|\^/| 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(5.0)/c(3.0) * expt((c(0.2) * c(x) + c(0.3)),c(3.0))) ;
> end;
exact_soln_y :=
proc(x) return c(5.0)*expt(c(0.2)*c(x) + c(0.3), c(3.0))/c(3.0) 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_0D2,
> array_const_0D3,
> array_const_2D0,
#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,
> array_tmp2,
> array_tmp3_c1,
> array_tmp3_a1,
> array_tmp3_a2,
> array_tmp3,
> array_tmp4,
> 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_0D2,
array_const_0D3, array_const_2D0, 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, array_tmp2, array_tmp3_c1, array_tmp3_a1, array_tmp3_a2,
array_tmp3, array_tmp4, 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_0D2,
> array_const_0D3,
> array_const_2D0,
#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,
> array_tmp2,
> array_tmp3_c1,
> array_tmp3_a1,
> array_tmp3_a2,
> array_tmp3,
> array_tmp4,
> 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_0D2,
array_const_0D3, array_const_2D0, 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, array_tmp2, array_tmp3_c1, array_tmp3_a1, array_tmp3_a2,
array_tmp3, array_tmp4, 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_0D2,
> array_const_0D3,
> array_const_2D0,
#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,
> array_tmp2,
> array_tmp3_c1,
> array_tmp3_a1,
> array_tmp3_a2,
> array_tmp3,
> array_tmp4,
> 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_0D2,
array_const_0D3, array_const_2D0, 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, array_tmp2, array_tmp3_c1, array_tmp3_a1, array_tmp3_a2,
array_tmp3, array_tmp4, 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_0D2,
> array_const_0D3,
> array_const_2D0,
#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,
> array_tmp2,
> array_tmp3_c1,
> array_tmp3_a1,
> array_tmp3_a2,
> array_tmp3,
> array_tmp4,
> 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_0D2,
array_const_0D3, array_const_2D0, 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, array_tmp2, array_tmp3_c1, array_tmp3_a1, array_tmp3_a2,
array_tmp3, array_tmp4, 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_0D2,
> array_const_0D3,
> array_const_2D0,
#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,
> array_tmp2,
> array_tmp3_c1,
> array_tmp3_a1,
> array_tmp3_a2,
> array_tmp3,
> array_tmp4,
> 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)*25*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_0D2,
array_const_0D3, array_const_2D0, 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, array_tmp2, array_tmp3_c1, array_tmp3_a1, array_tmp3_a2,
array_tmp3, array_tmp4, 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)*25*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_0D2,
> array_const_0D3,
> array_const_2D0,
#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,
> array_tmp2,
> array_tmp3_c1,
> array_tmp3_a1,
> array_tmp3_a2,
> array_tmp3,
> array_tmp4,
> 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_0D2,
array_const_0D3, array_const_2D0, 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, array_tmp2, array_tmp3_c1, array_tmp3_a1, array_tmp3_a2,
array_tmp3, array_tmp4, 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_0D2,
> array_const_0D3,
> array_const_2D0,
#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,
> array_tmp2,
> array_tmp3_c1,
> array_tmp3_a1,
> array_tmp3_a2,
> array_tmp3,
> array_tmp4,
> 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_0D2,
array_const_0D3, array_const_2D0, 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, array_tmp2, array_tmp3_c1, array_tmp3_a1, array_tmp3_a2,
array_tmp3, array_tmp4, 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_0D2,
> array_const_0D3,
> array_const_2D0,
#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,
> array_tmp2,
> array_tmp3_c1,
> array_tmp3_a1,
> array_tmp3_a2,
> array_tmp3,
> array_tmp4,
> 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 mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D2[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D3[1];
> #emit pre expt LINEAR - CONST $eq_no = 1 iii = 1
> array_tmp3[1] := expt(array_tmp2[1] , c(array_const_2D0[1]));
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp4[1] := array_const_0D0[1] + array_tmp3[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_tmp4[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 mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D2[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre expt LINEAR - CONST $eq_no = 1 i = 2
> array_tmp3[2] := (array_const_2D0[1] - c(0)) * array_tmp2[2] * array_tmp3[1] / array_tmp2[1] / c(1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[2];
