217604921665395213469704
absolute error = 1.02e-29
relative error = 2.5018173632982952905858214995633e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.77
y[1] (closed_form) = -4.0662504075054377456454906827573
y[1] (numeric) = -4.066250407505437745645490682747
absolute error = 1.03e-29
relative error = 2.5330461648373596724311742410152e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.76
y[1] (closed_form) = -4.0554645974059538258957678958004
y[1] (numeric) = -4.05546459740595382589576789579
absolute error = 1.04e-29
relative error = 2.5644410770229084392863426885386e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.75
y[1] (closed_form) = -4.0446787873064699061460451088435
y[1] (numeric) = -4.044678787306469906146045108833
absolute error = 1.05e-29
relative error = 2.5960034287401134662314053677821e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.74
y[1] (closed_form) = -4.0338929772069859863963223218866
y[1] (numeric) = -4.033892977206985986396322321876
absolute error = 1.06e-29
relative error = 2.6277345630868222633740352271286e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.73
y[1] (closed_form) = -4.0231071671075020666465995349297
y[1] (numeric) = -4.023107167107502066646599534919
absolute error = 1.07e-29
relative error = 2.6596358375640764159973226192329e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.72
y[1] (closed_form) = -4.0123213570080181468968767479728
y[1] (numeric) = -4.012321357008018146896876747962
absolute error = 1.08e-29
relative error = 2.6917086242697029027744986532303e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.71
y[1] (closed_form) = -4.0015355469085342271471539610158
y[1] (numeric) = -4.001535546908534227147153961005
absolute error = 1.08e-29
relative error = 2.6989639035804029105986886765544e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.7
y[1] (closed_form) = -3.9907497368090503073974311740589
y[1] (numeric) = -3.990749736809050307397431174048
absolute error = 1.09e-29
relative error = 2.7313163487709688013438531379175e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.69
y[1] (closed_form) = -3.979963926709566387647708387102
y[1] (numeric) = -3.979963926709566387647708387091
absolute error = 1.10e-29
relative error = 2.7638441459679876237461729622148e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.68
y[1] (closed_form) = -3.9691781166100824678979856001451
y[1] (numeric) = -3.969178116610082467897985600134
absolute error = 1.11e-29
relative error = 2.7965487246715119832267662638181e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.67
y[1] (closed_form) = -3.9583923065105985481482628131882
y[1] (numeric) = -3.958392306510598548148262813177
absolute error = 1.12e-29
relative error = 2.8294315299619765299524854144764e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.66
y[1] (closed_form) = -3.9476064964111146283985400262313
y[1] (numeric) = -3.94760649641111462839854002622
absolute error = 1.13e-29
relative error = 2.8624940227130447080810773473788e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.65
y[1] (closed_form) = -3.9368206863116307086488172392743
y[1] (numeric) = -3.936820686311630708648817239263
absolute error = 1.13e-29
relative error = 2.8703364720903407209799296140840e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=217.3MB, alloc=40.3MB, time=2.61
TOP MAIN SOLVE Loop
x[1] = -3.64
y[1] (closed_form) = -3.9260348762121467888990944523174
y[1] (numeric) = -3.926034876212146788899094452306
absolute error = 1.14e-29
relative error = 2.9036930031041300544582045911221e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.63
y[1] (closed_form) = -3.9152490661126628691493716653605
y[1] (numeric) = -3.915249066112662869149371665349
absolute error = 1.15e-29
relative error = 2.9372333166579402658068832870420e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.62
y[1] (closed_form) = -3.9044632560131789493996488784036
y[1] (numeric) = -3.904463256013178949399648878392
absolute error = 1.16e-29
relative error = 2.9709589358114952849530684950940e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.61
y[1] (closed_form) = -3.8936774459136950296499260914467
y[1] (numeric) = -3.893677445913695029649926091435
absolute error = 1.17e-29
relative error = 3.0048714005005270632080968344925e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.6
y[1] (closed_form) = -3.8828916358142111099002033044898
y[1] (numeric) = -3.882891635814211109900203304478
absolute error = 1.18e-29
relative error = 3.0389722677711645735645419979989e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.59
y[1] (closed_form) = -3.8721058257147271901504805175328
y[1] (numeric) = -3.872105825714727190150480517521
absolute error = 1.18e-29
relative error = 3.0474373715811121071956410007789e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.58
y[1] (closed_form) = -3.8613200156152432704007577305759
y[1] (numeric) = -3.861320015615243270400757730564
absolute error = 1.19e-29
relative error = 3.0818476458506933607495734114732e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.57
y[1] (closed_form) = -3.850534205515759350651034943619
y[1] (numeric) = -3.850534205515759350651034943607
absolute error = 1.20e-29
relative error = 3.1164506947660425765082897572415e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.56
y[1] (closed_form) = -3.8397483954162754309013121566621
y[1] (numeric) = -3.83974839541627543090131215665
absolute error = 1.21e-29
relative error = 3.1512481428326016193218303521432e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.55
y[1] (closed_form) = -3.8289625853167915111515893697052
y[1] (numeric) = -3.828962585316791511151589369693
absolute error = 1.22e-29
relative error = 3.1862416328600990229399542743402e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.54
y[1] (closed_form) = -3.8181767752173075914018665827483
y[1] (numeric) = -3.818176775217307591401866582736
absolute error = 1.23e-29
relative error = 3.2214328262210851124542257893180e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.53
y[1] (closed_form) = -3.8073909651178236716521437957913
y[1] (numeric) = -3.807390965117823671652143795779
absolute error = 1.23e-29
relative error = 3.2305586982500400277869573071348e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.52
y[1] (closed_form) = -3.7966051550183397519024210088344
y[1] (numeric) = -3.796605155018339751902421008822
absolute error = 1.24e-29
relative error = 3.2660757423272531433917843506999e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.51
y[1] (closed_form) = -3.7858193449188558321526982218775
y[1] (numeric) = -3.785819344918855832152698221865
absolute error = 1.25e-29
relative error = 3.3017951627239945388576075597555e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.5
y[1] (closed_form) = -3.7750335348193719124029754349206
y[1] (numeric) = -3.775033534819371912402975434908
absolute error = 1.26e-29
relative error = 3.3377186940944315994403783300056e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.49
y[1] (closed_form) = -3.7642477247198879926532526479637
y[1] (numeric) = -3.764247724719887992653252647951
absolute error = 1.27e-29
relative error = 3.3738480909741548322900990760165e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.48
y[1] (closed_form) = -3.7534619146204040729035298610068
y[1] (numeric) = -3.753461914620404072903529860994
absolute error = 1.28e-29
relative error = 3.4101851280658304975125193665446e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.47
y[1] (closed_form) = -3.7426761045209201531538070740499
y[1] (numeric) = -3.742676104520920153153807074037
absolute error = 1.29e-29
relative error = 3.4467316005297924778082677279116e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.46
y[1] (closed_form) = -3.7318902944214362334040842870929
y[1] (numeric) = -3.73189029442143623340408428708
absolute error = 1.29e-29
relative error = 3.4566932525544450572238985594952e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.45
y[1] (closed_form) = -3.721104484321952313654361500136
y[1] (numeric) = -3.721104484321952313654361500123
absolute error = 1.30e-29
relative error = 3.4935863947848317868538581554004e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.44
y[1] (closed_form) = -3.7103186742224683939046387131791
y[1] (numeric) = -3.710318674222468393904638713166
absolute error = 1.31e-29
relative error = 3.5306940320281858811909686791887e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.43
y[1] (closed_form) = -3.6995328641229844741549159262222
y[1] (numeric) = -3.699532864122984474154915926209
absolute error = 1.32e-29
relative error = 3.5680180403341834396350011302295e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.42
y[1] (closed_form) = -3.6887470540235005544051931392653
y[1] (numeric) = -3.688747054023500554405193139252
absolute error = 1.33e-29
relative error = 3.6055603176946020364325074552529e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.41
y[1] (closed_form) = -3.6779612439240166346554703523084
y[1] (numeric) = -3.677961243924016634655470352295
absolute error = 1.34e-29
relative error = 3.6433227843650524138563921164935e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.4
y[1] (closed_form) = -3.6671754338245327149057475653514
y[1] (numeric) = -3.667175433824532714905747565338
absolute error = 1.34e-29
relative error = 3.6540384396131849209559697403656e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.39
y[1] (closed_form) = -3.6563896237250487951560247783945
y[1] (numeric) = -3.656389623725048795156024778381
absolute error = 1.35e-29
relative error = 3.6921666970071146011508609845195e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=259.8MB, alloc=40.3MB, time=3.11
TOP MAIN SOLVE Loop
x[1] = -3.38
y[1] (closed_form) = -3.6456038136255648754063019914376
y[1] (numeric) = -3.645603813625564875406301991424
absolute error = 1.36e-29
relative error = 3.7305205653915409066723492182837e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.37
y[1] (closed_form) = -3.6348180035260809556565792044807
y[1] (numeric) = -3.634818003526080955656579204467
absolute error = 1.37e-29
relative error = 3.7691020531729074276568729905272e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.36
y[1] (closed_form) = -3.6240321934265970359068564175238
y[1] (numeric) = -3.62403219342659703590685641751
absolute error = 1.38e-29
relative error = 3.8079131926672582731710665471294e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.35
y[1] (closed_form) = -3.6132463833271131161571336305669
y[1] (numeric) = -3.613246383327113116157133630553
absolute error = 1.39e-29
relative error = 3.8469560404570977804495239458605e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.34
y[1] (closed_form) = -3.6024605732276291964074108436099
y[1] (numeric) = -3.602460573227629196407410843596
absolute error = 1.39e-29
relative error = 3.8584738729135561570376961732434e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.33
y[1] (closed_form) = -3.591674763128145276657688056653
y[1] (numeric) = -3.591674763128145276657688056639
absolute error = 1.40e-29
relative error = 3.8979030461563265258729810327059e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.32
y[1] (closed_form) = -3.5808889530286613569079652696961
y[1] (numeric) = -3.580888953028661356907965269682
absolute error = 1.41e-29
relative error = 3.9375697445391135836771531503580e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.31
y[1] (closed_form) = -3.5701031429291774371582424827392
y[1] (numeric) = -3.570103142929177437158242482725
absolute error = 1.42e-29
relative error = 3.9774761208577482974197190572406e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.3
y[1] (closed_form) = -3.5593173328296935174085196957823
y[1] (numeric) = -3.559317332829693517408519695768
absolute error = 1.43e-29
relative error = 4.0176243540025565548819368787104e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.29
y[1] (closed_form) = -3.5485315227302095976587969088254
y[1] (numeric) = -3.548531522730209597658796908811
absolute error = 1.44e-29
relative error = 4.0580166493549320357937730455995e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.28
y[1] (closed_form) = -3.5377457126307256779090741218684
y[1] (numeric) = -3.537745712630725677909074121854
absolute error = 1.44e-29
relative error = 4.0703886513346726822443638170800e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.27
y[1] (closed_form) = -3.5269599025312417581593513349115
y[1] (numeric) = -3.526959902531241758159351334897
absolute error = 1.45e-29
relative error = 4.1111893530724820074656375964221e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.26
y[1] (closed_form) = -3.5161740924317578384096285479546
y[1] (numeric) = -3.51617409243175783840962854794
absolute error = 1.46e-29
relative error = 4.1522403658638975248661829940424e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.25
y[1] (closed_form) = -3.5053882823322739186599057609977
y[1] (numeric) = -3.505388282332273918659905760983
absolute error = 1.47e-29
relative error = 4.1935440002724909839122702094942e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.24
y[1] (closed_form) = -3.4946024722327899989101829740408
y[1] (numeric) = -3.494602472232789998910182974026
absolute error = 1.48e-29
relative error = 4.2351025953873103285080246299796e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.23
y[1] (closed_form) = -3.4838166621333060791604601870839
y[1] (numeric) = -3.483816662133306079160460187069
absolute error = 1.49e-29
relative error = 4.2769185192644505359186134431616e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.22
y[1] (closed_form) = -3.473030852033822159410737400127
y[1] (numeric) = -3.473030852033822159410737400112
absolute error = 1.50e-29
relative error = 4.3189941693768524837479015657422e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.21
y[1] (closed_form) = -3.46224504193433823966101461317
y[1] (numeric) = -3.462245041934338239661014613155
absolute error = 1.50e-29
relative error = 4.3324489798733535818281130970997e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.2
y[1] (closed_form) = -3.4514592318348543199112918262131
y[1] (numeric) = -3.451459231834854319911291826198
absolute error = 1.51e-29
relative error = 4.3749611354883608638498014568650e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.19
y[1] (closed_form) = -3.4406734217353704001615690392562
y[1] (numeric) = -3.440673421735370400161569039241
absolute error = 1.52e-29
relative error = 4.4177398249943713263230364521147e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.18
y[1] (closed_form) = -3.4298876116358864804118462522993
y[1] (numeric) = -3.429887611635886480411846252284
absolute error = 1.53e-29
relative error = 4.4607875628620548105728326737496e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.17
y[1] (closed_form) = -3.4191018015364025606621234653424
y[1] (numeric) = -3.419101801536402560662123465327
absolute error = 1.54e-29
relative error = 4.5041068952904176858904509535652e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.16
y[1] (closed_form) = -3.4083159914369186409124006783855
y[1] (numeric) = -3.40831599143691864091240067837
absolute error = 1.55e-29
relative error = 4.5477004007088334907986870705948e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.15
y[1] (closed_form) = -3.3975301813374347211626778914285
y[1] (numeric) = -3.397530181337434721162677891413
absolute error = 1.55e-29
relative error = 4.5621375448380678828329686168507e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.14
y[1] (closed_form) = -3.3867443712379508014129551044716
y[1] (numeric) = -3.386744371237950801412955104456
absolute error = 1.56e-29
relative error = 4.6061935268819119737499913259101e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.13
y[1] (closed_form) = -3.3759585611384668816632323175147
y[1] (numeric) = -3.375958561138466881663232317499
absolute error = 1.57e-29
relative error = 4.6505310167982406914460365442925e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.12
y[1] (closed_form) = -3.3651727510389829619135095305578
y[1] (numeric) = -3.365172751038982961913509530542
absolute error = 1.58e-29
relative error = 4.6951527213935202342555179499722e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=302.3MB, alloc=40.3MB, time=3.61
TOP MAIN SOLVE Loop
x[1] = -3.11
y[1] (closed_form) = -3.3543869409394990421637867436009
y[1] (numeric) = -3.354386940939499042163786743585
absolute error = 1.59e-29
relative error = 4.7400613822884478770187580785181e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.1
y[1] (closed_form) = -3.343601130840015122414063956644
y[1] (numeric) = -3.343601130840015122414063956628
absolute error = 1.60e-29
relative error = 4.7852597764794718271546642724094e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.09
y[1] (closed_form) = -3.332815320740531202664341169687
y[1] (numeric) = -3.332815320740531202664341169671
absolute error = 1.60e-29
relative error = 4.8007460540732565256244204674658e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.08
y[1] (closed_form) = -3.3220295106410472829146183827301
y[1] (numeric) = -3.322029510641047282914618382714
absolute error = 1.61e-29
relative error = 4.8464349724856014385813574236193e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.07
y[1] (closed_form) = -3.3112437005415633631648955957732
y[1] (numeric) = -3.311243700541563363164895595757
absolute error = 1.62e-29
relative error = 4.8924215385748997385933884316043e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.06
y[1] (closed_form) = -3.3004578904420794434151728088163
y[1] (numeric) = -3.3004578904420794434151728088
absolute error = 1.63e-29
relative error = 4.9387086704556313608277202958507e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.05
y[1] (closed_form) = -3.2896720803425955236654500218594
y[1] (numeric) = -3.289672080342595523665450021843
absolute error = 1.64e-29
relative error = 4.9852993245126300756668674510101e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.04
y[1] (closed_form) = -3.2788862702431116039157272349025
y[1] (numeric) = -3.278886270243111603915727234886
absolute error = 1.65e-29
relative error = 5.0321964960305300978404826795588e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.03
y[1] (closed_form) = -3.2681004601436276841660044479455
y[1] (numeric) = -3.268100460143627684166004447929
absolute error = 1.65e-29
relative error = 5.0488044052583536295165238765212e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.02
y[1] (closed_form) = -3.2573146500441437644162816609886
y[1] (numeric) = -3.257314650044143764416281660972
absolute error = 1.66e-29
relative error = 5.0962224357953977695649632338202e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.01
y[1] (closed_form) = -3.2465288399446598446665588740317
y[1] (numeric) = -3.246528839944659844666558874015
absolute error = 1.67e-29
relative error = 5.1439555363027877178529271051212e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3
y[1] (closed_form) = -3.2357430298451759249168360870748
y[1] (numeric) = -3.235743029845175924916836087058
absolute error = 1.68e-29
relative error = 5.1920068574802269324628107355642e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.99
y[1] (closed_form) = -3.2249572197456920051671133001179
y[1] (numeric) = -3.224957219745692005167113300101
absolute error = 1.69e-29
relative error = 5.2403795921772476802807872331005e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.98
y[1] (closed_form) = -3.214171409646208085417390513161
y[1] (numeric) = -3.214171409646208085417390513144
absolute error = 1.70e-29
relative error = 5.2890769761004229297619716265934e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.97
y[1] (closed_form) = -3.2033855995467241656676677262041
y[1] (numeric) = -3.203385599546724165667667726187
absolute error = 1.71e-29
relative error = 5.3381022885348653526403357129718e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.96
y[1] (closed_form) = -3.1925997894472402459179449392471
y[1] (numeric) = -3.19259978944724024591794493923
absolute error = 1.71e-29
relative error = 5.3561364178880236815343909011915e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.95
y[1] (closed_form) = -3.1818139793477563261682221522902
y[1] (numeric) = -3.181813979347756326168222152273
absolute error = 1.72e-29
relative error = 5.4057214254636745301670910806117e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.94
y[1] (closed_form) = -3.1710281692482724064184993653333
y[1] (numeric) = -3.171028169248272406418499365316
absolute error = 1.73e-29
relative error = 5.4556437460160304866136191524090e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.93
y[1] (closed_form) = -3.1602423591487884866687765783764
y[1] (numeric) = -3.160242359148788486668776578359
absolute error = 1.74e-29
relative error = 5.5059068332615765861075637980752e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.92
y[1] (closed_form) = -3.1494565490493045669190537914195
y[1] (numeric) = -3.149456549049304566919053791402
absolute error = 1.75e-29
relative error = 5.5565141882279825903925628591226e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.91
y[1] (closed_form) = -3.1386707389498206471693310044626
y[1] (numeric) = -3.138670738949820647169331004445
absolute error = 1.76e-29
relative error = 5.6074693600670099417860498862254e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.9
y[1] (closed_form) = -3.1278849288503367274196082175056
y[1] (numeric) = -3.127884928850336727419608217488
absolute error = 1.76e-29
relative error = 5.6268054613086203208956569547988e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.89
y[1] (closed_form) = -3.1170991187508528076698854305487
y[1] (numeric) = -3.117099118750852807669885430531
absolute error = 1.77e-29
relative error = 5.6783564864928334592555456017973e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.88
y[1] (closed_form) = -3.1063133086513688879201626435918
y[1] (numeric) = -3.106313308651368887920162643574
absolute error = 1.78e-29
relative error = 5.7302655049074925221873779199556e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.87
y[1] (closed_form) = -3.0955274985518849681704398566349
y[1] (numeric) = -3.095527498551884968170439856617
absolute error = 1.79e-29
relative error = 5.7825362586421143660455644702961e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.86
y[1] (closed_form) = -3.084741688452401048420717069678
y[1] (numeric) = -3.08474168845240104842071706966
absolute error = 1.80e-29
relative error = 5.8351725421231321668538082692405e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.85
y[1] (closed_form) = -3.0739558783529171286709942827211
y[1] (numeric) = -3.073955878352917128670994282703
absolute error = 1.81e-29
relative error = 5.8881782030320869346852678141423e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=345.0MB, alloc=40.3MB, time=4.13
TOP MAIN SOLVE Loop
x[1] = -2.84
y[1] (closed_form) = -3.0631700682534332089212714957641
y[1] (numeric) = -3.063170068253433208921271495746
absolute error = 1.81e-29
relative error = 5.9089112248737492126243004472909e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.83
y[1] (closed_form) = -3.0523842581539492891715487088072
y[1] (numeric) = -3.052384258153949289171548708789
absolute error = 1.82e-29
relative error = 5.9625520448094478906375034949060e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.82
y[1] (closed_form) = -3.0415984480544653694218259218503
y[1] (numeric) = -3.041598448054465369421825921832
absolute error = 1.83e-29
relative error = 6.0165732960922082614025732308021e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.81
y[1] (closed_form) = -3.0308126379549814496721031348934
y[1] (numeric) = -3.030812637954981449672103134875
absolute error = 1.84e-29
relative error = 6.0709790402666608767994228224696e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.8
y[1] (closed_form) = -3.0200268278554975299223803479365
y[1] (numeric) = -3.020026827855497529922380347918
absolute error = 1.85e-29
relative error = 6.1257733968995024394491070540777e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.79
y[1] (closed_form) = -3.0092410177560136101726575609796
y[1] (numeric) = -3.009241017756013610172657560961
absolute error = 1.86e-29
relative error = 6.1809605446193177767414413518621e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.78
y[1] (closed_form) = -2.9984552076565296904229347740226
y[1] (numeric) = -2.998455207656529690422934774004
absolute error = 1.86e-29
relative error = 6.2031942156431282723412307092431e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.77
y[1] (closed_form) = -2.9876693975570457706732119870657
y[1] (numeric) = -2.987669397557045770673211987047
absolute error = 1.87e-29
relative error = 6.2590593240639661963031563147919e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.76
y[1] (closed_form) = -2.9768835874575618509234892001088
y[1] (numeric) = -2.97688358745756185092348920009
absolute error = 1.88e-29
relative error = 6.3153292521110420762358205116853e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.75
y[1] (closed_form) = -2.9660977773580779311737664131519
y[1] (numeric) = -2.966097777358077931173766413133
absolute error = 1.89e-29
relative error = 6.3720084159984603262043586300107e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.74
y[1] (closed_form) = -2.955311967258594011424043626195
y[1] (numeric) = -2.955311967258594011424043626176
absolute error = 1.90e-29
relative error = 6.4291012964106042568296014061340e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.73
y[1] (closed_form) = -2.9445261571591100916743208392381
y[1] (numeric) = -2.944526157159110091674320839219
absolute error = 1.91e-29
relative error = 6.4866124396829104140528313088223e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.72
y[1] (closed_form) = -2.9337403470596261719245980522812
y[1] (numeric) = -2.933740347059626171924598052262
absolute error = 1.92e-29
relative error = 6.5445464590086894106674084902069e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.71
y[1] (closed_form) = -2.9229545369601422521748752653242
y[1] (numeric) = -2.922954536960142252174875265305
absolute error = 1.92e-29
relative error = 6.5686960769386107738064026174772e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.7
y[1] (closed_form) = -2.9121687268606583324251524783673
y[1] (numeric) = -2.912168726860658332425152478348