> #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_tmp4[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 expt LINEAR - CONST $eq_no = 1 i = 3
> array_tmp3[3] := (array_const_2D0[1] - c(1)) * array_tmp2[2] * array_tmp3[2] / array_tmp2[1] / c(2);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp3[3];
> #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_tmp4[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 expt LINEAR - CONST $eq_no = 1 i = 4
> array_tmp3[4] := (array_const_2D0[1] - c(2)) * array_tmp2[2] * array_tmp3[3] / array_tmp2[1] / c(3);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp3[4];
> #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_tmp4[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 expt LINEAR - CONST $eq_no = 1 i = 5
> array_tmp3[5] := (array_const_2D0[1] - c(3)) * array_tmp2[2] * array_tmp3[4] / array_tmp2[1] / c(4);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp3[5];
> #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_tmp4[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 (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit expt LINEAR CONST (NOP) $eq_no = 1 i = 1
> array_tmp3[kkk] := (array_const_2D0[1] - c(kkk-2)) * array_tmp2[2] * array_tmp3[kkk-1] / array_tmp2[1] / c(kkk-1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp4[kkk] := array_tmp3[kkk];
> #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_tmp4[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_0D2,
array_const_0D3, array_const_2D0, 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, array_tmp2, array_tmp3_c1, array_tmp3_a1, array_tmp3_a2,
array_tmp3, array_tmp4, 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] := array_const_0D2[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D3[1];
array_tmp3[1] := expt(array_tmp2[1], c(array_const_2D0[1]));
array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[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;
array_tmp1[2] := array_const_0D2[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := (array_const_2D0[1] - c(0))*array_tmp2[2]*
array_tmp3[1]/(array_tmp2[1]*c(1));
array_tmp4[2] := array_tmp3[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[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;
array_tmp3[3] := (array_const_2D0[1] - c(1))*array_tmp2[2]*
array_tmp3[2]/(array_tmp2[1]*c(2));
array_tmp4[3] := array_tmp3[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[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;
array_tmp3[4] := (array_const_2D0[1] - c(2))*array_tmp2[2]*
array_tmp3[3]/(array_tmp2[1]*c(3));
array_tmp4[4] := array_tmp3[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[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;
array_tmp3[5] := (array_const_2D0[1] - c(3))*array_tmp2[2]*
array_tmp3[4]/(array_tmp2[1]*c(4));
array_tmp4[5] := array_tmp3[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[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;
while kkk <= ATS_MAX_TERMS do
array_tmp3[kkk] := (array_const_2D0[1] - c(kkk - 2))*array_tmp2[2]*
array_tmp3[kkk - 1]/(array_tmp2[1]*c(kkk - 1));
array_tmp4[kkk] := array_tmp3[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y_set_initial[1, kkk + order_d] then
temporary := c(array_tmp4[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
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
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_0D2,
> array_const_0D3,
> array_const_2D0,
> #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,
> array_tmp2,
> array_tmp3_c1,
> array_tmp3_a1,
> array_tmp3_a2,
> array_tmp3,
> array_tmp4,
> 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:= Array(0..(30),[]);
> array_tmp2:= Array(0..(30),[]);
> array_tmp3_c1:= Array(0..(30),[]);
> array_tmp3_a1:= Array(0..(30),[]);
> array_tmp3_a2:= Array(0..(30),[]);
> array_tmp3:= Array(0..(30),[]);
> array_tmp4:= 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[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_c1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp3_a1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp3_a2[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_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);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3_c1);
> zero_ats_ar(array_tmp3_a1);
> zero_ats_ar(array_tmp3_a2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> 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_0D2);
> array_const_0D2[1] := c(0.2);
> zero_ats_ar(array_const_0D3);
> array_const_0D3[1] := c(0.3);
> zero_ats_ar(array_const_2D0);
> array_const_2D0[1] := c(2.0);