absolute error = 1.93e-29
relative error = 6.6273632506196018383949898939412e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.69
y[1] (closed_form) = -2.9013829167611744126754296914104
y[1] (numeric) = -2.901382916761174412675429691391
absolute error = 1.94e-29
relative error = 6.6864666114655073346905555144680e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.68
y[1] (closed_form) = -2.8905971066616904929257069044535
y[1] (numeric) = -2.890597106661690492925706904434
absolute error = 1.95e-29
relative error = 6.7460110421684718272271328187302e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.67
y[1] (closed_form) = -2.8798112965622065731759841174966
y[1] (numeric) = -2.879811296562206573175984117477
absolute error = 1.96e-29
relative error = 6.8060014985695858665242837357583e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.66
y[1] (closed_form) = -2.8690254864627226534262613305397
y[1] (numeric) = -2.86902548646272265342626133052
absolute error = 1.97e-29
relative error = 6.8664430110338661767935936822378e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.65
y[1] (closed_form) = -2.8582396763632387336765385435827
y[1] (numeric) = -2.858239676363238733676538543563
absolute error = 1.97e-29
relative error = 6.8923541167358807661399846017936e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.64
y[1] (closed_form) = -2.8474538662637548139268157566258
y[1] (numeric) = -2.847453866263754813926815756606
absolute error = 1.98e-29
relative error = 6.9535806126967324988341215208450e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.63
y[1] (closed_form) = -2.8366680561642708941770929696689
y[1] (numeric) = -2.836668056164270894177092969649
absolute error = 1.99e-29
relative error = 7.0152727093873245488871492149463e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.62
y[1] (closed_form) = -2.825882246064786974427370182712
y[1] (numeric) = -2.825882246064786974427370182692
absolute error = 2.00e-29
relative error = 7.0774357381137226451237878074758e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.61
y[1] (closed_form) = -2.8150964359653030546776473957551
y[1] (numeric) = -2.815096435965303054677647395735
absolute error = 2.01e-29
relative error = 7.1400751118878326041668374237028e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.6
y[1] (closed_form) = -2.8043106258658191349279246087982
y[1] (numeric) = -2.804310625865819134927924608778
absolute error = 2.02e-29
relative error = 7.2031963269986664859717566523624e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.59
y[1] (closed_form) = -2.7935248157663352151782018218412
y[1] (numeric) = -2.793524815766335215178201821821
absolute error = 2.02e-29
relative error = 7.2310078958287771673847750178157e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.58
y[1] (closed_form) = -2.7827390056668512954284790348843
y[1] (numeric) = -2.782739005666851295428479034864
absolute error = 2.03e-29
relative error = 7.2949708753355901667355383396979e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=387.6MB, alloc=40.3MB, time=4.63
TOP MAIN SOLVE Loop
x[1] = -2.57
y[1] (closed_form) = -2.7719531955673673756787562479274
y[1] (numeric) = -2.771953195567367375678756247907
absolute error = 2.04e-29
relative error = 7.3594316212198880921512881465752e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.56
y[1] (closed_form) = -2.7611673854678834559290334609705
y[1] (numeric) = -2.76116738546788345592903346095
absolute error = 2.05e-29
relative error = 7.4243959666814070951093484988188e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.55
y[1] (closed_form) = -2.7503815753683995361793106740136
y[1] (numeric) = -2.750381575368399536179310673993
absolute error = 2.06e-29
relative error = 7.4898698364210556588749230499035e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.54
y[1] (closed_form) = -2.7395957652689156164295878870567
y[1] (numeric) = -2.739595765268915616429587887036
absolute error = 2.07e-29
relative error = 7.5558592484421187782606989754062e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.53
y[1] (closed_form) = -2.7288099551694316966798651000997
y[1] (numeric) = -2.728809955169431696679865100079
absolute error = 2.07e-29
relative error = 7.5857243047600718169099507500128e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.52
y[1] (closed_form) = -2.7180241450699477769301423131428
y[1] (numeric) = -2.718024145069947776930142313122
absolute error = 2.08e-29
relative error = 7.6526178171477267712036892927819e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.51
y[1] (closed_form) = -2.7072383349704638571804195261859
y[1] (numeric) = -2.707238334970463857180419526165
absolute error = 2.09e-29
relative error = 7.7200443455703431195555452741387e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.5
y[1] (closed_form) = -2.696452524870979937430696739229
y[1] (numeric) = -2.696452524870979937430696739208
absolute error = 2.10e-29
relative error = 7.7880102862203403986942161033464e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.49
y[1] (closed_form) = -2.6856667147714960176809739522721
y[1] (numeric) = -2.685666714771496017680973952251
absolute error = 2.11e-29
relative error = 7.8565221380402171740508682243549e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.48
y[1] (closed_form) = -2.6748809046720120979312511653152
y[1] (numeric) = -2.674880904672012097931251165294
absolute error = 2.12e-29
relative error = 7.9255865047941252137249127011780e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.47
y[1] (closed_form) = -2.6640950945725281781815283783583
y[1] (numeric) = -2.664095094572528178181528378337
absolute error = 2.13e-29
relative error = 7.9952100971897653023032004531171e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.46
y[1] (closed_form) = -2.6533092844730442584318055914013
y[1] (numeric) = -2.65330928447304425843180559138
absolute error = 2.13e-29
relative error = 8.0277109512433822344263841947967e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.45
y[1] (closed_form) = -2.6425234743735603386820828044444
y[1] (numeric) = -2.642523474373560338682082804423
absolute error = 2.14e-29
relative error = 8.0983197339706163523836843834603e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.44
y[1] (closed_form) = -2.6317376642740764189323600174875
y[1] (numeric) = -2.631737664274076418932360017466
absolute error = 2.15e-29
relative error = 8.1695072772120081270455526064572e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.43
y[1] (closed_form) = -2.6209518541745924991826372305306
y[1] (numeric) = -2.620951854174592499182637230509
absolute error = 2.16e-29
relative error = 8.2412807261590903689885884691496e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.42
y[1] (closed_form) = -2.6101660440751085794329144435737
y[1] (numeric) = -2.610166044075108579432914443552
absolute error = 2.17e-29
relative error = 8.3136473441057352740881783472360e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.41
y[1] (closed_form) = -2.5993802339756246596831916566168
y[1] (numeric) = -2.599380233975624659683191656595
absolute error = 2.18e-29
relative error = 8.3866145148984104273628685562610e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.4
y[1] (closed_form) = -2.5885944238761407399334688696598
y[1] (numeric) = -2.588594423876140739933468869638
absolute error = 2.18e-29
relative error = 8.4215587420438204708102138419124e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.39
y[1] (closed_form) = -2.5778086137766568201837460827029
y[1] (numeric) = -2.577808613776656820183746082681
absolute error = 2.19e-29
relative error = 8.4955880289014472370693032806977e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.38
y[1] (closed_form) = -2.567022803677172900434023295746
y[1] (numeric) = -2.567022803677172900434023295724
absolute error = 2.20e-29
relative error = 8.5702394106066170853977968324140e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.37
y[1] (closed_form) = -2.5562369935776889806843005087891
y[1] (numeric) = -2.556236993577688980684300508767
absolute error = 2.21e-29
relative error = 8.6455207617776533459484717643135e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.36
y[1] (closed_form) = -2.5454511834782050609345777218322
y[1] (numeric) = -2.54545118347820506093457772181
absolute error = 2.22e-29
relative error = 8.7214400905009865239614405515682e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.35
y[1] (closed_form) = -2.5346653733787211411848549348753
y[1] (numeric) = -2.534665373378721141184854934853
absolute error = 2.23e-29
relative error = 8.7980055411709012609362218391399e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.34
y[1] (closed_form) = -2.5238795632792372214351321479183
y[1] (numeric) = -2.523879563279237221435132147896
absolute error = 2.23e-29
relative error = 8.8356038554494093859829578299057e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.33
y[1] (closed_form) = -2.5130937531797533016854093609614
y[1] (numeric) = -2.513093753179753301685409360939
absolute error = 2.24e-29
relative error = 8.9133164935282865793352974001104e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.32
y[1] (closed_form) = -2.5023079430802693819356865740045
y[1] (numeric) = -2.502307943080269381935686573982
absolute error = 2.25e-29
relative error = 8.9916990681423265071130881735065e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.31
y[1] (closed_form) = -2.4915221329807854621859637870476
y[1] (numeric) = -2.491522132980785462185963787025
absolute error = 2.26e-29
relative error = 9.0707602797660118022309463994861e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=430.3MB, alloc=40.3MB, time=5.14
TOP MAIN SOLVE Loop
x[1] = -2.3
y[1] (closed_form) = -2.4807363228813015424362410000907
y[1] (numeric) = -2.480736322881301542436241000068
absolute error = 2.27e-29
relative error = 9.1505089801864247955672207839524e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.29
y[1] (closed_form) = -2.4699505127818176226865182131338
y[1] (numeric) = -2.469950512781817622686518213111
absolute error = 2.28e-29
relative error = 9.2309541758070160683212792241783e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.28
y[1] (closed_form) = -2.4591647026823337029367954261768
y[1] (numeric) = -2.459164702682333702936795426154
absolute error = 2.28e-29
relative error = 9.2714408169289766651121620277935e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.27
y[1] (closed_form) = -2.4483788925828497831870726392199
y[1] (numeric) = -2.448378892582849783187072639197
absolute error = 2.29e-29
relative error = 9.3531275201618310850690973760559e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.26
y[1] (closed_form) = -2.437593082483365863437349852263
y[1] (numeric) = -2.43759308248336586343734985224
absolute error = 2.30e-29
relative error = 9.4355371145737373140522002937720e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.25
y[1] (closed_form) = -2.4268072723838819436876270653061
y[1] (numeric) = -2.426807272383881943687627065283
absolute error = 2.31e-29
relative error = 9.5186792387137493761818196818678e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.24
y[1] (closed_form) = -2.4160214622843980239379042783492
y[1] (numeric) = -2.416021462284398023937904278326
absolute error = 2.32e-29
relative error = 9.6025637032478686888661678145001e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.23
y[1] (closed_form) = -2.4052356521849141041881814913923
y[1] (numeric) = -2.405235652184914104188181491369
absolute error = 2.33e-29
relative error = 9.6872004948181684438167432846449e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.22
y[1] (closed_form) = -2.3944498420854301844384587044354
y[1] (numeric) = -2.394449842085430184438458704412
absolute error = 2.34e-29
relative error = 9.7725997800062186470101167319981e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.21
y[1] (closed_form) = -2.3836640319859462646887359174784
y[1] (numeric) = -2.383664031985946264688735917455
absolute error = 2.34e-29
relative error = 9.8168196885130341160011127353107e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.2
y[1] (closed_form) = -2.3728782218864623449390131305215
y[1] (numeric) = -2.372878221886462344939013130498
absolute error = 2.35e-29
relative error = 9.9035845089923159831879912569611e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.19
y[1] (closed_form) = -2.3620924117869784251892903435646
y[1] (numeric) = -2.362092411786978425189290343541
absolute error = 2.36e-29
relative error = 9.9911417022613629815820558838321e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.18
y[1] (closed_form) = -2.3513066016874945054395675566077
y[1] (numeric) = -2.351306601687494505439567556584
absolute error = 2.37e-29
relative error = 1.0079502172532878301062304589849e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.17
y[1] (closed_form) = -2.3405207915880105856898447696508
y[1] (numeric) = -2.340520791588010585689844769627
absolute error = 2.38e-29
relative error = 1.0168677025018877632703661578870e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.16
y[1] (closed_form) = -2.3297349814885266659401219826939
y[1] (numeric) = -2.32973498148852666594012198267
absolute error = 2.39e-29
relative error = 1.0258677570583451032230586688160e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.15
y[1] (closed_form) = -2.3189491713890427461903991957369
y[1] (numeric) = -2.318949171389042746190399195713
absolute error = 2.39e-29
relative error = 1.0306392349981513595171194068105e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.14
y[1] (closed_form) = -2.30816336128955882644067640878
y[1] (numeric) = -2.308163361289558826440676408756
absolute error = 2.40e-29
relative error = 1.0397877551696048596387471433039e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.13
y[1] (closed_form) = -2.2973775511900749066909536218231
y[1] (numeric) = -2.297377551190074906690953621799
absolute error = 2.41e-29
relative error = 1.0490221769389123832356953280273e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.12
y[1] (closed_form) = -2.2865917410905909869412308348662
y[1] (numeric) = -2.286591741090590986941230834842
absolute error = 2.42e-29
relative error = 1.0583437158947228079986524578896e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.11
y[1] (closed_form) = -2.2758059309911070671915080479093
y[1] (numeric) = -2.275805930991107067191508047885
absolute error = 2.43e-29
relative error = 1.0677536106700195874986992287932e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.1
y[1] (closed_form) = -2.2650201208916231474417852609524
y[1] (numeric) = -2.265020120891623147441785260928
absolute error = 2.44e-29
relative error = 1.0772531234907953839463654927531e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.09
y[1] (closed_form) = -2.2542343107921392276920624739954
y[1] (numeric) = -2.254234310792139227692062473971
absolute error = 2.44e-29
relative error = 1.0824074446558231130561567152065e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.08
y[1] (closed_form) = -2.2434485006926553079423396870385
y[1] (numeric) = -2.243448500692655307942339687014
absolute error = 2.45e-29
relative error = 1.0920687500709611937271537003891e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.07
y[1] (closed_form) = -2.2326626905931713881926169000816
y[1] (numeric) = -2.232662690593171388192616900057
absolute error = 2.46e-29
relative error = 1.1018234014321392558539091105494e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.06
y[1] (closed_form) = -2.2218768804936874684428941131247
y[1] (numeric) = -2.2218768804936874684428941131
absolute error = 2.47e-29
relative error = 1.1116727581463384642149048644975e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.05
y[1] (closed_form) = -2.2110910703942035486931713261678
y[1] (numeric) = -2.211091070394203548693171326143
absolute error = 2.48e-29
relative error = 1.1216182061455542502184469184843e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.04
y[1] (closed_form) = -2.2003052602947196289434485392109
y[1] (numeric) = -2.200305260294719628943448539186
absolute error = 2.49e-29
relative error = 1.1316611585369192105945727180983e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=472.9MB, alloc=40.3MB, time=5.64
TOP MAIN SOLVE Loop
x[1] = -2.03
y[1] (closed_form) = -2.1895194501952357091937257522539
y[1] (numeric) = -2.189519450195235709193725752229
absolute error = 2.49e-29
relative error = 1.1372358440469532953758267708968e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.02
y[1] (closed_form) = -2.178733640095751789444002965297
y[1] (numeric) = -2.178733640095751789444002965272
absolute error = 2.50e-29
relative error = 1.1474555466496258248901190628457e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.01
y[1] (closed_form) = -2.1679478299962678696942801783401
y[1] (numeric) = -2.167947829996267869694280178315
absolute error = 2.51e-29
relative error = 1.1577769378354095238523147606846e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2
y[1] (closed_form) = -2.1571620198967839499445573913832
y[1] (numeric) = -2.157162019896783949944557391358
absolute error = 2.52e-29
relative error = 1.1682015429330510598041324155020e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.99
y[1] (closed_form) = -2.1463762097973000301948346044263
y[1] (numeric) = -2.146376209797300030194834604401
absolute error = 2.53e-29
relative error = 1.1787309179311714051625010015235e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.98
y[1] (closed_form) = -2.1355903996978161104451118174694
y[1] (numeric) = -2.135590399697816110445111817444
absolute error = 2.54e-29
relative error = 1.1893666502525050873426712904341e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.97
y[1] (closed_form) = -2.1248045895983321906953890305125
y[1] (numeric) = -2.124804589598332190695389030487
absolute error = 2.55e-29
relative error = 1.2001103595517203297480209731407e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.96
y[1] (closed_form) = -2.1140187794988482709456662435555
y[1] (numeric) = -2.11401877949884827094566624353
absolute error = 2.55e-29
relative error = 1.2062333715902495151038782230037e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.95
y[1] (closed_form) = -2.1032329693993643511959434565986
y[1] (numeric) = -2.103232969399364351195943456573
absolute error = 2.56e-29
relative error = 1.2171737687865733468044684508283e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.94
y[1] (closed_form) = -2.0924471592998804314462206696417
y[1] (numeric) = -2.092447159299880431446220669616
absolute error = 2.57e-29
relative error = 1.2282269535828592798627967222386e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.93
y[1] (closed_form) = -2.0816613492003965116964978826848
y[1] (numeric) = -2.081661349200396511696497882659
absolute error = 2.58e-29
relative error = 1.2393946791542362588595532658915e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.92
y[1] (closed_form) = -2.0708755391009125919467750957279
y[1] (numeric) = -2.070875539100912591946775095702
absolute error = 2.59e-29
relative error = 1.2506787352003150813875260235408e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.91
y[1] (closed_form) = -2.060089729001428672197052308771
y[1] (numeric) = -2.060089729001428672197052308745
absolute error = 2.60e-29
relative error = 1.2620809489013266664550587053540e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.9
y[1] (closed_form) = -2.049303918901944752447329521814
y[1] (numeric) = -2.049303918901944752447329521788
absolute error = 2.60e-29
relative error = 1.2687234802113336489100853301191e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.89
y[1] (closed_form) = -2.0385181088024608326976067348571
y[1] (numeric) = -2.038518108802460832697606734831
absolute error = 2.61e-29
relative error = 1.2803418270997158251821557086000e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.88
y[1] (closed_form) = -2.0277322987029769129478839479002
y[1] (numeric) = -2.027732298702976912947883947874
absolute error = 2.62e-29
relative error = 1.2920837734230807905635034315329e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.87
y[1] (closed_form) = -2.0169464886034929931981611609433
y[1] (numeric) = -2.016946488603492993198161160917
absolute error = 2.63e-29
relative error = 1.3039513020600646325799457825185e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.86
y[1] (closed_form) = -2.0061606785040090734484383739864
y[1] (numeric) = -2.00616067850400907344843837396
absolute error = 2.64e-29
relative error = 1.3159464385318547524675326749126e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.85
y[1] (closed_form) = -1.9953748684045251536987155870295
y[1] (numeric) = -1.995374868404525153698715587003
absolute error = 2.65e-29
relative error = 1.3280712521546912520295799661433e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.84
y[1] (closed_form) = -1.9845890583050412339489928000725
y[1] (numeric) = -1.984589058305041233948992800046
absolute error = 2.65e-29
relative error = 1.3352890306990102262253929007420e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.83
y[1] (closed_form) = -1.9738032482055573141992700131156
y[1] (numeric) = -1.973803248205557314199270013089
absolute error = 2.66e-29
relative error = 1.3476520531710971546010027865536e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.82
y[1] (closed_form) = -1.9630174381060733944495472261587
y[1] (numeric) = -1.963017438106073394449547226132
absolute error = 2.67e-29
relative error = 1.3601509330329872360356853084730e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.81
y[1] (closed_form) = -1.9522316280065894746998244392018
y[1] (numeric) = -1.952231628006589474699824439175
absolute error = 2.68e-29
relative error = 1.3727879220646219592541764770434e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.8
y[1] (closed_form) = -1.9414458179071055549501016522449
y[1] (numeric) = -1.941445817907105554950101652218
absolute error = 2.69e-29
relative error = 1.3855653220854970682862064363758e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.79
y[1] (closed_form) = -1.930660007807621635200378865288
y[1] (numeric) = -1.930660007807621635200378865261
absolute error = 2.70e-29
relative error = 1.3984854863524154746258568421811e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.78
y[1] (closed_form) = -1.919874197708137715450656078331
y[1] (numeric) = -1.919874197708137715450656078304
absolute error = 2.70e-29
relative error = 1.4063421463881032020113953637664e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.77
y[1] (closed_form) = -1.9090883876086537957009332913741
y[1] (numeric) = -1.909088387608653795700933291347
absolute error = 2.71e-29
relative error = 1.4195256843998602690651954291141e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=515.5MB, alloc=40.3MB, time=6.14
TOP MAIN SOLVE Loop
x[1] = -1.76
y[1] (closed_form) = -1.8983025775091698759512105044172
y[1] (numeric) = -1.89830257750916987595121050439
absolute error = 2.72e-29
relative error = 1.4328590353435691209718795861135e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.75
y[1] (closed_form) = -1.8875167674096859562014877174603
y[1] (numeric) = -1.887516767409685956201487717433
absolute error = 2.73e-29
relative error = 1.4463447674409203597574972763358e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.74
y[1] (closed_form) = -1.8767309573102020364517649305034
y[1] (numeric) = -1.876730957310202036451764930476
absolute error = 2.74e-29
relative error = 1.4599855079531836817475473538019e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.73
y[1] (closed_form) = -1.8659451472107181167020421435465
y[1] (numeric) = -1.865945147210718116702042143519
absolute error = 2.75e-29
relative error = 1.4737839448875540941652280680018e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.72
y[1] (closed_form) = -1.8551593371112341969523193565896
y[1] (numeric) = -1.855159337111234196952319356562
absolute error = 2.76e-29
relative error = 1.4877428287630218369598585579482e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.71
y[1] (closed_form) = -1.8443735270117502772025965696326
y[1] (numeric) = -1.844373527011750277202596569605
absolute error = 2.76e-29
relative error = 1.4964430792236243038426647483456e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.7
y[1] (closed_form) = -1.8335877169122663574528737826757
y[1] (numeric) = -1.833587716912266357452873782648
absolute error = 2.77e-29
relative error = 1.5106994742878391389623934598228e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.69
y[1] (closed_form) = -1.8228019068127824377031509957188
y[1] (numeric) = -1.822801906812782437703150995691
absolute error = 2.78e-29
relative error = 1.5251245840865417236101662980630e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.68
y[1] (closed_form) = -1.8120160967132985179534282087619
y[1] (numeric) = -1.812016096713298517953428208734
absolute error = 2.79e-29
relative error = 1.5397214213828479104561269081871e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.67
y[1] (closed_form) = -1.801230286613814598203705421805
y[1] (numeric) = -1.801230286613814598203705421777
absolute error = 2.80e-29
relative error = 1.5544930711018643510367696813066e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.66
y[1] (closed_form) = -1.7904444765143306784539826348481
y[1] (numeric) = -1.79044447651433067845398263482
absolute error = 2.81e-29
relative error = 1.5694426925042424354798298372348e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.65
y[1] (closed_form) = -1.7796586664148467587042598478911
y[1] (numeric) = -1.779658666414846758704259847863
absolute error = 2.81e-29
relative error = 1.5789544663982075411494045635212e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.64
y[1] (closed_form) = -1.7688728563153628389545370609342
y[1] (numeric) = -1.768872856315362838954537060906
absolute error = 2.82e-29
relative error = 1.5942355551060801338790424950230e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.63
y[1] (closed_form) = -1.7580870462158789192048142739773
y[1] (numeric) = -1.758087046215878919204814273949
absolute error = 2.83e-29
relative error = 1.6097041418349082185440134072795e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.62
y[1] (closed_form) = -1.7473012361163949994550914870204
y[1] (numeric) = -1.747301236116394999455091486992
absolute error = 2.84e-29
relative error = 1.6253636987702650449949716147489e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.61
y[1] (closed_form) = -1.7365154260169110797053687000635
y[1] (numeric) = -1.736515426016911079705368700035
absolute error = 2.85e-29
relative error = 1.6412177843632039438242025949820e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.6
y[1] (closed_form) = -1.7257296159174271599556459131066
y[1] (numeric) = -1.725729615917427159955645913078
absolute error = 2.86e-29
relative error = 1.6572700460260545788887989624680e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.59
y[1] (closed_form) = -1.7149438058179432402059231261496
y[1] (numeric) = -1.714943805817943240205923126121
absolute error = 2.86e-29
relative error = 1.6676931280765329095736341760685e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.58
y[1] (closed_form) = -1.7041579957184593204562003391927
y[1] (numeric) = -1.704157995718459320456200339164
absolute error = 2.87e-29
relative error = 1.6841161483915293056248041151751e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.57
y[1] (closed_form) = -1.6933721856189754007064775522358
y[1] (numeric) = -1.693372185618975400706477552207
absolute error = 2.88e-29
relative error = 1.7007483791563982672307660280283e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.56
y[1] (closed_form) = -1.6825863755194914809567547652789
y[1] (numeric) = -1.68258637551949148095675476525
absolute error = 2.89e-29
relative error = 1.7175938436490219591137274525848e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.55
y[1] (closed_form) = -1.671800565420007561207031978322
y[1] (numeric) = -1.671800565420007561207031978293
absolute error = 2.90e-29
relative error = 1.7346566689738085373435657987484e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.54
y[1] (closed_form) = -1.6610147553205236414573091913651
y[1] (numeric) = -1.661014755320523641457309191336
absolute error = 2.91e-29
relative error = 1.7519410894326832529530124351219e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.53
y[1] (closed_form) = -1.6502289452210397217075864044081
y[1] (numeric) = -1.650228945221039721707586404379
absolute error = 2.91e-29
relative error = 1.7633916847884524245409406209725e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.52
y[1] (closed_form) = -1.6394431351215558019578636174512
y[1] (numeric) = -1.639443135121555801957863617422
absolute error = 2.92e-29
relative error = 1.7810925779889876225083890211287e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.51
y[1] (closed_form) = -1.6286573250220718822081408304943
y[1] (numeric) = -1.628657325022071882208140830465
absolute error = 2.93e-29
relative error = 1.7990279201060862005813665391679e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.5
y[1] (closed_form) = -1.6178715149225879624584180435374
y[1] (numeric) = -1.617871514922587962458418043508
absolute error = 2.94e-29
relative error = 1.8172024001180794263619837574475e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=558.1MB, alloc=40.3MB, time=6.66
TOP MAIN SOLVE Loop
x[1] = -1.49
y[1] (closed_form) = -1.6070857048231040427086952565805
y[1] (numeric) = -1.607085704823104042708695256551
absolute error = 2.95e-29
relative error = 1.8356208328819114873879783880530e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.48
y[1] (closed_form) = -1.5962998947236201229589724696236
y[1] (numeric) = -1.596299894723620122958972469594
absolute error = 2.96e-29
relative error = 1.8542881633857953330224324055586e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.47
y[1] (closed_form) = -1.5855140846241362032092496826667
y[1] (numeric) = -1.585514084624136203209249682637
absolute error = 2.97e-29
relative error = 1.8732094711754463058083755933704e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.46
y[1] (closed_form) = -1.5747282745246522834595268957097
y[1] (numeric) = -1.57472827452465228345952689568
absolute error = 2.97e-29
relative error = 1.8860396730328123763961041933251e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.45
y[1] (closed_form) = -1.5639424644251683637098041087528
y[1] (numeric) = -1.563942464425168363709804108723
absolute error = 2.98e-29
relative error = 1.9054409403067827904851201960569e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.44
y[1] (closed_form) = -1.5531566543256844439600813217959
y[1] (numeric) = -1.553156654325684443960081321766
absolute error = 2.99e-29
relative error = 1.9251116696262250158809280877154e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.43
y[1] (closed_form) = -1.542370844226200524210358534839
y[1] (numeric) = -1.542370844226200524210358534809
absolute error = 3.00e-29
relative error = 1.9450575140410440556179360897468e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.42
y[1] (closed_form) = -1.5315850341267166044606357478821
y[1] (numeric) = -1.531585034126716604460635747852
absolute error = 3.01e-29
relative error = 1.9652842858419873071822258946238e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.41
y[1] (closed_form) = -1.5207992240272326847109129609252
y[1] (numeric) = -1.520799224027232684710912960895
absolute error = 3.02e-29
relative error = 1.9857979622074829452935269024067e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.4
y[1] (closed_form) = -1.5100134139277487649611901739682
y[1] (numeric) = -1.510013413927748764961190173938
absolute error = 3.02e-29
relative error = 1.9999822333661078234741949517097e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.39
y[1] (closed_form) = -1.4992276038282648452114673870113
y[1] (numeric) = -1.499227603828264845211467386981
absolute error = 3.03e-29
relative error = 2.0210406960643740500208525859147e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.38
y[1] (closed_form) = -1.4884417937287809254617446000544
y[1] (numeric) = -1.488441793728780925461744600024
absolute error = 3.04e-29
relative error = 2.0424043538742093523145632293110e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.37
y[1] (closed_form) = -1.4776559836292970057120218130975
y[1] (numeric) = -1.477655983629297005712021813067
absolute error = 3.05e-29
relative error = 2.0640798899002466298242404514430e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.36
y[1] (closed_form) = -1.4668701735298130859622990261406
y[1] (numeric) = -1.46687017352981308596229902611
absolute error = 3.06e-29
relative error = 2.0860741838090197496502364562535e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.35
y[1] (closed_form) = -1.4560843634303291662125762391837
y[1] (numeric) = -1.456084363430329166212576239153
absolute error = 3.07e-29
relative error = 2.1083943191090339527329138833574e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.34
y[1] (closed_form) = -1.4452985533308452464628534522267
y[1] (numeric) = -1.445298553330845246462853452196
absolute error = 3.07e-29
relative error = 2.1241286050725342061115177183079e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.33
y[1] (closed_form) = -1.4345127432313613267131306652698
y[1] (numeric) = -1.434512743231361326713130665239
absolute error = 3.08e-29
relative error = 2.1470705049730261750786059432785e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.32
y[1] (closed_form) = -1.4237269331318774069634078783129
y[1] (numeric) = -1.423726933131877406963407878282
absolute error = 3.09e-29
relative error = 2.1703600094174649920603470201425e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.31
y[1] (closed_form) = -1.412941123032393487213685091356
y[1] (numeric) = -1.412941123032393487213685091325
absolute error = 3.10e-29
relative error = 2.1940050788152540199883742203175e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.3
y[1] (closed_form) = -1.4021553129329095674639623043991
y[1] (numeric) = -1.402155312932909567463962304368
absolute error = 3.11e-29
relative error = 2.2180139185114705714229864543413e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.29
y[1] (closed_form) = -1.3913695028334256477142395174422
y[1] (numeric) = -1.391369502833425647714239517411
absolute error = 3.12e-29
relative error = 2.2423949882804966817945694206755e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.28
y[1] (closed_form) = -1.3805836927339417279645167304852
y[1] (numeric) = -1.380583692733941727964516730454
absolute error = 3.12e-29
relative error = 2.2599136991264380621210894942747e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.27
y[1] (closed_form) = -1.3697978826344578082147939435283
y[1] (numeric) = -1.369797882634457808214793943497
absolute error = 3.13e-29
relative error = 2.2850086422824958237638635548814e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.26
y[1] (closed_form) = -1.3590120725349738884650711565714
y[1] (numeric) = -1.35901207253497388846507115654
absolute error = 3.14e-29
relative error = 2.3105019178696021213057292672438e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.25
y[1] (closed_form) = -1.3482262624354899687153483696145
y[1] (numeric) = -1.348226262435489968715348369583
absolute error = 3.15e-29
relative error = 2.3364030858661021196082648310039e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.24
y[1] (closed_form) = -1.3374404523360060489656255826576
y[1] (numeric) = -1.337440452336006048965625582626
absolute error = 3.16e-29
relative error = 2.3627220146367392146576154845021e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.23
y[1] (closed_form) = -1.3266546422365221292159027957007
y[1] (numeric) = -1.326654642236522129215902795669
absolute error = 3.17e-29
relative error = 2.3894688934686874819841913518784e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=600.8MB, alloc=40.3MB, time=7.16
TOP MAIN SOLVE Loop
x[1] = -1.22
y[1] (closed_form) = -1.3158688321370382094661800087438
y[1] (numeric) = -1.315868832137038209466180008712
absolute error = 3.18e-29
relative error = 2.4166542457241103110702192826542e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.21
y[1] (closed_form) = -1.3050830220375542897164572217868
y[1] (numeric) = -1.305083022037554289716457221755
absolute error = 3.18e-29
relative error = 2.4366265948623260987650144833375e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.2
y[1] (closed_form) = -1.2942972119380703699667344348299
y[1] (numeric) = -1.294297211938070369966734434798
absolute error = 3.19e-29
relative error = 2.4646580171669529634756497390551e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.19
y[1] (closed_form) = -1.283511401838586450217011647873
y[1] (numeric) = -1.283511401838586450217011647841
absolute error = 3.20e-29
relative error = 2.4931605558128340612066318057932e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.18
y[1] (closed_form) = -1.2727255917391025304672888609161
y[1] (numeric) = -1.272725591739102530467288860884
absolute error = 3.21e-29
relative error = 2.5221461883340690758483084838319e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.17
y[1] (closed_form) = -1.2619397816396186107175660739592
y[1] (numeric) = -1.261939781639618610717566073927
absolute error = 3.22e-29
relative error = 2.5516273017531029796291591221790e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.16
y[1] (closed_form) = -1.2511539715401346909678432870023
y[1] (numeric) = -1.25115397154013469096784328697
absolute error = 3.23e-29
relative error = 2.5816167102310857438200244267044e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.15
y[1] (closed_form) = -1.2403681614406507712181205000453
y[1] (numeric) = -1.240368161440650771218120500013
absolute error = 3.23e-29
relative error = 2.6040655511896169242010681173716e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.14
y[1] (closed_form) = -1.2295823513411668514683977130884
y[1] (numeric) = -1.229582351341166851468397713056
absolute error = 3.24e-29
relative error = 2.6350410742850775785055618394781e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.13
y[1] (closed_form) = -1.2187965412416829317186749261315
y[1] (numeric) = -1.218796541241682931718674926099
absolute error = 3.25e-29
relative error = 2.6665648367273605452756218221530e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.12
y[1] (closed_form) = -1.2080107311421990119689521391746
y[1] (numeric) = -1.208010731142199011968952139142
absolute error = 3.26e-29
relative error = 2.6986515234989699935951471616612e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.11
y[1] (closed_form) = -1.1972249210427150922192293522177
y[1] (numeric) = -1.197224921042715092219229352185
absolute error = 3.27e-29
relative error = 2.7313163487709688013438531379174e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.1
y[1] (closed_form) = -1.1864391109432311724695065652608
y[1] (numeric) = -1.186439110943231172469506565228
absolute error = 3.28e-29
relative error = 2.7645750799570039510516264955601e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.09
y[1] (closed_form) = -1.1756533008437472527197837783038
y[1] (numeric) = -1.175653300843747252719783778271
absolute error = 3.28e-29
relative error = 2.7899381540850498588594395826755e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.08
y[1] (closed_form) = -1.1648674907442633329700609913469
y[1] (numeric) = -1.164867490744263332970060991314
absolute error = 3.29e-29
relative error = 2.8243555821941049285387975066149e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.07
y[1] (closed_form) = -1.15408168064477941322033820439
y[1] (numeric) = -1.154081680644779413220338204357
absolute error = 3.30e-29
relative error = 2.8594163267164133640065546440858e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.06
y[1] (closed_form) = -1.1432958705452954934706154174331
y[1] (numeric) = -1.1432958705452954934706154174
absolute error = 3.31e-29
relative error = 2.8951385947202747888227600294336e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.05
y[1] (closed_form) = -1.1325100604458115737208926304762
y[1] (numeric) = -1.132510060445811573720892630443
absolute error = 3.32e-29
relative error = 2.9315412868765907169687978983117e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.04
y[1] (closed_form) = -1.1217242503463276539711698435193
y[1] (numeric) = -1.121724250346327653971169843486
absolute error = 3.33e-29
relative error = 2.9686440308051434898868749569760e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.03
y[1] (closed_form) = -1.1109384402468437342214470565623
y[1] (numeric) = -1.110938440246843734221447056529
absolute error = 3.33e-29
relative error = 2.9974658175119895431867475293741e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.02
y[1] (closed_form) = -1.1001526301473598144717242696054
y[1] (numeric) = -1.100152630147359814471724269572
absolute error = 3.34e-29
relative error = 3.0359423851512531432818256051795e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.01
y[1] (closed_form) = -1.0893668200478758947220014826485
y[1] (numeric) = -1.089366820047875894722001482615
absolute error = 3.35e-29
relative error = 3.0751808650209972107055190884265e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1
y[1] (closed_form) = -1.0785810099483919749722786956916
y[1] (numeric) = -1.078581009948391974972278695658
absolute error = 3.36e-29
relative error = 3.1152041144881361594776864413385e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.99
y[1] (closed_form) = -1.0677951998489080552225559087347
y[1] (numeric) = -1.067795199848908055222555908701
absolute error = 3.37e-29
relative error = 3.1560359144495607435785844478447e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.98
y[1] (closed_form) = -1.0570093897494241354728331217778
y[1] (numeric) = -1.057009389749424135472833121744
absolute error = 3.38e-29
relative error = 3.1977010164510144008243987401980e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.97
y[1] (closed_form) = -1.0462235796499402157231103348209
y[1] (numeric) = -1.046223579649940215723110334787
absolute error = 3.39e-29
relative error = 3.2402251927205392674979617808472e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.96
y[1] (closed_form) = -1.0354377695504562959733875478639
y[1] (numeric) = -1.03543776955045629597338754783
absolute error = 3.39e-29
relative error = 3.2739775384780448848677322160646e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=643.6MB, alloc=40.3MB, time=7.66
TOP MAIN SOLVE Loop
x[1] = -0.95
y[1] (closed_form) = -1.024651959450972376223664760907
y[1] (numeric) = -1.024651959450972376223664760873
absolute error = 3.40e-29
relative error = 3.3181998713219495433033000941577e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.94
y[1] (closed_form) = -1.0138661493514884564739419739501
y[1] (numeric) = -1.013866149351488456473941973916
absolute error = 3.41e-29
relative error = 3.3633631048646606838332417568910e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.93
y[1] (closed_form) = -1.0030803392520045367242191869932
y[1] (numeric) = -1.003080339252004536724219186959
absolute error = 3.42e-29
relative error = 3.4094975907416236768476982940917e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.92
y[1] (closed_form) = -0.99229452915252061697449640003627
y[1] (numeric) = -0.99229452915252061697449640000208
absolute error = 3.419e-29
relative error = 3.4455495818565403497846176057636e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.91
y[1] (closed_form) = -0.98150871905303669722477361307936
y[1] (numeric) = -0.98150871905303669722477361304518
absolute error = 3.418e-29
relative error = 3.4823939244245321144344362429667e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.9
y[1] (closed_form) = -0.97072290895355277747505082612244
y[1] (numeric) = -0.97072290895355277747505082608828
absolute error = 3.416e-29
relative error = 3.5190268700699315875581272763269e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.89
y[1] (closed_form) = -0.95993709885406885772532803916552
y[1] (numeric) = -0.95993709885406885772532803913138
absolute error = 3.414e-29
relative error = 3.5564830279770254308643731643693e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.88
y[1] (closed_form) = -0.94915128875458493797560525220861
y[1] (numeric) = -0.94915128875458493797560525217448
absolute error = 3.413e-29
relative error = 3.5958440350202951543213419319157e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.87
y[1] (closed_form) = -0.93836547865510101822588246525169
y[1] (numeric) = -0.93836547865510101822588246521758
absolute error = 3.411e-29
relative error = 3.6350442099476711959422511122762e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.86
y[1] (closed_form) = -0.92757966855561709847615967829478
y[1] (numeric) = -0.92757966855561709847615967826068
absolute error = 3.410e-29
relative error = 3.6762340913636988869805200598576e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.85
y[1] (closed_form) = -0.91679385845613317872643689133786
y[1] (numeric) = -0.91679385845613317872643689130378
absolute error = 3.408e-29
relative error = 3.7173023887169355852590880224376e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.84
y[1] (closed_form) = -0.90600804835664925897671410438094
y[1] (numeric) = -0.90600804835664925897671410434688
absolute error = 3.406e-29
relative error = 3.7593485026738207763538123650791e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.83
y[1] (closed_form) = -0.89522223825716533922699131742403
y[1] (numeric) = -0.89522223825716533922699131738998
absolute error = 3.405e-29
relative error = 3.8035248170654416318923990005586e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.82
y[1] (closed_form) = -0.88443642815768141947726853046711
y[1] (numeric) = -0.88443642815768141947726853043308
absolute error = 3.403e-29
relative error = 3.8476479390255253160215472415342e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.81
y[1] (closed_form) = -0.8736506180581974997275457435102
y[1] (numeric) = -0.87365061805819749972754574347618
absolute error = 3.402e-29
relative error = 3.8940051431101701993471080516732e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.8
y[1] (closed_form) = -0.86286480795871357997782295655328
y[1] (numeric) = -0.86286480795871357997782295651928
absolute error = 3.400e-29
relative error = 3.9403623471948150826726688618121e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.79
y[1] (closed_form) = -0.85207899785922966022810016959636
y[1] (numeric) = -0.85207899785922966022810016956238
absolute error = 3.398e-29
relative error = 3.9878931513828686972216615911952e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.78
y[1] (closed_form) = -0.84129318775974574047837738263945
y[1] (numeric) = -0.84129318775974574047837738260548
absolute error = 3.397e-29
relative error = 4.0378313403984274014597454369761e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.77
y[1] (closed_form) = -0.83050737766026182072865459568253
y[1] (numeric) = -0.83050737766026182072865459564858
absolute error = 3.395e-29
relative error = 4.0878625420095942568903623486180e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.76
y[1] (closed_form) = -0.81972156756077790097893180872562
y[1] (numeric) = -0.81972156756077790097893180869168
absolute error = 3.394e-29
relative error = 4.1404302806127561580777207792540e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.75
y[1] (closed_form) = -0.8089357574612939812292090217687
y[1] (numeric) = -0.80893575746129398122920902173478
absolute error = 3.392e-29
relative error = 4.1931636334697451797413938131033e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.74
y[1] (closed_form) = -0.79814994736181006147948623481178
y[1] (numeric) = -0.79814994736181006147948623477788
absolute error = 3.390e-29
relative error = 4.2473222120796257965851661181378e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.73
y[1] (closed_form) = -0.78736413726232614172976344785487
y[1] (numeric) = -0.78736413726232614172976344782098
absolute error = 3.389e-29
relative error = 4.3042346477496303997349475496153e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.72
y[1] (closed_form) = -0.77657832716284222198004066089795
y[1] (numeric) = -0.77657832716284222198004066086408
absolute error = 3.387e-29
relative error = 4.3614402842970061062131795539078e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.71
y[1] (closed_form) = -0.76579251706335830223031787394104
y[1] (numeric) = -0.76579251706335830223031787390718
absolute error = 3.386e-29
relative error = 4.4215631839607767588830676938180e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.7
y[1] (closed_form) = -0.75500670696387438248059508698412
y[1] (numeric) = -0.75500670696387438248059508695028
absolute error = 3.384e-29
relative error = 4.4820793892125224335342223288646e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.69
y[1] (closed_form) = -0.7442208968643904627308723000272
y[1] (numeric) = -0.74422089686439046273087229999338
absolute error = 3.382e-29
relative error = 4.5443496873701158088999031852170e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=686.3MB, alloc=40.3MB, time=8.17
TOP MAIN SOLVE Loop
x[1] = -0.68
y[1] (closed_form) = -0.73343508676490654298114951307029
y[1] (numeric) = -0.73343508676490654298114951303648
absolute error = 3.381e-29
relative error = 4.6098149120642456036388558552896e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.67
y[1] (closed_form) = -0.72264927666542262323142672611337
y[1] (numeric) = -0.72264927666542262323142672607958
absolute error = 3.379e-29
relative error = 4.6758505254332853957334321629722e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.66
y[1] (closed_form) = -0.71186346656593870348170393915646
y[1] (numeric) = -0.71186346656593870348170393912268
absolute error = 3.378e-29
relative error = 4.7452919817554671476892247469524e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.65
y[1] (closed_form) = -0.70107765646645478373198115219954
y[1] (numeric) = -0.70107765646645478373198115216578
absolute error = 3.376e-29
relative error = 4.8154437227618808032951783085893e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.64
y[1] (closed_form) = -0.69029184636697086398225836524262
y[1] (numeric) = -0.69029184636697086398225836520888
absolute error = 3.374e-29
relative error = 4.8877877056747448856388179190273e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.63
y[1] (closed_form) = -0.67950603626748694423253557828571
y[1] (numeric) = -0.67950603626748694423253557825198
absolute error = 3.373e-29
relative error = 4.9638999802383235383211623047217e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.62
y[1] (closed_form) = -0.66872022616800302448281279132879
y[1] (numeric) = -0.66872022616800302448281279129508
absolute error = 3.371e-29
relative error = 5.0409720957850936029182416444663e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.61
y[1] (closed_form) = -0.65793441606851910473309000437188
y[1] (numeric) = -0.65793441606851910473309000433818
absolute error = 3.370e-29
relative error = 5.1220910742705985838406534481415e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.6
y[1] (closed_form) = -0.64714860596903518498336721741496
y[1] (numeric) = -0.64714860596903518498336721738128
absolute error = 3.368e-29
relative error = 5.2043687785694655680162936182680e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.59
y[1] (closed_form) = -0.63636279586955126523364443045804
y[1] (numeric) = -0.63636279586955126523364443042438
absolute error = 3.366e-29
relative error = 5.2894355575903280431809385399241e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.58
y[1] (closed_form) = -0.62557698577006734548392164350113
y[1] (numeric) = -0.62557698577006734548392164346748
absolute error = 3.365e-29
relative error = 5.3790341980975873238107629695732e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.57
y[1] (closed_form) = -0.61479117567058342573419885654421
y[1] (numeric) = -0.61479117567058342573419885651058
absolute error = 3.363e-29
relative error = 5.4701500819880962324161755963981e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.56
y[1] (closed_form) = -0.6040053655710995059844760695873
y[1] (numeric) = -0.60400536557109950598447606955368
absolute error = 3.362e-29
relative error = 5.5661757190205749193048372745430e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.55
y[1] (closed_form) = -0.59321955547161558623475328263038
y[1] (numeric) = -0.59321955547161558623475328259678
absolute error = 3.360e-29