> 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/expt_lin_cpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = expt ( ( 0.2 * x + 0.3 ) , 2.0 ) ; ");
> 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(0.1);");
> 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,"");
> omniout_str(ALWAYS,"return(c(5.0)/c(3.0) * expt((c(0.2) * c(x) + c(0.3)),c(3.0))) ;");
> 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(0.1);
> 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 ) = expt ( ( 0.2 * x + 0.3 ) , 2.0 ) ; ");
> 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,"2015-05-01T22:01:25-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"expt_lin_c")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = expt ( ( 0.2 * x + 0.3 ) , 2.0 ) ; ")
> ;
> 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,"expt_lin_c diffeq.mxt")
> ;
> logitem_str(html_log_file,"expt_lin_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_0D2,
array_const_0D3, array_const_2D0, 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, array_tmp2, array_tmp3_c1, array_tmp3_a1, array_tmp3_a2,
array_tmp3, array_tmp4, 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 := Array(0 .. 30, []);
array_tmp2 := Array(0 .. 30, []);
array_tmp3_c1 := Array(0 .. 30, []);
array_tmp3_a1 := Array(0 .. 30, []);
array_tmp3_a2 := Array(0 .. 30, []);
array_tmp3 := Array(0 .. 30, []);
array_tmp4 := 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[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_c1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp3_a1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp3_a2[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_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);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3_c1);
zero_ats_ar(array_tmp3_a1);
zero_ats_ar(array_tmp3_a2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
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_0D2);
array_const_0D2[1] := c(0.2);
zero_ats_ar(array_const_0D3);
array_const_0D3[1] := c(0.3);
zero_ats_ar(array_const_2D0);
array_const_2D0[1] := c(2.0);
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/expt_lin_cpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = expt ( ( 0.2 *\
x + 0.3 ) , 2.0 ) ; ");
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(0.1);");
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, "");
omniout_str(ALWAYS,
"return(c(5.0)/c(3.0) * expt((c(0.2) * c(x) + c(0.3)),c(3.0))) ;");
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(0.1);
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 ) = expt ( ( 0.2 \
* x + 0.3 ) , 2.0 ) ; ");
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, "2015-05-01T22:01:25-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"expt_lin_c");
logitem_str(html_log_file, "diff ( y , x , 1 ) = e\
xpt ( ( 0.2 * x + 0.3 ) , 2.0 ) ; ");
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, "expt_lin_c diffeq.mxt");
logitem_str(html_log_file, "expt_lin_c maple results");
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/expt_lin_cpostode.ode#################
diff ( y , x , 1 ) = expt ( ( 0.2 * x + 0.3 ) , 2.0 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(0.1);
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(5.0)/c(3.0) * expt((c(0.2) * c(x) + c(0.3)),c(3.0))) ;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (closed_form) = 0.054613333333333333333333333333334
y[1] (numeric) = 0.054613333333333333333333333333334
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=4.1MB, alloc=40.3MB, time=0.09
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (closed_form) = 0.055643746666666666666666666666668
y[1] (numeric) = 0.055643746666666666666666666666664
absolute error = 4e-33
relative error = 7.1885885469969551535111103230286e-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] = 0.12
y[1] (closed_form) = 0.056687040000000000000000000000001
y[1] (numeric) = 0.056687039999999999999999999999994
absolute error = 7e-33
relative error = 1.2348501526980417393464185111800e-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] = 0.13
y[1] (closed_form) = 0.057743293333333333333333333333334
y[1] (numeric) = 0.057743293333333333333333333333324
absolute error = 1.0e-32
relative error = 1.7318028506398549719020760159852e-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] = 0.14
y[1] (closed_form) = 0.058812586666666666666666666666668
y[1] (numeric) = 0.058812586666666666666666666666654
absolute error = 1.4e-32
relative error = 2.3804428258440823551602559452126e-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] = 0.15
y[1] (closed_form) = 0.059895000000000000000000000000001
y[1] (numeric) = 0.059894999999999999999999999999984
absolute error = 1.7e-32