relative error = 5.6640074808875202899594298933428e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.54
y[1] (closed_form) = -0.58243374537213166648503049567346
y[1] (numeric) = -0.58243374537213166648503049563988
absolute error = 3.358e-29
relative error = 5.7654626413421303039716000165426e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.53
y[1] (closed_form) = -0.57164793527264774673530770871655
y[1] (numeric) = -0.57164793527264774673530770868298
absolute error = 3.357e-29
relative error = 5.8724956268736933329776467787362e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.52
y[1] (closed_form) = -0.56086212517316382698558492175963
y[1] (numeric) = -0.56086212517316382698558492172608
absolute error = 3.355e-29
relative error = 5.9818622963070609060483276160090e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.51
y[1] (closed_form) = -0.55007631507367990723586213480272
y[1] (numeric) = -0.55007631507367990723586213476918
absolute error = 3.354e-29
relative error = 6.0973357843097623009384689100428e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.5
y[1] (closed_form) = -0.5392905049741959874861393478458
y[1] (numeric) = -0.53929050497419598748613934781228
absolute error = 3.352e-29
relative error = 6.2155739236691859562911934234326e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.49
y[1] (closed_form) = -0.52850469487471206773641656088888
y[1] (numeric) = -0.52850469487471206773641656085538
absolute error = 3.350e-29
relative error = 6.3386381095330758832909679169608e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.48
y[1] (closed_form) = -0.51771888477522814798669377393197
y[1] (numeric) = -0.51771888477522814798669377389848
absolute error = 3.349e-29
relative error = 6.4687615199781547607209647148083e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.47
y[1] (closed_form) = -0.50693307467574422823697098697505
y[1] (numeric) = -0.50693307467574422823697098694158
absolute error = 3.347e-29
relative error = 6.6024494498428265740702992142605e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.46
y[1] (closed_form) = -0.49614726457626030848724820001814
y[1] (numeric) = -0.49614726457626030848724819998468
absolute error = 3.346e-29
relative error = 6.7439654290096425916228900315209e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.45
y[1] (closed_form) = -0.48536145447677638873752541306122
y[1] (numeric) = -0.48536145447677638873752541302778
absolute error = 3.344e-29
relative error = 6.8897106870689995484744599602091e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.44
y[1] (closed_form) = -0.4745756443772924689878026261043
y[1] (numeric) = -0.47457564437729246898780262607088
absolute error = 3.342e-29
relative error = 7.0420807295856000033647376129285e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.43
y[1] (closed_form) = -0.46378983427780854923807983914739
y[1] (numeric) = -0.46378983427780854923807983911398
absolute error = 3.341e-29
relative error = 7.2036938998510955902650542639203e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=728.8MB, alloc=40.3MB, time=8.67
x[1] = -0.42
y[1] (closed_form) = -0.45300402417832462948835705219047
y[1] (numeric) = -0.45300402417832462948835705215708
absolute error = 3.339e-29
relative error = 7.3707954494585364487641688120957e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.41
y[1] (closed_form) = -0.44221821407884070973863426523356
y[1] (numeric) = -0.44221821407884070973863426520018
absolute error = 3.338e-29
relative error = 7.5483096211972985629620480118960e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.4
y[1] (closed_form) = -0.43143240397935678998891147827664
y[1] (numeric) = -0.43143240397935678998891147824328
absolute error = 3.336e-29
relative error = 7.7323816413187665387035431311796e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.39
y[1] (closed_form) = -0.42064659387987287023918869131972
y[1] (numeric) = -0.42064659387987287023918869128638
absolute error = 3.334e-29
relative error = 7.9258932522156944106369097950418e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.38
y[1] (closed_form) = -0.40986078378038895048946590436281
y[1] (numeric) = -0.40986078378038895048946590432948
absolute error = 3.333e-29
relative error = 8.1320295375853366381102200101671e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.37
y[1] (closed_form) = -0.39907497368090503073974311740589
y[1] (numeric) = -0.39907497368090503073974311737258
absolute error = 3.331e-29
relative error = 8.3468025300514652085104355985350e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.36
y[1] (closed_form) = -0.38828916358142111099002033044898
y[1] (numeric) = -0.38828916358142111099002033041568
absolute error = 3.330e-29
relative error = 8.5760827556593034152287498757087e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.35
y[1] (closed_form) = -0.37750335348193719124029754349206
y[1] (numeric) = -0.37750335348193719124029754345878
absolute error = 3.328e-29
relative error = 8.8158157253541812404266500652846e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.34
y[1] (closed_form) = -0.36671754338245327149057475653514
y[1] (numeric) = -0.36671754338245327149057475650188
absolute error = 3.326e-29
relative error = 9.0696506344428754082832502660120e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.33
y[1] (closed_form) = -0.35593173328296935174085196957823
y[1] (numeric) = -0.35593173328296935174085196954498
absolute error = 3.325e-29
relative error = 9.3416790049360143671205874977008e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.32
y[1] (closed_form) = -0.34514592318348543199112918262131
y[1] (numeric) = -0.34514592318348543199112918258808
absolute error = 3.323e-29
relative error = 9.6278118233296842056774107557366e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.31
y[1] (closed_form) = -0.3343601130840015122414063956644
y[1] (numeric) = -0.33436011308400151224140639563118
absolute error = 3.322e-29
relative error = 9.9353956109155033811298716955900e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.3
y[1] (closed_form) = -0.32357430298451759249168360870748
y[1] (numeric) = -0.32357430298451759249168360867428
absolute error = 3.320e-29
relative error = 1.0260394504068067509390792644091e-26 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.29
y[1] (closed_form) = -0.31278849288503367274196082175056
y[1] (numeric) = -0.31278849288503367274196082171738
absolute error = 3.318e-29
relative error = 1.0607807113989773991324880554558e-26 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.28
y[1] (closed_form) = -0.30200268278554975299223803479365
y[1] (numeric) = -0.30200268278554975299223803476048
absolute error = 3.317e-29
relative error = 1.0983346139197648427920371945068e-26 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.27
y[1] (closed_form) = -0.29121687268606583324251524783673
y[1] (numeric) = -0.29121687268606583324251524780358
absolute error = 3.315e-29
relative error = 1.1383269003007243572165487823013e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.26
y[1] (closed_form) = -0.28043106258658191349279246087982
y[1] (numeric) = -0.28043106258658191349279246084668
absolute error = 3.314e-29
relative error = 1.1817521102808703333916040369272e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.25
y[1] (closed_form) = -0.2696452524870979937430696739229
y[1] (numeric) = -0.26964525248709799374306967388978
absolute error = 3.312e-29
relative error = 1.2282804794267508285940592254421e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.24
y[1] (closed_form) = -0.25885944238761407399334688696598
y[1] (numeric) = -0.25885944238761407399334688693288
absolute error = 3.310e-29
relative error = 1.2786862126681213650633856796665e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.23
y[1] (closed_form) = -0.24807363228813015424362410000907
y[1] (numeric) = -0.24807363228813015424362409997598
absolute error = 3.309e-29
relative error = 1.3338781592703471210807019195638e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.22
y[1] (closed_form) = -0.23728782218864623449390131305215
y[1] (numeric) = -0.23728782218864623449390131301908
absolute error = 3.307e-29
relative error = 1.3936661264356420832511781739051e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.21
y[1] (closed_form) = -0.22650201208916231474417852609524
y[1] (numeric) = -0.22650201208916231474417852606218
absolute error = 3.306e-29
relative error = 1.4595896828936760407076575078040e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.2
y[1] (closed_form) = -0.21571620198967839499445573913832
y[1] (numeric) = -0.21571620198967839499445573910528
absolute error = 3.304e-29
relative error = 1.5316420229566669450765291669915e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.19
y[1] (closed_form) = -0.2049303918901944752447329521814
y[1] (numeric) = -0.20493039189019447524473295214838
absolute error = 3.302e-29
relative error = 1.6112788198683937341158083692513e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.18
y[1] (closed_form) = -0.19414458179071055549501016522449
y[1] (numeric) = -0.19414458179071055549501016519148
absolute error = 3.301e-29
relative error = 1.7002792298156973317519581585414e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.17
y[1] (closed_form) = -0.18335877169122663574528737826757
y[1] (numeric) = -0.18335877169122663574528737823458
absolute error = 3.299e-29
relative error = 1.7992048973558055304826483840994e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.16
y[1] (closed_form) = -0.17257296159174271599556459131066
y[1] (numeric) = -0.17257296159174271599556459127768
absolute error = 3.298e-29
relative error = 1.9110757383894853150962443979788e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=771.6MB, alloc=40.3MB, time=9.17
TOP MAIN SOLVE Loop
x[1] = -0.15
y[1] (closed_form) = -0.16178715149225879624584180435374
y[1] (numeric) = -0.16178715149225879624584180432078
absolute error = 3.296e-29
relative error = 2.0372445955065271392139790695738e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.14
y[1] (closed_form) = -0.15100134139277487649611901739682
y[1] (numeric) = -0.15100134139277487649611901736388
absolute error = 3.294e-29
relative error = 2.1814375750688606524913901228251e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.13
y[1] (closed_form) = -0.14021553129329095674639623043991
y[1] (numeric) = -0.14021553129329095674639623040698
absolute error = 3.293e-29
relative error = 2.3485272777036246275549499659633e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.12
y[1] (closed_form) = -0.12942972119380703699667344348299
y[1] (numeric) = -0.12942972119380703699667344345008
absolute error = 3.291e-29
relative error = 2.5426926440427718504070104361223e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.11
y[1] (closed_form) = -0.11864391109432311724695065652608
y[1] (numeric) = -0.11864391109432311724695065649318
absolute error = 3.290e-29
relative error = 2.7730036625178484752926375519490e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.1
y[1] (closed_form) = -0.10785810099483919749722786956916
y[1] (numeric) = -0.10785810099483919749722786953628
absolute error = 3.288e-29
relative error = 3.0484497406062475274888788747384e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.09
y[1] (closed_form) = -0.097072290895355277747505082612244
y[1] (numeric) = -0.097072290895355277747505082579374
absolute error = 3.2870e-29
relative error = 3.3861362183606162553581862872618e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.08
y[1] (closed_form) = -0.086286480795871357997782295655328
y[1] (numeric) = -0.086286480795871357997782295622454
absolute error = 3.2874e-29
relative error = 3.8098668176965397361112151812710e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.07
y[1] (closed_form) = -0.075500670696387438248059508698412
y[1] (numeric) = -0.075500670696387438248059508665534
absolute error = 3.2878e-29
relative error = 4.3546633025570127827936809021398e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.06
y[1] (closed_form) = -0.064714860596903518498336721741496
y[1] (numeric) = -0.064714860596903518498336721708614
absolute error = 3.2882e-29
relative error = 5.0810586157043101783703018632983e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.05
y[1] (closed_form) = -0.05392905049741959874861393478458
y[1] (numeric) = -0.053929050497419598748613934751694
absolute error = 3.2886e-29
relative error = 6.0980120541105265321775712089202e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.04
y[1] (closed_form) = -0.043143240397935678998891147827664
y[1] (numeric) = -0.043143240397935678998891147794774
absolute error = 3.2890e-29
relative error = 7.6234422117198510628884752273530e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.03
y[1] (closed_form) = -0.032357430298451759249168360870748
y[1] (numeric) = -0.032357430298451759249168360837854
absolute error = 3.2894e-29
relative error = 1.0165825807735391947406648591408e-25 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.02
y[1] (closed_form) = -0.021571620198967839499445573913832
y[1] (numeric) = -0.021571620198967839499445573880934
absolute error = 3.2898e-29
relative error = 1.5250592999766473716442995319517e-25 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.01
y[1] (closed_form) = -0.010785810099483919749722786956916
y[1] (numeric) = -0.010785810099483919749722786924014
absolute error = 3.2902e-29
relative error = 3.0504894575859719023552035503845e-25 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0
y[1] (closed_form) = 0
y[1] (numeric) = 3.2902000000000000000000000000000e-29
absolute error = 3.2902000000000000000000000000000e-29
relative error = -1 %
Desired digits = 8
Estimated correct digits = -16
Correct digits = -16
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.01
y[1] (closed_form) = 0.010785810099483919749722786956916
y[1] (numeric) = 0.010785810099483919749722786989818
absolute error = 3.2902e-29
relative error = 3.0504894575859719023552035503845e-25 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.02
y[1] (closed_form) = 0.021571620198967839499445573913832
y[1] (numeric) = 0.021571620198967839499445573946738
absolute error = 3.2906e-29
relative error = 1.5254301576093245307109040184328e-25 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.03
y[1] (closed_form) = 0.032357430298451759249168360870748
y[1] (numeric) = 0.032357430298451759249168360903658
absolute error = 3.2910e-29
relative error = 1.0170770576171087401628041744489e-25 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.04
y[1] (closed_form) = 0.043143240397935678998891147827664
y[1] (numeric) = 0.043143240397935678998891147860578
absolute error = 3.2914e-29
relative error = 7.6290050762100084488875425245697e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.05
y[1] (closed_form) = 0.05392905049741959874861393478458
y[1] (numeric) = 0.053929050497419598748613934817498
absolute error = 3.2918e-29
relative error = 6.1039457762333610772432429926180e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.06
y[1] (closed_form) = 0.064714860596903518498336721741496
y[1] (numeric) = 0.064714860596903518498336721774418
absolute error = 3.2922e-29
relative error = 5.0872395762489294961470433046502e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.07
y[1] (closed_form) = 0.075500670696387438248059508698412
y[1] (numeric) = 0.075500670696387438248059508731338
absolute error = 3.2926e-29
relative error = 4.3610208619743355096497578132446e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.08
y[1] (closed_form) = 0.086286480795871357997782295655328
y[1] (numeric) = 0.086286480795871357997782295688258
absolute error = 3.2930e-29
relative error = 3.8163568262683900197767936946904e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.09
y[1] (closed_form) = 0.097072290895355277747505082612244
y[1] (numeric) = 0.097072290895355277747505082645178
absolute error = 3.2934e-29
relative error = 3.3927292429415435276533771580372e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (closed_form) = 0.10785810099483919749722786956916
y[1] (numeric) = 0.10785810099483919749722786960208
absolute error = 3.292e-29
relative error = 3.0521583169330191181549237395496e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (closed_form) = 0.11864391109432311724695065652608
y[1] (numeric) = 0.11864391109432311724695065655898
absolute error = 3.290e-29
relative error = 2.7730036625178484752926375519490e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=814.1MB, alloc=40.3MB, time=9.69
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (closed_form) = 0.12942972119380703699667344348299
y[1] (numeric) = 0.12942972119380703699667344351588
absolute error = 3.289e-29
relative error = 2.5411474039066170209628250757844e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (closed_form) = 0.14021553129329095674639623043991
y[1] (numeric) = 0.14021553129329095674639623047278
absolute error = 3.287e-29
relative error = 2.3442481511727343306325905065659e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (closed_form) = 0.15100134139277487649611901739682
y[1] (numeric) = 0.15100134139277487649611901742968
absolute error = 3.286e-29
relative error = 2.1761396088877583801113260302378e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (closed_form) = 0.16178715149225879624584180435374
y[1] (numeric) = 0.16178715149225879624584180438658
absolute error = 3.284e-29
relative error = 2.0298274428529839578818893399515e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (closed_form) = 0.17257296159174271599556459131066
y[1] (numeric) = 0.17257296159174271599556459134348
absolute error = 3.282e-29
relative error = 1.9018042975725563384311322359511e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (closed_form) = 0.18335877169122663574528737826757
y[1] (numeric) = 0.18335877169122663574528737830038
absolute error = 3.281e-29
relative error = 1.7893880776672924963666472713641e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (closed_form) = 0.19414458179071055549501016522449
y[1] (numeric) = 0.19414458179071055549501016525728
absolute error = 3.279e-29
relative error = 1.6889474688172285824945988493963e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (closed_form) = 0.2049303918901944752447329521814
y[1] (numeric) = 0.20493039189019447524473295221418
absolute error = 3.278e-29
relative error = 1.5995675262049045004335614277425e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (closed_form) = 0.21571620198967839499445573913832
y[1] (numeric) = 0.21571620198967839499445573917108
absolute error = 3.276e-29
relative error = 1.5186620058129663777453721401525e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (closed_form) = 0.22650201208916231474417852609524
y[1] (numeric) = 0.22650201208916231474417852612798
absolute error = 3.274e-29
relative error = 1.4454617730774033143608199275712e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (closed_form) = 0.23728782218864623449390131305215
y[1] (numeric) = 0.23728782218864623449390131308488
absolute error = 3.273e-29
relative error = 1.3793375360822063920414593780440e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (closed_form) = 0.24807363228813015424362410000907
y[1] (numeric) = 0.24807363228813015424362410004178
absolute error = 3.271e-29
relative error = 1.3185601266162905509383426953440e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (closed_form) = 0.25885944238761407399334688696598
y[1] (numeric) = 0.25885944238761407399334688699868
absolute error = 3.270e-29
relative error = 1.2632338113065730706215320762869e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (closed_form) = 0.2696452524870979937430696739229
y[1] (numeric) = 0.26964525248709799374306967395558
absolute error = 3.268e-29
relative error = 1.2119627435889558296634618202731e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (closed_form) = 0.28043106258658191349279246087982
y[1] (numeric) = 0.28043106258658191349279246091248
absolute error = 3.266e-29
relative error = 1.1646356041573091457021661993374e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (closed_form) = 0.29121687268606583324251524783673
y[1] (numeric) = 0.29121687268606583324251524786938
absolute error = 3.265e-29
relative error = 1.1211575654545595856144892229906e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (closed_form) = 0.30200268278554975299223803479365
y[1] (numeric) = 0.30200268278554975299223803482628
absolute error = 3.263e-29
relative error = 1.0804539780585446735093208820246e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (closed_form) = 0.31278849288503367274196082175056
y[1] (numeric) = 0.31278849288503367274196082178318
absolute error = 3.262e-29
relative error = 1.0428772394766317890205473287815e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (closed_form) = 0.32357430298451759249168360870748
y[1] (numeric) = 0.32357430298451759249168360874008
absolute error = 3.260e-29
relative error = 1.0074965687729487976088549403535e-26 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (closed_form) = 0.3343601130840015122414063956644
y[1] (numeric) = 0.33436011308400151224140639569698
absolute error = 3.258e-29
relative error = 9.7439852198563245080436851246936e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (closed_form) = 0.34514592318348543199112918262131
y[1] (numeric) = 0.34514592318348543199112918265388
absolute error = 3.257e-29
relative error = 9.4365883564805240619594724139134e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (closed_form) = 0.35593173328296935174085196957823
y[1] (numeric) = 0.35593173328296935174085196961078
absolute error = 3.255e-29
relative error = 9.1450120785163088014969961819597e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (closed_form) = 0.36671754338245327149057475653514
y[1] (numeric) = 0.36671754338245327149057475656768
absolute error = 3.254e-29
relative error = 8.8733142406726147259632280113058e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (closed_form) = 0.37750335348193719124029754349206
y[1] (numeric) = 0.37750335348193719124029754352458
absolute error = 3.252e-29
relative error = 8.6144930104722948899842145469668e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (closed_form) = 0.38828916358142111099002033044898
y[1] (numeric) = 0.38828916358142111099002033048148
absolute error = 3.250e-29
relative error = 8.3700507375053261560040351639800e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (closed_form) = 0.39907497368090503073974311740589
y[1] (numeric) = 0.39907497368090503073974311743838
absolute error = 3.249e-29
relative error = 8.1413273551897959959322741698110e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (closed_form) = 0.40986078378038895048946590436281
y[1] (numeric) = 0.40986078378038895048946590439528
absolute error = 3.247e-29
relative error = 7.9222021927811545346366289748012e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=856.8MB, alloc=40.3MB, time=10.19
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (closed_form) = 0.42064659387987287023918869131972
y[1] (numeric) = 0.42064659387987287023918869135218
absolute error = 3.246e-29
relative error = 7.7166915107055021166548917800557e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (closed_form) = 0.43143240397935678998891147827664
y[1] (numeric) = 0.43143240397935678998891147830908
absolute error = 3.244e-29
relative error = 7.5191385025294000754059634045404e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (closed_form) = 0.44221821407884070973863426523356
y[1] (numeric) = 0.44221821407884070973863426526598
absolute error = 3.242e-29
relative error = 7.3312222264594493532423486083184e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (closed_form) = 0.45300402417832462948835705219047
y[1] (numeric) = 0.45300402417832462948835705222288
absolute error = 3.241e-29
relative error = 7.1544618303968603265782183647805e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (closed_form) = 0.46378983427780854923807983914739
y[1] (numeric) = 0.46378983427780854923807983917978
absolute error = 3.239e-29
relative error = 6.9837666990774314926275099553540e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (closed_form) = 0.4745756443772924689878026261043
y[1] (numeric) = 0.47457564437729246898780262613668
absolute error = 3.238e-29
relative error = 6.8229375830036423730984501468170e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (closed_form) = 0.48536145447677638873752541306122
y[1] (numeric) = 0.48536145447677638873752541309358
absolute error = 3.236e-29
relative error = 6.6671961074627041085117680715420e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (closed_form) = 0.49614726457626030848724820001814
y[1] (numeric) = 0.49614726457626030848724820005048
absolute error = 3.234e-29
relative error = 6.5182260004235457684723330430181e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (closed_form) = 0.50693307467574422823697098697505
y[1] (numeric) = 0.50693307467574422823697098700738
absolute error = 3.233e-29
relative error = 6.3775676938577407570867276246502e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (closed_form) = 0.51771888477522814798669377393197
y[1] (numeric) = 0.51771888477522814798669377396428
absolute error = 3.231e-29
relative error = 6.2408385998953174177036240649583e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (closed_form) = 0.52850469487471206773641656088888
y[1] (numeric) = 0.52850469487471206773641656092118
absolute error = 3.230e-29
relative error = 6.1115824160572642098596496632189e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (closed_form) = 0.5392905049741959874861393478458
y[1] (numeric) = 0.53929050497419598748613934787808
absolute error = 3.228e-29
relative error = 5.9856421914093473349964118051433e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (closed_form) = 0.55007631507367990723586213480272
y[1] (numeric) = 0.55007631507367990723586213483498
absolute error = 3.226e-29
relative error = 5.8646407991005644552258499415021e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (closed_form) = 0.56086212517316382698558492175963
y[1] (numeric) = 0.56086212517316382698558492179188
absolute error = 3.225e-29
relative error = 5.7500762758838364894205235653141e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (closed_form) = 0.57164793527264774673530770871655
y[1] (numeric) = 0.57164793527264774673530770874878
absolute error = 3.223e-29
relative error = 5.6380856137664324135200940029392e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (closed_form) = 0.58243374537213166648503049567346
y[1] (numeric) = 0.58243374537213166648503049570568
absolute error = 3.222e-29
relative error = 5.5319596874342894101835900099167e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (closed_form) = 0.59321955547161558623475328263038
y[1] (numeric) = 0.59321955547161558623475328266258
absolute error = 3.220e-29
relative error = 5.4280071691838736112111203144535e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (closed_form) = 0.6040053655710995059844760695873
y[1] (numeric) = 0.60400536557109950598447606961948
absolute error = 3.218e-29
relative error = 5.3277672408709726622019531081140e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (closed_form) = 0.61479117567058342573419885654421
y[1] (numeric) = 0.61479117567058342573419885657638
absolute error = 3.217e-29
relative error = 5.2326710715895645494150570602476e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (closed_form) = 0.62557698577006734548392164350113
y[1] (numeric) = 0.62557698577006734548392164353328
absolute error = 3.215e-29
relative error = 5.1392555562804586169544139516130e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (closed_form) = 0.63636279586955126523364443045804
y[1] (numeric) = 0.63636279586955126523364443049018
absolute error = 3.214e-29
relative error = 5.0505780992558866104526252131064e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (closed_form) = 0.64714860596903518498336721741496
y[1] (numeric) = 0.64714860596903518498336721744708
absolute error = 3.212e-29
relative error = 4.9633113173293121747233774055453e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (closed_form) = 0.65793441606851910473309000437188
y[1] (numeric) = 0.65793441606851910473309000440398
absolute error = 3.210e-29
relative error = 4.8789057413675434581983672310191e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (closed_form) = 0.66872022616800302448281279132879
y[1] (numeric) = 0.66872022616800302448281279136088
absolute error = 3.209e-29
relative error = 4.7987183196008203416685367656756e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (closed_form) = 0.67950603626748694423253557828571
y[1] (numeric) = 0.67950603626748694423253557831778
absolute error = 3.207e-29
relative error = 4.7196048729986076452404291465290e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (closed_form) = 0.69029184636697086398225836524262
y[1] (numeric) = 0.69029184636697086398225836527468
absolute error = 3.206e-29
relative error = 4.6444123842303592481796236657977e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (closed_form) = 0.70107765646645478373198115219954
y[1] (numeric) = 0.70107765646645478373198115223158
absolute error = 3.204e-29
relative error = 4.5701071349908371130799026364692e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=899.4MB, alloc=40.3MB, time=10.70
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (closed_form) = 0.71186346656593870348170393915646
y[1] (numeric) = 0.71186346656593870348170393918848
absolute error = 3.202e-29
relative error = 4.4980535599706944366195670928779e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (closed_form) = 0.72264927666542262323142672611337
y[1] (numeric) = 0.72264927666542262323142672614538
absolute error = 3.201e-29
relative error = 4.4295346350730827320931389031293e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (closed_form) = 0.73343508676490654298114951307029
y[1] (numeric) = 0.73343508676490654298114951310228
absolute error = 3.199e-29
relative error = 4.3616675254934994634843832833692e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (closed_form) = 0.7442208968643904627308723000272
y[1] (numeric) = 0.74422089686439046273087230005918
absolute error = 3.198e-29
relative error = 4.2971112655853430978302455311425e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (closed_form) = 0.75500670696387438248059508698412
y[1] (numeric) = 0.75500670696387438248059508701608
absolute error = 3.196e-29
relative error = 4.2330749787007156316712099772610e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (closed_form) = 0.76579251706335830223031787394104
y[1] (numeric) = 0.76579251706335830223031787397298
absolute error = 3.194e-29
relative error = 4.1708425308832607701927106361650e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (closed_form) = 0.77657832716284222198004066089795
y[1] (numeric) = 0.77657832716284222198004066092988
absolute error = 3.193e-29
relative error = 4.1116264622853086794032129659367e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (closed_form) = 0.78736413726232614172976344785487
y[1] (numeric) = 0.78736413726232614172976344788678
absolute error = 3.191e-29
relative error = 4.0527626913452554162154669905052e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (closed_form) = 0.79814994736181006147948623481178
y[1] (numeric) = 0.79814994736181006147948623484368
absolute error = 3.190e-29
relative error = 3.9967427305410048056361887660352e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (closed_form) = 0.8089357574612939812292090217687
y[1] (numeric) = 0.80893575746129398122920902180058
absolute error = 3.188e-29
relative error = 3.9409804432492770144503430059473e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (closed_form) = 0.81972156756077790097893180872562
y[1] (numeric) = 0.81972156756077790097893180875748
absolute error = 3.186e-29
relative error = 3.8866855845704894282957037132302e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (closed_form) = 0.83050737766026182072865459568253
y[1] (numeric) = 0.83050737766026182072865459571438
absolute error = 3.185e-29
relative error = 3.8350050651842585296600306569509e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (closed_form) = 0.84129318775974574047837738263945
y[1] (numeric) = 0.84129318775974574047837738267128
absolute error = 3.183e-29
relative error = 3.7834610410621708621861553505726e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (closed_form) = 0.85207899785922966022810016959636
y[1] (numeric) = 0.85207899785922966022810016962818
absolute error = 3.182e-29
relative error = 3.7343955290465827529603670344859e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (closed_form) = 0.86286480795871357997782295655328
y[1] (numeric) = 0.86286480795871357997782295658508
absolute error = 3.180e-29
relative error = 3.6853977247292682243820844060478e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (closed_form) = 0.8736506180581974997275457435102
y[1] (numeric) = 0.87365061805819749972754574354198
absolute error = 3.178e-29
relative error = 3.6376097427407762767563519659663e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (closed_form) = 0.88443642815768141947726853046711
y[1] (numeric) = 0.88443642815768141947726853049888
absolute error = 3.177e-29
relative error = 3.5921179848028486420806510685731e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (closed_form) = 0.89522223825716533922699131742403
y[1] (numeric) = 0.89522223825716533922699131745578
absolute error = 3.175e-29
relative error = 3.5466053727409037243049535467763e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (closed_form) = 0.90600804835664925897671410438094
y[1] (numeric) = 0.90600804835664925897671410441268
absolute error = 3.174e-29
relative error = 3.5032801372538776113173812233591e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (closed_form) = 0.91679385845613317872643689133786
y[1] (numeric) = 0.91679385845613317872643689136958
absolute error = 3.172e-29
relative error = 3.4598835613292604684395032884894e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (closed_form) = 0.92757966855561709847615967829478
y[1] (numeric) = 0.92757966855561709847615967832648
absolute error = 3.170e-29
relative error = 3.4174962081005646544657620497796e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (closed_form) = 0.93836547865510101822588246525169
y[1] (numeric) = 0.93836547865510101822588246528338
absolute error = 3.169e-29
relative error = 3.3771489596376927645678668351813e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (closed_form) = 0.94915128875458493797560525220861
y[1] (numeric) = 0.94915128875458493797560525224028
absolute error = 3.167e-29
relative error = 3.3366651212743260339102519479570e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (closed_form) = 0.95993709885406885772532803916552
y[1] (numeric) = 0.95993709885406885772532803919718
absolute error = 3.166e-29
relative error = 3.2981327670109146204207983123588e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (closed_form) = 0.97072290895355277747505082612244
y[1] (numeric) = 0.97072290895355277747505082615408
absolute error = 3.164e-29
relative error = 3.2594265271959202409349867395487e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (closed_form) = 0.98150871905303669722477361307936
y[1] (numeric) = 0.98150871905303669722477361311098
absolute error = 3.162e-29
relative error = 3.2215709739702663972620501463607e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (closed_form) = 0.99229452915252061697449640003627
y[1] (numeric) = 0.99229452915252061697449640006788
absolute error = 3.161e-29
relative error = 3.1855461328600538302629939315059e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=942.1MB, alloc=40.3MB, time=11.20
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (closed_form) = 1.0030803392520045367242191869932
y[1] (numeric) = 1.0030803392520045367242191870248
absolute error = 3.16e-29
relative error = 3.1502960195156522862101539793362e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (closed_form) = 1.0138661493514884564739419739501
y[1] (numeric) = 1.0138661493514884564739419739818
absolute error = 3.17e-29
relative error = 3.1266454669856229817452716625643e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (closed_form) = 1.024651959450972376223664760907
y[1] (numeric) = 1.0246519594509723762236647609388
absolute error = 3.18e-29
relative error = 3.1034928208246469257954394998298e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (closed_form) = 1.0354377695504562959733875478639
y[1] (numeric) = 1.0354377695504562959733875478958
absolute error = 3.19e-29
relative error = 3.0808225214586912043445621738189e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (closed_form) = 1.0462235796499402157231103348209
y[1] (numeric) = 1.0462235796499402157231103348528
absolute error = 3.19e-29
relative error = 3.0490614645364366558461646256350e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (closed_form) = 1.0570093897494241354728331217778
y[1] (numeric) = 1.0570093897494241354728331218098
absolute error = 3.20e-29
relative error = 3.0274092463441556457509100498916e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (closed_form) = 1.0677951998489080552225559087347
y[1] (numeric) = 1.0677951998489080552225559087668
absolute error = 3.21e-29
relative error = 3.0061944467012136459606101120420e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (closed_form) = 1.0785810099483919749722786956916
y[1] (numeric) = 1.0785810099483919749722786957238
absolute error = 3.22e-29
relative error = 2.9854039430511304861661161729494e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (closed_form) = 1.0893668200478758947220014826485
y[1] (numeric) = 1.0893668200478758947220014826808
absolute error = 3.23e-29
relative error = 2.9650251325426331315160676583933e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (closed_form) = 1.1001526301473598144717242696054
y[1] (numeric) = 1.1001526301473598144717242696378
absolute error = 3.24e-29
relative error = 2.9450459065539102348003338205932e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (closed_form) = 1.1109384402468437342214470565623
y[1] (numeric) = 1.1109384402468437342214470565948
absolute error = 3.25e-29
relative error = 2.9254546267008906953023812223621e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (closed_form) = 1.1217242503463276539711698435193
y[1] (numeric) = 1.1217242503463276539711698435518
absolute error = 3.25e-29
relative error = 2.8973252552903052078475506336853e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (closed_form) = 1.1325100604458115737208926304762
y[1] (numeric) = 1.1325100604458115737208926305088
absolute error = 3.26e-29
relative error = 2.8785616250655679931681569724386e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (closed_form) = 1.1432958705452954934706154174331
y[1] (numeric) = 1.1432958705452954934706154174658
absolute error = 3.27e-29
relative error = 2.8601520255997880844261103614041e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (closed_form) = 1.15408168064477941322033820439
y[1] (numeric) = 1.1540816806447794132203382044228
absolute error = 3.28e-29
relative error = 2.8420865307969199496792421916974e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (closed_form) = 1.1648674907442633329700609913469
y[1] (numeric) = 1.1648674907442633329700609913798
absolute error = 3.29e-29
relative error = 2.8243555821941049285387975066149e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (closed_form) = 1.1756533008437472527197837783038
y[1] (numeric) = 1.1756533008437472527197837783368
absolute error = 3.30e-29
relative error = 2.8069499720977635775110215313504e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (closed_form) = 1.1864391109432311724695065652608
y[1] (numeric) = 1.1864391109432311724695065652938
absolute error = 3.30e-29
relative error = 2.7814322450786929995336486083379e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (closed_form) = 1.1972249210427150922192293522177
y[1] (numeric) = 1.1972249210427150922192293522508
absolute error = 3.31e-29
relative error = 2.7647269463094516001370501181978e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (closed_form) = 1.2080107311421990119689521391746
y[1] (numeric) = 1.2080107311421990119689521392078
absolute error = 3.32e-29
relative error = 2.7483199564468037971582480296673e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (closed_form) = 1.2187965412416829317186749261315
y[1] (numeric) = 1.2187965412416829317186749261648
absolute error = 3.33e-29
relative error = 2.7322033557852648048516371285444e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (closed_form) = 1.2295823513411668514683977130884
y[1] (numeric) = 1.2295823513411668514683977131218
absolute error = 3.34e-29
relative error = 2.7163695025037528124100544888448e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (closed_form) = 1.2403681614406507712181205000453
y[1] (numeric) = 1.2403681614406507712181205000788
absolute error = 3.35e-29
relative error = 2.7008110205836584198370211124442e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (closed_form) = 1.2511539715401346909678432870023
y[1] (numeric) = 1.2511539715401346909678432870358
absolute error = 3.35e-29
relative error = 2.6775281669579372265625640338885e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (closed_form) = 1.2619397816396186107175660739592
y[1] (numeric) = 1.2619397816396186107175660739928
absolute error = 3.36e-29
relative error = 2.6625676192206291961347747361867e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (closed_form) = 1.2727255917391025304672888609161
y[1] (numeric) = 1.2727255917391025304672888609498
absolute error = 3.37e-29
relative error = 2.6478606400890382509684733926833e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (closed_form) = 1.283511401838586450217011647873
y[1] (numeric) = 1.2835114018385864502170116479068
absolute error = 3.38e-29
relative error = 2.6334008370773059771495048448690e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=984.8MB, alloc=40.3MB, time=11.72
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (closed_form) = 1.2942972119380703699667344348299
y[1] (numeric) = 1.2942972119380703699667344348638
absolute error = 3.39e-29
relative error = 2.6191820307824359078941857728516e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (closed_form) = 1.3050830220375542897164572217868
y[1] (numeric) = 1.3050830220375542897164572218208
absolute error = 3.40e-29
relative error = 2.6051982460792165835852356111155e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (closed_form) = 1.3158688321370382094661800087438
y[1] (numeric) = 1.3158688321370382094661800087778
absolute error = 3.40e-29
relative error = 2.5838441620949607099492910569259e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (closed_form) = 1.3266546422365221292159027957007
y[1] (numeric) = 1.3266546422365221292159027957348
absolute error = 3.41e-29
relative error = 2.5703750557502284900839408548597e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (closed_form) = 1.3374404523360060489656255826576
y[1] (numeric) = 1.3374404523360060489656255826918
absolute error = 3.42e-29
relative error = 2.5571231930562177576357737205688e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (closed_form) = 1.3482262624354899687153483696145
y[1] (numeric) = 1.3482262624354899687153483696488
absolute error = 3.43e-29
relative error = 2.5440833601653111969067772604265e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (closed_form) = 1.3590120725349738884650711565714
y[1] (numeric) = 1.3590120725349738884650711566058
absolute error = 3.44e-29
relative error = 2.5312505087488634704750664583817e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (closed_form) = 1.3697978826344578082147939435283
y[1] (numeric) = 1.3697978826344578082147939435628
absolute error = 3.45e-29
relative error = 2.5186197494807062594202329918022e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (closed_form) = 1.3805836927339417279645167304852
y[1] (numeric) = 1.3805836927339417279645167305198
absolute error = 3.46e-29
relative error = 2.5061863458261140047881312981380e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (closed_form) = 1.3913695028334256477142395174422
y[1] (numeric) = 1.3913695028334256477142395174768
absolute error = 3.46e-29
relative error = 2.4867585446956790125029519857491e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (closed_form) = 1.4021553129329095674639623043991
y[1] (numeric) = 1.4021553129329095674639623044338
absolute error = 3.47e-29
relative error = 2.4747615103648883867645540181879e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (closed_form) = 1.412941123032393487213685091356
y[1] (numeric) = 1.4129411230323934872136850913908
absolute error = 3.48e-29
relative error = 2.4629476368635754805030781570016e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (closed_form) = 1.4237269331318774069634078783129
y[1] (numeric) = 1.4237269331318774069634078783478
absolute error = 3.49e-29
relative error = 2.4513127614456158000940488997726e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (closed_form) = 1.4345127432313613267131306652698
y[1] (numeric) = 1.4345127432313613267131306653048
absolute error = 3.50e-29
relative error = 2.4398528465602570171347794809983e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (closed_form) = 1.4452985533308452464628534522267
y[1] (numeric) = 1.4452985533308452464628534522618
absolute error = 3.51e-29
relative error = 2.4285639751806498578017678147429e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (closed_form) = 1.4560843634303291662125762391837
y[1] (numeric) = 1.4560843634303291662125762392188
absolute error = 3.51e-29
relative error = 2.4105746124015339329291621272262e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (closed_form) = 1.4668701735298130859622990261406
y[1] (numeric) = 1.4668701735298130859622990261758
absolute error = 3.52e-29
relative error = 2.3996670349698527839113831130759e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (closed_form) = 1.4776559836292970057120218130975
y[1] (numeric) = 1.4776559836292970057120218131328
absolute error = 3.53e-29
relative error = 2.3889186922452034764851045224898e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (closed_form) = 1.4884417937287809254617446000544
y[1] (numeric) = 1.4884417937287809254617446000898
absolute error = 3.54e-29
relative error = 2.3783261226035201010505111288687e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (closed_form) = 1.4992276038282648452114673870113
y[1] (numeric) = 1.4992276038282648452114673870468
absolute error = 3.55e-29
relative error = 2.3678859640358177813775665610552e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (closed_form) = 1.5100134139277487649611901739682
y[1] (numeric) = 1.5100134139277487649611901740038
absolute error = 3.56e-29
relative error = 2.3575949505905112091285212013532e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (closed_form) = 1.5207992240272326847109129609252
y[1] (numeric) = 1.5207992240272326847109129609608
absolute error = 3.56e-29
relative error = 2.3408744190260394984254820438967e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (closed_form) = 1.5315850341267166044606357478821
y[1] (numeric) = 1.5315850341267166044606357479178
absolute error = 3.57e-29
relative error = 2.3309185715800314573556632703677e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (closed_form) = 1.542370844226200524210358534839
y[1] (numeric) = 1.5423708442262005242103585348748
absolute error = 3.58e-29
relative error = 2.3211019667556459063707370670979e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (closed_form) = 1.5531566543256844439600813217959
y[1] (numeric) = 1.5531566543256844439600813218318
absolute error = 3.59e-29
relative error = 2.3114217036649323769272681722068e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (closed_form) = 1.5639424644251683637098041087528
y[1] (numeric) = 1.5639424644251683637098041087888
absolute error = 3.60e-29
relative error = 2.3018749614444355858209505724177e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (closed_form) = 1.5747282745246522834595268957097
y[1] (numeric) = 1.5747282745246522834595268957458
absolute error = 3.61e-29
relative error = 2.2924589965146305315791030767352e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1027.6MB, alloc=40.3MB, time=12.22
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (closed_form) = 1.5855140846241362032092496826667
y[1] (numeric) = 1.5855140846241362032092496827028
absolute error = 3.61e-29
relative error = 2.2768640373546670585751636000226e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (closed_form) = 1.5962998947236201229589724696236
y[1] (numeric) = 1.5962998947236201229589724696598
absolute error = 3.62e-29
relative error = 2.2677443079245199680882450365278e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (closed_form) = 1.6070857048231040427086952565805
y[1] (numeric) = 1.6070857048231040427086952566168
absolute error = 3.63e-29
relative error = 2.2587469909699453217689361181805e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (closed_form) = 1.6178715149225879624584180435374
y[1] (numeric) = 1.6178715149225879624584180435738
absolute error = 3.64e-29
relative error = 2.2498696382414316707338846520778e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (closed_form) = 1.6286573250220718822081408304943
y[1] (numeric) = 1.6286573250220718822081408305308
absolute error = 3.65e-29
relative error = 2.2411098663437592601098934702944e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (closed_form) = 1.6394431351215558019578636174512
y[1] (numeric) = 1.6394431351215558019578636174878
absolute error = 3.66e-29
relative error = 2.2324653546026351706783232251134e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (closed_form) = 1.6502289452210397217075864044081
y[1] (numeric) = 1.6502289452210397217075864044448
absolute error = 3.67e-29
relative error = 2.2239338430149898275138323295426e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (closed_form) = 1.6610147553205236414573091913651
y[1] (numeric) = 1.6610147553205236414573091914018
absolute error = 3.67e-29
relative error = 2.2094927141642431403221840676624e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (closed_form) = 1.671800565420007561207031978322
y[1] (numeric) = 1.6718005654200075612070319783588
absolute error = 3.68e-29
relative error = 2.2012194971805570404911455653083e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (closed_form) = 1.6825863755194914809567547652789
y[1] (numeric) = 1.6825863755194914809567547653158
absolute error = 3.69e-29
relative error = 2.1930523470812771727092229411896e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (closed_form) = 1.6933721856189754007064775522358
y[1] (numeric) = 1.6933721856189754007064775522728
absolute error = 3.70e-29
relative error = 2.1849892371106505516506369110086e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (closed_form) = 1.7041579957184593204562003391927
y[1] (numeric) = 1.7041579957184593204562003392298
absolute error = 3.71e-29
relative error = 2.1770281918231964194662101976654e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (closed_form) = 1.7149438058179432402059231261496
y[1] (numeric) = 1.7149438058179432402059231261868
absolute error = 3.72e-29
relative error = 2.1691672854701756725922794178234e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (closed_form) = 1.7257296159174271599556459131066
y[1] (numeric) = 1.7257296159174271599556459131438
absolute error = 3.72e-29
relative error = 2.1556099899359870746385776714619e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (closed_form) = 1.7365154260169110797053687000635
y[1] (numeric) = 1.7365154260169110797053687001008
absolute error = 3.73e-29
relative error = 2.1479797669034213019172897120291e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (closed_form) = 1.7473012361163949994550914870204
y[1] (numeric) = 1.7473012361163949994550914870578
absolute error = 3.74e-29
relative error = 2.1404437441552081930567583940708e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (closed_form) = 1.7580870462158789192048142739773
y[1] (numeric) = 1.7580870462158789192048142740148
absolute error = 3.75e-29
relative error = 2.1330001879437829751024912640629e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (closed_form) = 1.7688728563153628389545370609342
y[1] (numeric) = 1.7688728563153628389545370609718
absolute error = 3.76e-29
relative error = 2.1256474068081068451720566600307e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (closed_form) = 1.7796586664148467587042598478911
y[1] (numeric) = 1.7796586664148467587042598479288
absolute error = 3.77e-29
relative error = 2.1183837502922570925741121724110e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (closed_form) = 1.7904444765143306784539826348481
y[1] (numeric) = 1.7904444765143306784539826348858
absolute error = 3.77e-29
relative error = 2.1056224023989302426188464364325e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (closed_form) = 1.801230286613814598203705421805
y[1] (numeric) = 1.8012302866138145982037054218428
absolute error = 3.78e-29
relative error = 2.0985656459875168738996390697640e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (closed_form) = 1.8120160967132985179534282087619
y[1] (numeric) = 1.8120160967132985179534282087998
absolute error = 3.79e-29
relative error = 2.0915928985810012833794698860319e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (closed_form) = 1.8228019068127824377031509957188
y[1] (numeric) = 1.8228019068127824377031509957568
absolute error = 3.80e-29
relative error = 2.0847026688952728596110186808056e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (closed_form) = 1.8335877169122663574528737826757
y[1] (numeric) = 1.8335877169122663574528737827138
absolute error = 3.81e-29
relative error = 2.0778935007352588878869021956408e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (closed_form) = 1.8443735270117502772025965696326
y[1] (numeric) = 1.8443735270117502772025965696708
absolute error = 3.82e-29
relative error = 2.0711639719689292901010794705363e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (closed_form) = 1.8551593371112341969523193565896
y[1] (numeric) = 1.8551593371112341969523193566278
absolute error = 3.82e-29
relative error = 2.0591223209691099337632824968703e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (closed_form) = 1.8659451472107181167020421435465
y[1] (numeric) = 1.8659451472107181167020421435848
absolute error = 3.83e-29
relative error = 2.0525790941524844293282994547080e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1070.3MB, alloc=40.3MB, time=12.72
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (closed_form) = 1.8767309573102020364517649305034
y[1] (numeric) = 1.8767309573102020364517649305418
absolute error = 3.84e-29
relative error = 2.0461110768394982985075116199268e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (closed_form) = 1.8875167674096859562014877174603
y[1] (numeric) = 1.8875167674096859562014877174988
absolute error = 3.85e-29
relative error = 2.0397169797243748663246756461145e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (closed_form) = 1.8983025775091698759512105044172
y[1] (numeric) = 1.8983025775091698759512105044558
absolute error = 3.86e-29
relative error = 2.0333955428037414731439173538229e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (closed_form) = 1.9090883876086537957009332913741
y[1] (numeric) = 1.9090883876086537957009332914128
absolute error = 3.87e-29
relative error = 2.0271455345488779488126591552294e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (closed_form) = 1.919874197708137715450656078331
y[1] (numeric) = 1.9198741977081377154506560783698
absolute error = 3.88e-29
relative error = 2.0209657511058668236311903745977e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (closed_form) = 1.930660007807621635200378865288
y[1] (numeric) = 1.9306600078076216352003788653268
absolute error = 3.88e-29
relative error = 2.0096754396471748302030831658010e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (closed_form) = 1.9414458179071055549501016522449
y[1] (numeric) = 1.9414458179071055549501016522838
absolute error = 3.89e-29
relative error = 2.0036613765474288459603505715620e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (closed_form) = 1.9522316280065894746998244392018
y[1] (numeric) = 1.9522316280065894746998244392408
absolute error = 3.90e-29
relative error = 1.9977137671835916571236150225632e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (closed_form) = 1.9630174381060733944495472261587
y[1] (numeric) = 1.9630174381060733944495472261978
absolute error = 3.91e-29
relative error = 1.9918315161644120198125578861908e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (closed_form) = 1.9738032482055573141992700131156
y[1] (numeric) = 1.9738032482055573141992700131548
absolute error = 3.92e-29
relative error = 1.9860135520416168594120041065000e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (closed_form) = 1.9845890583050412339489928000725
y[1] (numeric) = 1.9845890583050412339489928001118
absolute error = 3.93e-29
relative error = 1.9802588266592868637984128678928e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (closed_form) = 1.9953748684045251536987155870295
y[1] (numeric) = 1.9953748684045251536987155870688
absolute error = 3.93e-29
relative error = 1.9695547248935609888589619875258e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (closed_form) = 2.0061606785040090734484383739864
y[1] (numeric) = 2.0061606785040090734484383740258
absolute error = 3.94e-29
relative error = 1.9639503665967832290613934618014e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (closed_form) = 2.0169464886034929931981611609433
y[1] (numeric) = 2.0169464886034929931981611609828
absolute error = 3.95e-29
relative error = 1.9584059479609335736466866315392e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (closed_form) = 2.0277322987029769129478839479002
y[1] (numeric) = 2.0277322987029769129478839479398
absolute error = 3.96e-29
relative error = 1.9529205125020610422257532781948e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (closed_form) = 2.0385181088024608326976067348571
y[1] (numeric) = 2.0385181088024608326976067348968
absolute error = 3.97e-29
relative error = 1.9474931239792612360050414418169e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (closed_form) = 2.049303918901944752447329521814
y[1] (numeric) = 2.0493039189019447524473295218538
absolute error = 3.98e-29
relative error = 1.9421228658619645856392844668746e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (closed_form) = 2.060089729001428672197052308771
y[1] (numeric) = 2.0600897290014286721970523088108
absolute error = 3.98e-29
relative error = 1.9319546833181846663427437105035e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (closed_form) = 2.0708755391009125919467750957279
y[1] (numeric) = 2.0708755391009125919467750957678
absolute error = 3.99e-29
relative error = 1.9267212947680529632186211714008e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.93
y[1] (closed_form) = 2.0816613492003965116964978826848
y[1] (numeric) = 2.0816613492003965116964978827248
absolute error = 4.00e-29
relative error = 1.9215421382236221067589973114597e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (closed_form) = 2.0924471592998804314462206696417
y[1] (numeric) = 2.0924471592998804314462206696818
absolute error = 4.01e-29
relative error = 1.9164163750456286818092664810026e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (closed_form) = 2.1032329693993643511959434565986
y[1] (numeric) = 2.1032329693993643511959434566388
absolute error = 4.02e-29
relative error = 1.9113431837976659586538918641913e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (closed_form) = 2.1140187794988482709456662435555
y[1] (numeric) = 2.1140187794988482709456662435958
absolute error = 4.03e-29
relative error = 1.9063217598073355081837761720412e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (closed_form) = 2.1248045895983321906953890305125
y[1] (numeric) = 2.1248045895983321906953890305528
absolute error = 4.03e-29
relative error = 1.8966449996052678152488331457871e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (closed_form) = 2.1355903996978161104451118174694
y[1] (numeric) = 2.1355903996978161104451118175098
absolute error = 4.04e-29
relative error = 1.8917485303228821074269259895093e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (closed_form) = 2.1463762097973000301948346044263
y[1] (numeric) = 2.1463762097973000301948346044668
absolute error = 4.05e-29
relative error = 1.8869012717870530398846359905810e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (closed_form) = 2.1571620198967839499445573913832
y[1] (numeric) = 2.1571620198967839499445573914238
absolute error = 4.06e-29
relative error = 1.8821024858365822630177688916420e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1113.0MB, alloc=40.3MB, time=13.23
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (closed_form) = 2.1679478299962678696942801783401
y[1] (numeric) = 2.1679478299962678696942801783808
absolute error = 4.07e-29
relative error = 1.8773514490000465187565422613492e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (closed_form) = 2.178733640095751789444002965297
y[1] (numeric) = 2.1787336400957517894440029653378
absolute error = 4.08e-29
relative error = 1.8726474521321893462206743105642e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (closed_form) = 2.1895194501952357091937257522539
y[1] (numeric) = 2.1895194501952357091937257522948
absolute error = 4.09e-29
relative error = 1.8679898000610598305570809208707e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (closed_form) = 2.2003052602947196289434485392109
y[1] (numeric) = 2.2003052602947196289434485392518
absolute error = 4.09e-29
relative error = 1.8588329873156624784465069947879e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (closed_form) = 2.2110910703942035486931713261678
y[1] (numeric) = 2.2110910703942035486931713262088
absolute error = 4.10e-29
relative error = 1.8542881633857953330224324055586e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (closed_form) = 2.2218768804936874684428941131247
y[1] (numeric) = 2.2218768804936874684428941131658
absolute error = 4.11e-29
relative error = 1.8497874639601016550296595113704e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (closed_form) = 2.2326626905931713881926169000816
y[1] (numeric) = 2.2326626905931713881926169001228
absolute error = 4.12e-29
relative error = 1.8453302495530137130561404615705e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (closed_form) = 2.2434485006926553079423396870385
y[1] (numeric) = 2.2434485006926553079423396870798
absolute error = 4.13e-29
relative error = 1.8409158929767631551400590949417e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (closed_form) = 2.2542343107921392276920624739954
y[1] (numeric) = 2.2542343107921392276920624740368
absolute error = 4.14e-29
relative error = 1.8365437790471752819887249184242e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (closed_form) = 2.2650201208916231474417852609524
y[1] (numeric) = 2.2650201208916231474417852609938
absolute error = 4.14e-29
relative error = 1.8277983324802839711221119426221e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (closed_form) = 2.2758059309911070671915080479093
y[1] (numeric) = 2.2758059309911070671915080479508
absolute error = 4.15e-29
relative error = 1.8235298289220499128064204936181e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (closed_form) = 2.2865917410905909869412308348662
y[1] (numeric) = 2.2865917410905909869412308349078
absolute error = 4.16e-29
relative error = 1.8193015942653086286257827375292e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (closed_form) = 2.2973775511900749066909536218231
y[1] (numeric) = 2.2973775511900749066909536218648
absolute error = 4.17e-29
relative error = 1.8151130613424334597895641153004e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (closed_form) = 2.30816336128955882644067640878
y[1] (numeric) = 2.3081633612895588264406764088218
absolute error = 4.18e-29
relative error = 1.8109636735870617972041512745877e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (closed_form) = 2.3189491713890427461903991957369
y[1] (numeric) = 2.3189491713890427461903991957788
absolute error = 4.19e-29
relative error = 1.8068528847875540570613934370444e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (closed_form) = 2.3297349814885266659401219826939
y[1] (numeric) = 2.3297349814885266659401219827358
absolute error = 4.19e-29
relative error = 1.7984878251357598253157388377988e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (closed_form) = 2.3405207915880105856898447696508
y[1] (numeric) = 2.3405207915880105856898447696928
absolute error = 4.20e-29
relative error = 1.7944724161798019351829991021535e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (closed_form) = 2.3513066016874945054395675566077
y[1] (numeric) = 2.3513066016874945054395675566498
absolute error = 4.21e-29
relative error = 1.7904938458381188880790000980280e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (closed_form) = 2.3620924117869784251892903435646
y[1] (numeric) = 2.3620924117869784251892903436068
absolute error = 4.22e-29
relative error = 1.7865516094721589738252659249903e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (closed_form) = 2.3728782218864623449390131305215
y[1] (numeric) = 2.3728782218864623449390131305638
absolute error = 4.23e-29
relative error = 1.7826452116186168769738384262530e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (closed_form) = 2.3836640319859462646887359174784
y[1] (numeric) = 2.3836640319859462646887359175208
absolute error = 4.24e-29
relative error = 1.7787741657818489167455007691332e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (closed_form) = 2.3944498420854301844384587044354
y[1] (numeric) = 2.3944498420854301844384587044778
absolute error = 4.24e-29
relative error = 1.7707616695395883360394399548578e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (closed_form) = 2.4052356521849141041881814913923
y[1] (numeric) = 2.4052356521849141041881814914348
absolute error = 4.25e-29
relative error = 1.7669786310290650594944703416198e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (closed_form) = 2.4160214622843980239379042783492
y[1] (numeric) = 2.4160214622843980239379042783918
absolute error = 4.26e-29
relative error = 1.7632293696481000264900808142142e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (closed_form) = 2.4268072723838819436876270653061
y[1] (numeric) = 2.4268072723838819436876270653488
absolute error = 4.27e-29
relative error = 1.7595134350349657937790636381634e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (closed_form) = 2.437593082483365863437349852263
y[1] (numeric) = 2.4375930824833658634373498523058
absolute error = 4.28e-29
relative error = 1.7558303847989389436584094459715e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (closed_form) = 2.4483788925828497831870726392199
y[1] (numeric) = 2.4483788925828497831870726392628
absolute error = 4.29e-29
relative error = 1.7521797843447273080762632202306e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1155.7MB, alloc=40.3MB, time=13.73
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (closed_form) = 2.4591647026823337029367954261768
y[1] (numeric) = 2.4591647026823337029367954262198
absolute error = 4.30e-29
relative error = 1.7485612067015175289465919613821e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (closed_form) = 2.4699505127818176226865182131338
y[1] (numeric) = 2.4699505127818176226865182131768
absolute error = 4.30e-29
relative error = 1.7409255682443056620079605554371e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (closed_form) = 2.4807363228813015424362410000907
y[1] (numeric) = 2.4807363228813015424362410001338
absolute error = 4.31e-29
relative error = 1.7373873878679951924623225365126e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (closed_form) = 2.4915221329807854621859637870476
y[1] (numeric) = 2.4915221329807854621859637870908
absolute error = 4.32e-29
relative error = 1.7338798410880164152937030285743e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (closed_form) = 2.5023079430802693819356865740045
y[1] (numeric) = 2.5023079430802693819356865740478
absolute error = 4.33e-29
relative error = 1.7304025317802788344799854129459e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (closed_form) = 2.5130937531797533016854093609614
y[1] (numeric) = 2.5130937531797533016854093610048
absolute error = 4.34e-29
relative error = 1.7269550706211055247462138712714e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (closed_form) = 2.5238795632792372214351321479183
y[1] (numeric) = 2.5238795632792372214351321479618
absolute error = 4.35e-29
relative error = 1.7235370749419251492836711461924e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (closed_form) = 2.5346653733787211411848549348753
y[1] (numeric) = 2.5346653733787211411848549349188
absolute error = 4.35e-29
relative error = 1.7162028746230233401377831838681e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (closed_form) = 2.5454511834782050609345777218322
y[1] (numeric) = 2.5454511834782050609345777218758
absolute error = 4.36e-29
relative error = 1.7128594051614550110122468831008e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (closed_form) = 2.5562369935776889806843005087891
y[1] (numeric) = 2.5562369935776889806843005088328
absolute error = 4.37e-29
relative error = 1.7095441506320518154658290321290e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (closed_form) = 2.567022803677172900434023295746
y[1] (numeric) = 2.5670228036771729004340232957898
absolute error = 4.38e-29
relative error = 1.7062567553844083106382886420897e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (closed_form) = 2.5778086137766568201837460827029
y[1] (numeric) = 2.5778086137766568201837460827468
absolute error = 4.39e-29
relative error = 1.7029968697204270945540749498750e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (closed_form) = 2.5885944238761407399334688696598
y[1] (numeric) = 2.5885944238761407399334688697038
absolute error = 4.40e-29
relative error = 1.6997641497703123886038963717621e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (closed_form) = 2.5993802339756246596831916566168
y[1] (numeric) = 2.5993802339756246596831916566608
absolute error = 4.40e-29
relative error = 1.6927111864932571504769092498875e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (closed_form) = 2.6101660440751085794329144435737
y[1] (numeric) = 2.6101660440751085794329144436178
absolute error = 4.41e-29
relative error = 1.6895476860601978137663072125028e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (closed_form) = 2.6209518541745924991826372305306
y[1] (numeric) = 2.6209518541745924991826372305748
absolute error = 4.42e-29
relative error = 1.6864102226677397884689611589649e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (closed_form) = 2.6317376642740764189323600174875
y[1] (numeric) = 2.6317376642740764189323600175318
absolute error = 4.43e-29
relative error = 1.6832984761883346978051999091444e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (closed_form) = 2.6425234743735603386820828044444
y[1] (numeric) = 2.6425234743735603386820828044888
absolute error = 4.44e-29
relative error = 1.6802121317210063833917550776899e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (closed_form) = 2.6533092844730442584318055914013
y[1] (numeric) = 2.6533092844730442584318055914458
absolute error = 4.45e-29
relative error = 1.6771508794851197625914276838895e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (closed_form) = 2.6640950945725281781815283783583
y[1] (numeric) = 2.6640950945725281781815283784028
absolute error = 4.45e-29
relative error = 1.6703607949527913424999644139141e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (closed_form) = 2.6748809046720120979312511653152
y[1] (numeric) = 2.6748809046720120979312511653598
absolute error = 4.46e-29
relative error = 1.6673639533670659647742033324176e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (closed_form) = 2.6856667147714960176809739522721
y[1] (numeric) = 2.6856667147714960176809739523168
absolute error = 4.47e-29
relative error = 1.6643911827980934013273640266761e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (closed_form) = 2.696452524870979937430696739229
y[1] (numeric) = 2.6964525248709799374306967392738
absolute error = 4.48e-29
relative error = 1.6614421943936726183880994353806e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (closed_form) = 2.7072383349704638571804195261859
y[1] (numeric) = 2.7072383349704638571804195262308
absolute error = 4.49e-29
relative error = 1.6585167039048249094164783866451e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (closed_form) = 2.7180241450699477769301423131428
y[1] (numeric) = 2.7180241450699477769301423131878
absolute error = 4.50e-29
relative error = 1.6556144315944601187700289335345e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (closed_form) = 2.7288099551694316966798651000997
y[1] (numeric) = 2.7288099551694316966798651001448
absolute error = 4.51e-29
relative error = 1.6527351021482088837808636658241e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (closed_form) = 2.7395957652689156164295878870567
y[1] (numeric) = 2.7395957652689156164295878871018
absolute error = 4.51e-29
relative error = 1.6462282710373891637659783758011e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1198.4MB, alloc=40.3MB, time=14.23
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (closed_form) = 2.7503815753683995361793106740136
y[1] (numeric) = 2.7503815753683995361793106740588
absolute error = 4.52e-29
relative error = 1.6434083330399597853453714653186e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (closed_form) = 2.7611673854678834559290334609705
y[1] (numeric) = 2.7611673854678834559290334610158
absolute error = 4.53e-29
relative error = 1.6406104258081353239436755463244e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (closed_form) = 2.7719531955673673756787562479274
y[1] (numeric) = 2.7719531955673673756787562479728
absolute error = 4.54e-29
relative error = 1.6378342921734456832532768718359e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (closed_form) = 2.7827390056668512954284790348843
y[1] (numeric) = 2.7827390056668512954284790349298
absolute error = 4.55e-29
relative error = 1.6350796789545288304752068692426e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (closed_form) = 2.7935248157663352151782018218412
y[1] (numeric) = 2.7935248157663352151782018218868
absolute error = 4.56e-29
relative error = 1.6323463368801595981819096079822e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (closed_form) = 2.8043106258658191349279246087982
y[1] (numeric) = 2.8043106258658191349279246088438
absolute error = 4.56e-29
relative error = 1.6260680817383128304965945710283e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (closed_form) = 2.8150964359653030546776473957551
y[1] (numeric) = 2.8150964359653030546776473958008
absolute error = 4.57e-29
relative error = 1.6233902120063380597533555734488e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (closed_form) = 2.825882246064786974427370182712
y[1] (numeric) = 2.8258822460647869744273701827578
absolute error = 4.58e-29
relative error = 1.6207327840280424857333474079120e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (closed_form) = 2.8366680561642708941770929696689
y[1] (numeric) = 2.8366680561642708941770929697148
absolute error = 4.59e-29
relative error = 1.6180955646275286271051263767137e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (closed_form) = 2.8474538662637548139268157566258
y[1] (numeric) = 2.8474538662637548139268157566718
absolute error = 4.60e-29
relative error = 1.6154783241618671461937858078731e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (closed_form) = 2.8582396763632387336765385435827
y[1] (numeric) = 2.8582396763632387336765385436288
absolute error = 4.61e-29
relative error = 1.6128808364544370726855496961558e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (closed_form) = 2.8690254864627226534262613305397
y[1] (numeric) = 2.8690254864627226534262613305858
absolute error = 4.61e-29
relative error = 1.6068173746632549784273333439145e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (closed_form) = 2.8798112965622065731759841174966
y[1] (numeric) = 2.8798112965622065731759841175428
absolute error = 4.62e-29
relative error = 1.6042717818056880971092954520002e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (closed_form) = 2.8905971066616904929257069044535
y[1] (numeric) = 2.8905971066616904929257069044998
absolute error = 4.63e-29
relative error = 1.6017451859097448492339294846523e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (closed_form) = 2.9013829167611744126754296914104
y[1] (numeric) = 2.9013829167611744126754296914568
absolute error = 4.64e-29
relative error = 1.5992373751133996924208338962439e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (closed_form) = 2.9121687268606583324251524783673
y[1] (numeric) = 2.9121687268606583324251524784138
absolute error = 4.65e-29
relative error = 1.5967481406933237589915390158977e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (closed_form) = 2.9229545369601422521748752653242
y[1] (numeric) = 2.9229545369601422521748752653708
absolute error = 4.66e-29
relative error = 1.5942772770069753232259289686169e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (closed_form) = 2.9337403470596261719245980522812
y[1] (numeric) = 2.9337403470596261719245980523278
absolute error = 4.66e-29
relative error = 1.5884159634885673257140689356440e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (closed_form) = 2.9445261571591100916743208392381
y[1] (numeric) = 2.9445261571591100916743208392848
absolute error = 4.67e-29
relative error = 1.5859937221633084624935456655602e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (closed_form) = 2.955311967258594011424043626195
y[1] (numeric) = 2.9553119672585940114240436262418
absolute error = 4.68e-29
relative error = 1.5835891614316646274717123463530e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (closed_form) = 2.9660977773580779311737664131519
y[1] (numeric) = 2.9660977773580779311737664131988
absolute error = 4.69e-29
relative error = 1.5812020884144327476136741785582e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (closed_form) = 2.9768835874575618509234892001088
y[1] (numeric) = 2.9768835874575618509234892001558
absolute error = 4.70e-29
relative error = 1.5788323130277605190589551279213e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (closed_form) = 2.9876693975570457706732119870657
y[1] (numeric) = 2.9876693975570457706732119871128
absolute error = 4.71e-29
relative error = 1.5764796479326888120100463231374e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (closed_form) = 2.9984552076565296904229347740226
y[1] (numeric) = 2.9984552076565296904229347740698
absolute error = 4.72e-29
relative error = 1.5741439084857830884650865025606e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (closed_form) = 3.0092410177560136101726575609796
y[1] (numeric) = 3.0092410177560136101726575610268
absolute error = 4.72e-29
relative error = 1.5685018156238268766784732892897e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (closed_form) = 3.0200268278554975299223803479365
y[1] (numeric) = 3.0200268278554975299223803479838
absolute error = 4.73e-29
relative error = 1.5662112522883592723564473711236e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (closed_form) = 3.0308126379549814496721031348934
y[1] (numeric) = 3.0308126379549814496721031349408
absolute error = 4.74e-29
relative error = 1.5639369918947811171755034879623e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1241.1MB, alloc=40.3MB, time=14.75
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (closed_form) = 3.0415984480544653694218259218503
y[1] (numeric) = 3.0415984480544653694218259218978
absolute error = 4.75e-29
relative error = 1.5616788610075403957192471500716e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (closed_form) = 3.0523842581539492891715487088072
y[1] (numeric) = 3.0523842581539492891715487088548
absolute error = 4.76e-29
relative error = 1.5594366886424709867821162986677e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (closed_form) = 3.0631700682534332089212714957641
y[1] (numeric) = 3.0631700682534332089212714958118
absolute error = 4.77e-29
relative error = 1.5572103062236344610065145377667e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (closed_form) = 3.0739558783529171286709942827211
y[1] (numeric) = 3.0739558783529171286709942827688
absolute error = 4.77e-29
relative error = 1.5517464104123234628977197499149e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (closed_form) = 3.084741688452401048420717069678
y[1] (numeric) = 3.0847416884524010484207170697258
absolute error = 4.78e-29
relative error = 1.5495624861860317643089557514983e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (closed_form) = 3.0955274985518849681704398566349
y[1] (numeric) = 3.0955274985518849681704398566828
absolute error = 4.79e-29
relative error = 1.5473937809438954085675002130010e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (closed_form) = 3.1063133086513688879201626435918
y[1] (numeric) = 3.1063133086513688879201626436398
absolute error = 4.80e-29
relative error = 1.5452401361548294441853603379656e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (closed_form) = 3.1170991187508528076698854305487
y[1] (numeric) = 3.1170991187508528076698854305968
absolute error = 4.81e-29
relative error = 1.5431013954819507875152075900929e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (closed_form) = 3.1278849288503367274196082175056
y[1] (numeric) = 3.1278849288503367274196082175538
absolute error = 4.82e-29
relative error = 1.5409774047447471560634696887574e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (closed_form) = 3.1386707389498206471693310044626
y[1] (numeric) = 3.1386707389498206471693310045108
absolute error = 4.82e-29
relative error = 1.5356819497456243136027704802049e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (closed_form) = 3.1494565490493045669190537914195
y[1] (numeric) = 3.1494565490493045669190537914678
absolute error = 4.83e-29
relative error = 1.5335979159509231949483473491178e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (closed_form) = 3.1602423591487884866687765783764
y[1] (numeric) = 3.1602423591487884866687765784248
absolute error = 4.84e-29
relative error = 1.5315281076428753262506097001542e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (closed_form) = 3.1710281692482724064184993653333
y[1] (numeric) = 3.1710281692482724064184993653818
absolute error = 4.85e-29
relative error = 1.5294723796634536335304076814557e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (closed_form) = 3.1818139793477563261682221522902
y[1] (numeric) = 3.1818139793477563261682221523388
absolute error = 4.86e-29
relative error = 1.5274305888228754777100036425449e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (closed_form) = 3.1925997894472402459179449392471
y[1] (numeric) = 3.1925997894472402459179449392958
absolute error = 4.87e-29
relative error = 1.5254025938663552824018996309241e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (closed_form) = 3.2033855995467241656676677262041
y[1] (numeric) = 3.2033855995467241656676677262528
absolute error = 4.87e-29
relative error = 1.5202665581967715945823646153317e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (closed_form) = 3.214171409646208085417390513161
y[1] (numeric) = 3.2141714096462080854173905132098
absolute error = 4.88e-29
relative error = 1.5182762143158861116022600904574e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (closed_form) = 3.2249572197456920051671133001179
y[1] (numeric) = 3.2249572197456920051671133001668
absolute error = 4.89e-29
relative error = 1.5162991837719965181404171343113e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (closed_form) = 3.2357430298451759249168360870748
y[1] (numeric) = 3.2357430298451759249168360871238
absolute error = 4.90e-29
relative error = 1.5143353334317328553016531312062e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (closed_form) = 3.2465288399446598446665588740317
y[1] (numeric) = 3.2465288399446598446665588740808
absolute error = 4.91e-29
relative error = 1.5123845319309393829136450350985e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (closed_form) = 3.2573146500441437644162816609886
y[1] (numeric) = 3.2573146500441437644162816610378
absolute error = 4.92e-29
relative error = 1.5104466496453829533891336813491e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (closed_form) = 3.2681004601436276841660044479455
y[1] (numeric) = 3.2681004601436276841660044479948
absolute error = 4.93e-29
relative error = 1.5085215586620414177888765279545e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (closed_form) = 3.2788862702431116039157272349025
y[1] (numeric) = 3.2788862702431116039157272349518
absolute error = 4.93e-29
relative error = 1.5035593166927583868093078551651e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (closed_form) = 3.2896720803425955236654500218594
y[1] (numeric) = 3.2896720803425955236654500219088
absolute error = 4.94e-29
relative error = 1.5016694306763654008411173907311e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (closed_form) = 3.3004578904420794434151728088163
y[1] (numeric) = 3.3004578904420794434151728088658
absolute error = 4.95e-29
relative error = 1.4997918968561579899446144456724e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (closed_form) = 3.3112437005415633631648955957732
y[1] (numeric) = 3.3112437005415633631648955958228
absolute error = 4.96e-29
relative error = 1.4979265945266359693471115197998e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (closed_form) = 3.3220295106410472829146183827301
y[1] (numeric) = 3.3220295106410472829146183827798
absolute error = 4.97e-29
relative error = 1.4960734045499030527794625090303e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1283.8MB, alloc=40.3MB, time=15.25
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (closed_form) = 3.332815320740531202664341169687
y[1] (numeric) = 3.3328153207405312026643411697368
absolute error = 4.98e-29
relative error = 1.4942322093303010936006008704987e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (closed_form) = 3.343601130840015122414063956644
y[1] (numeric) = 3.3436011308400151224140639566938
absolute error = 4.98e-29
relative error = 1.4894121054292356062018892547874e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (closed_form) = 3.3543869409394990421637867436009
y[1] (numeric) = 3.3543869409394990421637867436508
absolute error = 4.99e-29
relative error = 1.4876041696615946481964530070318e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (closed_form) = 3.3651727510389829619135095305578
y[1] (numeric) = 3.3651727510389829619135095306078
absolute error = 5.00e-29
relative error = 1.4858078232257975424859234018899e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (closed_form) = 3.3759585611384668816632323175147
y[1] (numeric) = 3.3759585611384668816632323175648
absolute error = 5.01e-29
relative error = 1.4840229550419863607735441456628e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (closed_form) = 3.3867443712379508014129551044716
y[1] (numeric) = 3.3867443712379508014129551045218
absolute error = 5.02e-29
relative error = 1.4822494554453332120657023369275e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (closed_form) = 3.3975301813374347211626778914285
y[1] (numeric) = 3.3975301813374347211626778914788
absolute error = 5.03e-29
relative error = 1.4804872161635794484290214285651e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (closed_form) = 3.4083159914369186409124006783855
y[1] (numeric) = 3.4083159914369186409124006784358
absolute error = 5.03e-29
relative error = 1.4758021300364795134656384493607e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (closed_form) = 3.4191018015364025606621234653424
y[1] (numeric) = 3.4191018015364025606621234653928
absolute error = 5.04e-29
relative error = 1.4740713475495912426550566757122e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (closed_form) = 3.4298876116358864804118462522993
y[1] (numeric) = 3.4298876116358864804118462523498
absolute error = 5.05e-29
relative error = 1.4723514504871488100256735295709e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (closed_form) = 3.4406734217353704001615690392562
y[1] (numeric) = 3.4406734217353704001615690393068
absolute error = 5.06e-29
relative error = 1.4706423364783894020522739768224e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (closed_form) = 3.4514592318348543199112918262131
y[1] (numeric) = 3.4514592318348543199112918262638
absolute error = 5.07e-29
relative error = 1.4689439044321847403787081712785e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (closed_form) = 3.46224504193433823966101461317
y[1] (numeric) = 3.4622450419343382396610146132208
absolute error = 5.08e-29
relative error = 1.4672560545171090797124543022178e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (closed_form) = 3.473030852033822159410737400127
y[1] (numeric) = 3.4730308520338221594107374001778
absolute error = 5.08e-29
relative error = 1.4626993586956273744959559969313e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (closed_form) = 3.4838166621333060791604601870839
y[1] (numeric) = 3.4838166621333060791604601871348
absolute error = 5.09e-29
relative error = 1.4610412928225539079077679480330e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (closed_form) = 3.4946024722327899989101829740408
y[1] (numeric) = 3.4946024722327899989101829740918
absolute error = 5.10e-29
relative error = 1.4593934619240055861750625414119e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (closed_form) = 3.5053882823322739186599057609977
y[1] (numeric) = 3.5053882823322739186599057610488
absolute error = 5.11e-29
relative error = 1.4577557715232944848837891680623e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (closed_form) = 3.5161740924317578384096285479546
y[1] (numeric) = 3.5161740924317578384096285480058
absolute error = 5.12e-29
relative error = 1.4561281283029558443366340362669e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (closed_form) = 3.5269599025312417581593513349115
y[1] (numeric) = 3.5269599025312417581593513349628
absolute error = 5.13e-29
relative error = 1.4545104400870229447102566116997e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (closed_form) = 3.5377457126307256779090741218684
y[1] (numeric) = 3.5377457126307256779090741219198
absolute error = 5.14e-29
relative error = 1.4529026158236262213011131958188e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (closed_form) = 3.5485315227302095976587969088254
y[1] (numeric) = 3.5485315227302095976587969088768
absolute error = 5.14e-29
relative error = 1.4484864984503021294430551009987e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (closed_form) = 3.5593173328296935174085196957823
y[1] (numeric) = 3.5593173328296935174085196958338
absolute error = 5.15e-29
relative error = 1.4469066729449766613735646800950e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (closed_form) = 3.5701031429291774371582424827392
y[1] (numeric) = 3.5701031429291774371582424827908
absolute error = 5.16e-29
relative error = 1.4453363932130972686398415729128e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (closed_form) = 3.5808889530286613569079652696961
y[1] (numeric) = 3.5808889530286613569079652697478
absolute error = 5.17e-29
relative error = 1.4437755729976749806816228217979e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (closed_form) = 3.591674763128145276657688056653
y[1] (numeric) = 3.5916747631281452766576880567048
absolute error = 5.18e-29
relative error = 1.4422241270778408145730029821012e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (closed_form) = 3.6024605732276291964074108436099
y[1] (numeric) = 3.6024605732276291964074108436618
absolute error = 5.19e-29
relative error = 1.4406819712533349967644347582110e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (closed_form) = 3.6132463833271131161571336305669
y[1] (numeric) = 3.6132463833271131161571336306188
absolute error = 5.19e-29
relative error = 1.4363814280555638475203618186342e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1326.5MB, alloc=40.3MB, time=15.77
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (closed_form) = 3.6240321934265970359068564175238
y[1] (numeric) = 3.6240321934265970359068564175758
absolute error = 5.20e-29
relative error = 1.4348658407151987696006917423966e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (closed_form) = 3.6348180035260809556565792044807
y[1] (numeric) = 3.6348180035260809556565792045328
absolute error = 5.21e-29
relative error = 1.4333592479584560363571027942078e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (closed_form) = 3.6456038136255648754063019914376
y[1] (numeric) = 3.6456038136255648754063019914898
absolute error = 5.22e-29
relative error = 1.4318615699517532009433575676059e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (closed_form) = 3.6563896237250487951560247783945
y[1] (numeric) = 3.6563896237250487951560247784468
absolute error = 5.23e-29
relative error = 1.4303727278034969899273335517805e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (closed_form) = 3.6671754338245327149057475653514
y[1] (numeric) = 3.6671754338245327149057475654038
absolute error = 5.24e-29
relative error = 1.4288926435502305213290508536952e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (closed_form) = 3.6779612439240166346554703523084
y[1] (numeric) = 3.6779612439240166346554703523608
absolute error = 5.24e-29
relative error = 1.4247023425427518394483204992855e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (closed_form) = 3.6887470540235005544051931392653
y[1] (numeric) = 3.6887470540235005544051931393178
absolute error = 5.25e-29
relative error = 1.4232474938268165933286213639156e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (closed_form) = 3.6995328641229844741549159262222
y[1] (numeric) = 3.6995328641229844741549159262748
absolute error = 5.26e-29
relative error = 1.4218011281937730979151595412884e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (closed_form) = 3.7103186742224683939046387131791
y[1] (numeric) = 3.7103186742224683939046387132318
absolute error = 5.27e-29
relative error = 1.4203631716632472972424736594904e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (closed_form) = 3.721104484321952313654361500136
y[1] (numeric) = 3.7211044843219523136543615001888
absolute error = 5.28e-29
relative error = 1.4189335511126086026606439277319e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (closed_form) = 3.7318902944214362334040842870929
y[1] (numeric) = 3.7318902944214362334040842871458
absolute error = 5.29e-29
relative error = 1.4175121942645747560243739054054e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (closed_form) = 3.7426761045209201531538070740499
y[1] (numeric) = 3.7426761045209201531538070741028
absolute error = 5.29e-29
relative error = 1.4134271447133800160934679287327e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (closed_form) = 3.7534619146204040729035298610068
y[1] (numeric) = 3.7534619146204040729035298610598
absolute error = 5.30e-29
relative error = 1.4120297795897579403762775502099e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (closed_form) = 3.7642477247198879926532526479637
y[1] (numeric) = 3.7642477247198879926532526480168
absolute error = 5.31e-29
relative error = 1.4106404222891938708236555979250e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (closed_form) = 3.7750335348193719124029754349206
y[1] (numeric) = 3.7750335348193719124029754349738
absolute error = 5.32e-29
relative error = 1.4092590041732044530970486282246e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (closed_form) = 3.7858193449188558321526982218775
y[1] (numeric) = 3.7858193449188558321526982219308
absolute error = 5.33e-29
relative error = 1.4078854573855112713688838634797e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (closed_form) = 3.7966051550183397519024210088344
y[1] (numeric) = 3.7966051550183397519024210088878
absolute error = 5.34e-29
relative error = 1.4065197148409299827187200348982e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (closed_form) = 3.8073909651178236716521437957913
y[1] (numeric) = 3.8073909651178236716521437958448
absolute error = 5.35e-29
relative error = 1.4051617102144483047691237067619e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (closed_form) = 3.8181767752173075914018665827483
y[1] (numeric) = 3.8181767752173075914018665828018
absolute error = 5.35e-29
relative error = 1.4011923268522605976935047132399e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (closed_form) = 3.8289625853167915111515893697052
y[1] (numeric) = 3.8289625853167915111515893697588
absolute error = 5.36e-29
relative error = 1.3998569796827976035211602385626e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (closed_form) = 3.8397483954162754309013121566621
y[1] (numeric) = 3.8397483954162754309013121567158
absolute error = 5.37e-29
relative error = 1.3985291344637248508891098339677e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (closed_form) = 3.850534205515759350651034943619
y[1] (numeric) = 3.8505342055157593506510349436728
absolute error = 5.38e-29
relative error = 1.3972087281534424218012165744966e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (closed_form) = 3.8613200156152432704007577305759
y[1] (numeric) = 3.8613200156152432704007577306298
absolute error = 5.39e-29
relative error = 1.3958956984147258163395126628437e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (closed_form) = 3.8721058257147271901504805175328
y[1] (numeric) = 3.8721058257147271901504805175868
absolute error = 5.40e-29
relative error = 1.3945899836049157100725814749327e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (closed_form) = 3.8828916358142111099002033044898
y[1] (numeric) = 3.8828916358142111099002033045438
absolute error = 5.40e-29
relative error = 1.3907161225393464997668243041690e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (closed_form) = 3.8936774459136950296499260914467
y[1] (numeric) = 3.8936774459136950296499260915008
absolute error = 5.41e-29
relative error = 1.3894319894622095223893849465474e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (closed_form) = 3.9044632560131789493996488784036
y[1] (numeric) = 3.9044632560131789493996488784578
absolute error = 5.42e-29
relative error = 1.3881549510429572796935889002939e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1369.3MB, alloc=40.3MB, time=16.27
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (closed_form) = 3.9152490661126628691493716653605
y[1] (numeric) = 3.9152490661126628691493716654148
absolute error = 5.43e-29
relative error = 1.3868849486480535342027283694468e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (closed_form) = 3.9260348762121467888990944523174
y[1] (numeric) = 3.9260348762121467888990944523718
absolute error = 5.44e-29
relative error = 1.3856219242882866224783011382197e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (closed_form) = 3.9368206863116307086488172392743
y[1] (numeric) = 3.9368206863116307086488172393288
absolute error = 5.45e-29
relative error = 1.3843658206099430910920899466157e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (closed_form) = 3.9476064964111146283985400262313
y[1] (numeric) = 3.9476064964111146283985400262858
absolute error = 5.45e-29
relative error = 1.3805834003350525361983957117889e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (closed_form) = 3.9583923065105985481482628131882
y[1] (numeric) = 3.9583923065105985481482628132428
absolute error = 5.46e-29
relative error = 1.3793478708564635583518366395572e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (closed_form) = 3.9691781166100824678979856001451
y[1] (numeric) = 3.9691781166100824678979856001998
absolute error = 5.47e-29
relative error = 1.3781190562119973466892262579356e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (closed_form) = 3.979963926709566387647708387102
y[1] (numeric) = 3.9799639267095663876477083871568
absolute error = 5.48e-29
relative error = 1.3768969018095065616480934393579e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (closed_form) = 3.9907497368090503073974311740589
y[1] (numeric) = 3.9907497368090503073974311741138
absolute error = 5.49e-29
relative error = 1.3756813536470292403098856630428e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (closed_form) = 4.0015355469085342271471539610158
y[1] (numeric) = 4.0015355469085342271471539610708
absolute error = 5.50e-29
relative error = 1.3744723583048348155826655297268e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (closed_form) = 4.0123213570080181468968767479728
y[1] (numeric) = 4.0123213570080181468968767480278
absolute error = 5.50e-29
relative error = 1.3707775401373487004870132030339e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (closed_form) = 4.0231071671075020666465995349297
y[1] (numeric) = 4.0231071671075020666465995349848
absolute error = 5.51e-29
relative error = 1.3695881742970150516023595917732e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (closed_form) = 4.0338929772069859863963223218866
y[1] (numeric) = 4.0338929772069859863963223219418
absolute error = 5.52e-29
relative error = 1.3684051687018168767759126843160e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (closed_form) = 4.0446787873064699061460451088435
y[1] (numeric) = 4.0446787873064699061460451088988
absolute error = 5.53e-29
relative error = 1.3672284724697930922152068270319e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (closed_form) = 4.0554645974059538258957678958004
y[1] (numeric) = 4.0554645974059538258957678958558
absolute error = 5.54e-29
relative error = 1.3660580352602800724659940860100e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (closed_form) = 4.0662504075054377456454906827573
y[1] (numeric) = 4.0662504075054377456454906828128
absolute error = 5.55e-29
relative error = 1.3648938072667326390284482560810e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (closed_form) = 4.0770362176049216653952134697142
y[1] (numeric) = 4.0770362176049216653952134697698
absolute error = 5.56e-29
relative error = 1.3637357392096590015350164252522e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (closed_form) = 4.0878220277044055851449362566712
y[1] (numeric) = 4.0878220277044055851449362567268
absolute error = 5.56e-29
relative error = 1.3601374918766519856998316853438e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (closed_form) = 4.0986078378038895048946590436281
y[1] (numeric) = 4.0986078378038895048946590436838
absolute error = 5.57e-29
relative error = 1.3589980355340631585440721709160e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (closed_form) = 4.109393647903373424644381830585
y[1] (numeric) = 4.1093936479033734246443818306408
absolute error = 5.58e-29
relative error = 1.3578645605895981572526473521020e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (closed_form) = 4.1201794580028573443941046175419
y[1] (numeric) = 4.1201794580028573443941046175978
absolute error = 5.59e-29
relative error = 1.3567370200689261664391881082556e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (closed_form) = 4.1309652681023412641438274044988
y[1] (numeric) = 4.1309652681023412641438274045548
absolute error = 5.60e-29
relative error = 1.3556153674883099040372873983197e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (closed_form) = 4.1417510782018251838935501914557
y[1] (numeric) = 4.1417510782018251838935501915118
absolute error = 5.61e-29
relative error = 1.3544995568482176846687299212479e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (closed_form) = 4.1525368883013091036432729784127
y[1] (numeric) = 4.1525368883013091036432729784688
absolute error = 5.61e-29
relative error = 1.3509813761810794569163436097642e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (closed_form) = 4.1633226984007930233929957653696
y[1] (numeric) = 4.1633226984007930233929957654258
absolute error = 5.62e-29
relative error = 1.3498833521020945299981956113005e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (closed_form) = 4.1741085085002769431427185523265
y[1] (numeric) = 4.1741085085002769431427185523828
absolute error = 5.63e-29
relative error = 1.3487910025661534528315625895730e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (closed_form) = 4.1848943185997608628924413392834
y[1] (numeric) = 4.1848943185997608628924413393398
absolute error = 5.64e-29
relative error = 1.3477042836979234121451699442462e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (closed_form) = 4.1956801286992447826421641262403
y[1] (numeric) = 4.1956801286992447826421641262968
absolute error = 5.65e-29
relative error = 1.3466231520732318292515093947823e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1412.0MB, alloc=40.3MB, time=16.78
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (closed_form) = 4.2064659387987287023918869131972
y[1] (numeric) = 4.2064659387987287023918869132538
absolute error = 5.66e-29
relative error = 1.3455475647132822544752522327516e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (closed_form) = 4.2172517488982126221416097001542
y[1] (numeric) = 4.2172517488982126221416097002108
absolute error = 5.66e-29
relative error = 1.3421062665938109443615047845859e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (closed_form) = 4.2280375589976965418913324871111
y[1] (numeric) = 4.2280375589976965418913324871678
absolute error = 5.67e-29
relative error = 1.3410476895915126962037234361629e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (closed_form) = 4.238823369097180461641055274068
y[1] (numeric) = 4.2388233690971804616410552741248
absolute error = 5.68e-29
relative error = 1.3399944997495314874767704915487e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (closed_form) = 4.2496091791966643813907780610249
y[1] (numeric) = 4.2496091791966643813907780610818
absolute error = 5.69e-29
relative error = 1.3389466560488801326012233994453e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (closed_form) = 4.2603949892961483011405008479818
y[1] (numeric) = 4.2603949892961483011405008480388
absolute error = 5.70e-29
relative error = 1.3379041178859535947123879381879e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (closed_form) = 4.2711807993956322208902236349387
y[1] (numeric) = 4.2711807993956322208902236349958
absolute error = 5.71e-29
relative error = 1.3368668450672842615603647772399e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (closed_form) = 4.2819666094951161406399464218957
y[1] (numeric) = 4.2819666094951161406399464219528
absolute error = 5.71e-29
relative error = 1.3334994222837394649317492488337e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (closed_form) = 4.2927524195946000603896692088526
y[1] (numeric) = 4.2927524195946000603896692089098
absolute error = 5.72e-29
relative error = 1.3324784289656720232271750452004e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (closed_form) = 4.3035382296940839801393919958095
y[1] (numeric) = 4.3035382296940839801393919958668
absolute error = 5.73e-29
relative error = 1.3314625534085974007792653739162e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (closed_form) = 4.3143240397935678998891147827664
y[1] (numeric) = 4.3143240397935678998891147828238
absolute error = 5.74e-29
relative error = 1.3304517572293081514435952509883e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (closed_form) = 4.3251098498930518196388375697233
y[1] (numeric) = 4.3251098498930518196388375697808
absolute error = 5.75e-29
relative error = 1.3294460024274717163190756024891e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (closed_form) = 4.3358956599925357393885603566802
y[1] (numeric) = 4.3358956599925357393885603567378
absolute error = 5.76e-29
relative error = 1.3284452513808682982847276935346e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (closed_form) = 4.3466814700920196591382831436371
y[1] (numeric) = 4.3466814700920196591382831436948
absolute error = 5.77e-29
relative error = 1.3274494668406996366674236947982e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (closed_form) = 4.3574672801915035788880059305941
y[1] (numeric) = 4.3574672801915035788880059306518
absolute error = 5.77e-29
relative error = 1.3241637008336682019231973985239e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (closed_form) = 4.368253090290987498637728717551
y[1] (numeric) = 4.3682530902909874986377287176088
absolute error = 5.78e-29
relative error = 1.3231834054777650647987233708801e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (closed_form) = 4.3790389003904714183874515045079
y[1] (numeric) = 4.3790389003904714183874515045658
absolute error = 5.79e-29
relative error = 1.3222079391630240120935817276089e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (closed_form) = 4.3898247104899553381371742914648
y[1] (numeric) = 4.3898247104899553381371742915228
absolute error = 5.80e-29
relative error = 1.3212372662945470431855169474497e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (closed_form) = 4.4006105205894392578868970784217
y[1] (numeric) = 4.4006105205894392578868970784798
absolute error = 5.81e-29
relative error = 1.3202713516264057456936681711147e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (closed_form) = 4.4113963306889231776366198653786
y[1] (numeric) = 4.4113963306889231776366198654368
absolute error = 5.82e-29
relative error = 1.3193101602573751635929775795051e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (closed_form) = 4.4221821407884070973863426523356
y[1] (numeric) = 4.4221821407884070973863426523938
absolute error = 5.82e-29
relative error = 1.3160923305982108339256776341892e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (closed_form) = 4.4329679508878910171360654392925
y[1] (numeric) = 4.4329679508878910171360654393508
absolute error = 5.83e-29
relative error = 1.3151459844938183444672482876407e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (closed_form) = 4.4437537609873749368857882262494
y[1] (numeric) = 4.4437537609873749368857882263078
absolute error = 5.84e-29
relative error = 1.3142042323025539738896851029688e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (closed_form) = 4.4545395710868588566355110132063
y[1] (numeric) = 4.4545395710868588566355110132648
absolute error = 5.85e-29
relative error = 1.3132670406545887043802941371087e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (closed_form) = 4.4653253811863427763852338001632
y[1] (numeric) = 4.4653253811863427763852338002218
absolute error = 5.86e-29
relative error = 1.3123343765025073250617697942722e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (closed_form) = 4.4761111912858266961349565871201
y[1] (numeric) = 4.4761111912858266961349565871788
absolute error = 5.87e-29
relative error = 1.3114062071174239282941780988710e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (closed_form) = 4.4868970013853106158846793740771
y[1] (numeric) = 4.4868970013853106158846793741358
absolute error = 5.87e-29
relative error = 1.3082537883503147361588555553641e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1454.7MB, alloc=40.3MB, time=17.28
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (closed_form) = 4.497682811484794535634402161034
y[1] (numeric) = 4.4976828114847945356344021610928
absolute error = 5.88e-29
relative error = 1.3073398562000571412676142139910e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (closed_form) = 4.5084686215842784553841249479909
y[1] (numeric) = 4.5084686215842784553841249480498
absolute error = 5.89e-29
relative error = 1.3064302969309012573567137402800e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (closed_form) = 4.5192544316837623751338477349478
y[1] (numeric) = 4.5192544316837623751338477350068
absolute error = 5.90e-29
relative error = 1.3055250792334358549919273499757e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (closed_form) = 4.5300402417832462948835705219047
y[1] (numeric) = 4.5300402417832462948835705219638
absolute error = 5.91e-29
relative error = 1.3046241720964345735907827996252e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (closed_form) = 4.5408260518827302146332933088616
y[1] (numeric) = 4.5408260518827302146332933089208
absolute error = 5.92e-29
relative error = 1.3037275448033145334314489122218e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (closed_form) = 4.5516118619822141343830160958186
y[1] (numeric) = 4.5516118619822141343830160958778
absolute error = 5.92e-29
relative error = 1.3006381430383777691342179906288e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (closed_form) = 4.5623976720816980541327388827755
y[1] (numeric) = 4.5623976720816980541327388828348
absolute error = 5.93e-29
relative error = 1.2997551783543459012793172771824e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (closed_form) = 4.5731834821811819738824616697324
y[1] (numeric) = 4.5731834821811819738824616697918
absolute error = 5.94e-29
relative error = 1.2988763785980689007256189255918e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (closed_form) = 4.5839692922806658936321844566893
y[1] (numeric) = 4.5839692922806658936321844567488
absolute error = 5.95e-29
relative error = 1.2980017143700567331157026838911e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (closed_form) = 4.5947551023801498133819072436462
y[1] (numeric) = 4.5947551023801498133819072437058
absolute error = 5.96e-29
relative error = 1.2971311565468709137105278329964e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (closed_form) = 4.6055409124796337331316300306031
y[1] (numeric) = 4.6055409124796337331316300306628
absolute error = 5.97e-29
relative error = 1.2962646762778920536468292109116e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (closed_form) = 4.61632672257911765288135281756
y[1] (numeric) = 4.6163267225791176528813528176198
absolute error = 5.98e-29
relative error = 1.2954022449821327209666058160328e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (closed_form) = 4.627112532678601572631075604517
y[1] (numeric) = 4.6271125326786015726310756045768
absolute error = 5.98e-29
relative error = 1.2923826593294937169550286462984e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (closed_form) = 4.6378983427780854923807983914739
y[1] (numeric) = 4.6378983427780854923807983915338
absolute error = 5.99e-29
relative error = 1.2915332672884783773028337336391e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (closed_form) = 4.6486841528775694121305211784308
y[1] (numeric) = 4.6486841528775694121305211784908
absolute error = 6.00e-29
relative error = 1.2906878167418529000156142034051e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (closed_form) = 4.6594699629770533318802439653877
y[1] (numeric) = 4.6594699629770533318802439654478
absolute error = 6.01e-29
relative error = 1.2898462803181284666047243932185e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (closed_form) = 4.6702557730765372516299667523446
y[1] (numeric) = 4.6702557730765372516299667524048
absolute error = 6.02e-29
relative error = 1.2890086308986706587523144435870e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (closed_form) = 4.6810415831760211713796895393015
y[1] (numeric) = 4.6810415831760211713796895393618
absolute error = 6.03e-29
relative error = 1.2881748416147863891849386411888e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (closed_form) = 4.6918273932755050911294123262585
y[1] (numeric) = 4.6918273932755050911294123263188
absolute error = 6.03e-29
relative error = 1.2852135201398098687500307362665e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (closed_form) = 4.7026132033749890108791351132154
y[1] (numeric) = 4.7026132033749890108791351132758
absolute error = 6.04e-29
relative error = 1.2843922599598857581944371249512e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (closed_form) = 4.7133990134744729306288579001723
y[1] (numeric) = 4.7133990134744729306288579002328
absolute error = 6.05e-29
relative error = 1.2835747584077873872752535530469e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (closed_form) = 4.7241848235739568503785806871292
y[1] (numeric) = 4.7241848235739568503785806871898
absolute error = 6.06e-29
relative error = 1.2827609897394885522963402257632e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (closed_form) = 4.7349706336734407701283034740861
y[1] (numeric) = 4.7349706336734407701283034741468
absolute error = 6.07e-29
relative error = 1.2819509284455327644016132917701e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (closed_form) = 4.745756443772924689878026261043
y[1] (numeric) = 4.7457564437729246898780262611038
absolute error = 6.08e-29
relative error = 1.2811445492483676846336805711133e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (closed_form) = 4.756542253872408609627749048
y[1] (numeric) = 4.7565422538724086096277490480608
absolute error = 6.08e-29
relative error = 1.2782394595675323837614953543987e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (closed_form) = 4.7673280639718925293774718349569
y[1] (numeric) = 4.7673280639718925293774718350178
absolute error = 6.09e-29
relative error = 1.2774451261334268753514268495308e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (closed_form) = 4.7781138740713764491271946219138
y[1] (numeric) = 4.7781138740713764491271946219748
absolute error = 6.10e-29
relative error = 1.2766543788547800825549478187255e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1497.4MB, alloc=40.3MB, time=17.78
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (closed_form) = 4.7888996841708603688769174088707
y[1] (numeric) = 4.7888996841708603688769174089318
absolute error = 6.11e-29
relative error = 1.2758671935008118789152096844553e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (closed_form) = 4.7996854942703442886266401958276
y[1] (numeric) = 4.7996854942703442886266401958888
absolute error = 6.12e-29
relative error = 1.2750835460585469031569984631482e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (closed_form) = 4.8104713043698282083763629827845
y[1] (numeric) = 4.8104713043698282083763629828458
absolute error = 6.13e-29
relative error = 1.2743034127303728017295415522505e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (closed_form) = 4.8212571144693121281260857697415
y[1] (numeric) = 4.8212571144693121281260857698028
absolute error = 6.13e-29
relative error = 1.2714526220978663748800347478830e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (closed_form) = 4.8320429245687960478758085566984
y[1] (numeric) = 4.8320429245687960478758085567598
absolute error = 6.14e-29
relative error = 1.2706840762487481411559972064877e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (closed_form) = 4.8428287346682799676255313436553
y[1] (numeric) = 4.8428287346682799676255313437168
absolute error = 6.15e-29
relative error = 1.2699189537664411245086814358781e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (closed_form) = 4.8536145447677638873752541306122
y[1] (numeric) = 4.8536145447677638873752541306738
absolute error = 6.16e-29
relative error = 1.2691572318284999168242426242490e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (closed_form) = 4.8644003548672478071249769175691
y[1] (numeric) = 4.8644003548672478071249769176308
absolute error = 6.17e-29
relative error = 1.2683988878148954772448345834032e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (closed_form) = 4.875186164966731726874699704526
y[1] (numeric) = 4.8751861649667317268746997045878
absolute error = 6.18e-29
relative error = 1.2676438993057760130617956046850e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (closed_form) = 4.8859719750662156466244224914829
y[1] (numeric) = 4.8859719750662156466244224915448
absolute error = 6.19e-29
relative error = 1.2668922440792575178155470850340e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (closed_form) = 4.8967577851656995663741452784399
y[1] (numeric) = 4.8967577851656995663741452785018
absolute error = 6.19e-29
relative error = 1.2641017325284221488335745143621e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (closed_form) = 4.9075435952651834861238680653968
y[1] (numeric) = 4.9075435952651834861238680654588
absolute error = 6.20e-29
relative error = 1.2633611662628495675537451554356e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (closed_form) = 4.9183294053646674058735908523537
y[1] (numeric) = 4.9183294053646674058735908524158
absolute error = 6.21e-29
relative error = 1.2626238480949330063672483814166e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (closed_form) = 4.9291152154641513256233136393106
y[1] (numeric) = 4.9291152154641513256233136393728
absolute error = 6.22e-29
relative error = 1.2618897567023683776148281797128e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (closed_form) = 4.9399010255636352453730364262675
y[1] (numeric) = 4.9399010255636352453730364263298
absolute error = 6.23e-29
relative error = 1.2611588709490725900359993326016e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (closed_form) = 4.9506868356631191651227592132244
y[1] (numeric) = 4.9506868356631191651227592132868
absolute error = 6.24e-29
relative error = 1.2604311698831549976100194129288e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (closed_form) = 4.9614726457626030848724820001814
y[1] (numeric) = 4.9614726457626030848724820002438
absolute error = 6.24e-29
relative error = 1.2576911021225394432673889359441e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (closed_form) = 4.9722584558620870046222047871383
y[1] (numeric) = 4.9722584558620870046222047872008
absolute error = 6.25e-29
relative error = 1.2569740803862495478731239191694e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (closed_form) = 4.9830442659615709243719275740952
y[1] (numeric) = 4.9830442659615709243719275741578
absolute error = 6.26e-29
relative error = 1.2562601626401600416364098332032e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (closed_form) = 4.9938300760610548441216503610521
y[1] (numeric) = 4.9938300760610548441216503611148
absolute error = 6.27e-29
relative error = 1.2555493287720234058370033674787e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (closed_form) = 5.004615886160538763871373148009
y[1] (numeric) = 5.0046158861605387638713731480718
absolute error = 6.28e-29
relative error = 1.2548415588429735658815598606582e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (closed_form) = 5.0154016962600226836210959349659
y[1] (numeric) = 5.0154016962600226836210959350288
absolute error = 6.29e-29
relative error = 1.2541368330856615747001182613940e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (closed_form) = 5.0261875063595066033708187219229
y[1] (numeric) = 5.0261875063595066033708187219858
absolute error = 6.29e-29
relative error = 1.2514455523279670219647102822923e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (closed_form) = 5.0369733164589905231205415088798
y[1] (numeric) = 5.0369733164589905231205415089428
absolute error = 6.30e-29
relative error = 1.2507511166306756528952167189528e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (closed_form) = 5.0477591265584744428702642958367
y[1] (numeric) = 5.0477591265584744428702642958998
absolute error = 6.31e-29
relative error = 1.2500596486073043324114902221234e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (closed_form) = 5.0585449366579583626199870827936
y[1] (numeric) = 5.0585449366579583626199870828568
absolute error = 6.32e-29
relative error = 1.2493711292748642329106367593956e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (closed_form) = 5.0693307467574422823697098697505
y[1] (numeric) = 5.0693307467574422823697098698138
absolute error = 6.33e-29
relative error = 1.2486855398119238785140422475730e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1540.1MB, alloc=40.3MB, time=18.30
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (closed_form) = 5.0801165568569262021194326567074
y[1] (numeric) = 5.0801165568569262021194326567708
absolute error = 6.34e-29
relative error = 1.2480028615568940988707241455671e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (closed_form) = 5.0909023669564101218691554436644
y[1] (numeric) = 5.0909023669564101218691554437278
absolute error = 6.34e-29
relative error = 1.2453587876976633910341336283095e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (closed_form) = 5.1016881770558940416188782306213
y[1] (numeric) = 5.1016881770558940416188782306848
absolute error = 6.35e-29
relative error = 1.2446860293340169518702373969659e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (closed_form) = 5.1124739871553779613686010175782
y[1] (numeric) = 5.1124739871553779613686010176418
absolute error = 6.36e-29
relative error = 1.2440161096132550968378343986659e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (closed_form) = 5.1232597972548618811183238045351
y[1] (numeric) = 5.1232597972548618811183238045988
absolute error = 6.37e-29
relative error = 1.2433490106071069759318836235167e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (closed_form) = 5.134045607354345800868046591492
y[1] (numeric) = 5.1340456073543458008680465915558
absolute error = 6.38e-29
relative error = 1.2426847145379594773826805407000e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (closed_form) = 5.1448314174538297206177693784489
y[1] (numeric) = 5.1448314174538297206177693785128
absolute error = 6.39e-29
relative error = 1.2420232037772780060810632150440e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (closed_form) = 5.1556172275533136403674921654058
y[1] (numeric) = 5.1556172275533136403674921654698
absolute error = 6.40e-29
relative error = 1.2413644608440470848685739953531e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (closed_form) = 5.1664030376527975601172149523628
y[1] (numeric) = 5.1664030376527975601172149524268
absolute error = 6.40e-29
relative error = 1.2387728857692160888667606884734e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (closed_form) = 5.1771888477522814798669377393197
y[1] (numeric) = 5.1771888477522814798669377393838
absolute error = 6.41e-29
relative error = 1.2381236590940570921535199707949e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (closed_form) = 5.1879746578517653996166605262766
y[1] (numeric) = 5.1879746578517653996166605263408
absolute error = 6.42e-29
relative error = 1.2374771319061128937634112311525e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (closed_form) = 5.1987604679512493193663833132335
y[1] (numeric) = 5.1987604679512493193663833132978
absolute error = 6.43e-29
relative error = 1.2368332874035958497234689178156e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (closed_form) = 5.2095462780507332391161061001904
y[1] (numeric) = 5.2095462780507332391161061002548
absolute error = 6.44e-29
relative error = 1.2361921089238635553482882703724e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (closed_form) = 5.2203320881502171588658288871473
y[1] (numeric) = 5.2203320881502171588658288872118
absolute error = 6.45e-29
relative error = 1.2355535799419813944209389479187e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (closed_form) = 5.2311178982497010786155516741043
y[1] (numeric) = 5.2311178982497010786155516741688
absolute error = 6.45e-29
relative error = 1.2330060467874618451540916511189e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (closed_form) = 5.2419037083491849983652744610612
y[1] (numeric) = 5.2419037083491849983652744611258
absolute error = 6.46e-29
relative error = 1.2323767011802713838811639238589e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (closed_form) = 5.2526895184486689181149972480181
y[1] (numeric) = 5.2526895184486689181149972480828
absolute error = 6.47e-29
relative error = 1.2317499401546299594101784049245e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (closed_form) = 5.263475328548152837864720034975
y[1] (numeric) = 5.2634753285481528378647200350398
absolute error = 6.48e-29
relative error = 1.2311257478217165735640739741824e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (closed_form) = 5.2742611386476367576144428219319
y[1] (numeric) = 5.2742611386476367576144428219968
absolute error = 6.49e-29
relative error = 1.2305041084226801340813482936683e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (closed_form) = 5.2850469487471206773641656088888
y[1] (numeric) = 5.2850469487471206773641656089538
absolute error = 6.50e-29
relative error = 1.2298850063273132310863072077685e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (closed_form) = 5.2958327588466045971138883958458
y[1] (numeric) = 5.2958327588466045971138883959108
absolute error = 6.50e-29
relative error = 1.2273801488806180921227913071417e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (closed_form) = 5.3066185689460885168636111828027
y[1] (numeric) = 5.3066185689460885168636111828678
absolute error = 6.51e-29
relative error = 1.2267699129716999611764263170922e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (closed_form) = 5.3174043790455724366133339697596
y[1] (numeric) = 5.3174043790455724366133339698248
absolute error = 6.52e-29
relative error = 1.2261621526648464068261926251767e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (closed_form) = 5.3281901891450563563630567567165
y[1] (numeric) = 5.3281901891450563563630567567818
absolute error = 6.53e-29
relative error = 1.2255568529260367939915469239168e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (closed_form) = 5.3389759992445402761127795436734
y[1] (numeric) = 5.3389759992445402761127795437388
absolute error = 6.54e-29
relative error = 1.2249539988427375230269401951872e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (closed_form) = 5.3497618093440241958625023306303
y[1] (numeric) = 5.3497618093440241958625023306958
absolute error = 6.55e-29
relative error = 1.2243535756226773620259004290735e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (closed_form) = 5.3605476194435081156122251175873
y[1] (numeric) = 5.3605476194435081156122251176528
absolute error = 6.55e-29
relative error = 1.2218900875429536651204157199607e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1582.8MB, alloc=40.3MB, time=18.80
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (closed_form) = 5.3713334295429920353619479045442
y[1] (numeric) = 5.3713334295429920353619479046098
absolute error = 6.56e-29
relative error = 1.2212982280934555607055378092836e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (closed_form) = 5.3821192396424759551116706915011
y[1] (numeric) = 5.3821192396424759551116706915668
absolute error = 6.57e-29
relative error = 1.2207087408261197733424229363247e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = sin ( 0.1 ) + cos ( 0.05 ) - tan ( 0.02 ) ;
Iterations = 10000
Total Elapsed Time = 18 Seconds
Elapsed Time(since restart) = 18 Seconds
Time to Timeout = 2 Minutes 41 Seconds
Percent Done = 100 %
> quit
memory used=1586.3MB, alloc=40.3MB, time=18.84