relative error = 2.8383003589615159863093747391268e-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] = 0.16
y[1] (closed_form) = 0.060990613333333333333333333333335
y[1] (numeric) = 0.060990613333333333333333333333314
absolute error = 2.1e-32
relative error = 3.4431527824172287932394405609081e-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] = 0.17
y[1] (closed_form) = 0.062099506666666666666666666666668
y[1] (numeric) = 0.062099506666666666666666666666644
absolute error = 2.4e-32
relative error = 3.8647650018905142134247765360669e-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] = 0.18
y[1] (closed_form) = 0.063221760000000000000000000000001
y[1] (numeric) = 0.063221759999999999999999999999974
absolute error = 2.7e-32
relative error = 4.2706814868804664723032069970845e-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] = 0.19
y[1] (closed_form) = 0.064357453333333333333333333333335
y[1] (numeric) = 0.064357453333333333333333333333304
absolute error = 3.1e-32
relative error = 4.8168469065173285290551169520069e-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] = 0.2
y[1] (closed_form) = 0.065506666666666666666666666666668
y[1] (numeric) = 0.065506666666666666666666666666634
absolute error = 3.4e-32
relative error = 5.1903114186851211072664359861591e-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] = 0.21
y[1] (closed_form) = 0.066669480000000000000000000000001
y[1] (numeric) = 0.066669479999999999999999999999964
absolute error = 3.7e-32
relative error = 5.5497657998832449270640778959127e-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] = 0.22
y[1] (closed_form) = 0.067845973333333333333333333333335
y[1] (numeric) = 0.067845973333333333333333333333294
absolute error = 4.1e-32
relative error = 6.0430999786182348724011722238292e-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] = 0.23
y[1] (closed_form) = 0.069036226666666666666666666666668
y[1] (numeric) = 0.069036226666666666666666666666624
absolute error = 4.4e-32
relative error = 6.3734653709347189118292869231747e-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] = 0.24
y[1] (closed_form) = 0.070240320000000000000000000000001
y[1] (numeric) = 0.070240319999999999999999999999954
absolute error = 4.7e-32
relative error = 6.6913134792096619149798861964181e-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] = 0.25
y[1] (closed_form) = 0.071458333333333333333333333333335
y[1] (numeric) = 0.071458333333333333333333333333284
absolute error = 5.1e-32
relative error = 7.1370262390670553935860058309036e-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] = 0.26
y[1] (closed_form) = 0.072690346666666666666666666666668
y[1] (numeric) = 0.072690346666666666666666666666614
absolute error = 5.4e-32
relative error = 7.4287718350864012021036814425243e-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] = 0.27
y[1] (closed_form) = 0.073936440000000000000000000000001
y[1] (numeric) = 0.073936439999999999999999999999944
absolute error = 5.7e-32
relative error = 7.7093243872710127780022949441438e-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] = 0.28
y[1] (closed_form) = 0.075196693333333333333333333333335
y[1] (numeric) = 0.075196693333333333333333333333274
absolute error = 6.1e-32
relative error = 8.1120588281186832328797436483021e-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] = 0.29
y[1] (closed_form) = 0.076471186666666666666666666666668
y[1] (numeric) = 0.076471186666666666666666666666604
absolute error = 6.4e-32
relative error = 8.3691652751476416651221488389787e-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] = 0.3
y[1] (closed_form) = 0.077760000000000000000000000000002
y[1] (numeric) = 0.077759999999999999999999999999934
absolute error = 6.8e-32
relative error = 8.7448559670781893004115226337446e-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=46.5MB, alloc=40.3MB, time=0.61
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (closed_form) = 0.079063213333333333333333333333335
y[1] (numeric) = 0.079063213333333333333333333333264
absolute error = 7.1e-32
relative error = 8.9801561316084463048217451655981e-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] = 0.32
y[1] (closed_form) = 0.080380906666666666666666666666668
y[1] (numeric) = 0.080380906666666666666666666666594
absolute error = 7.4e-32
relative error = 9.2061663731751885356522477643114e-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] = 0.33
y[1] (closed_form) = 0.081713160000000000000000000000002
y[1] (numeric) = 0.081713159999999999999999999999924
absolute error = 7.8e-32
relative error = 9.5455860475840121713564865194294e-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] = 0.34
y[1] (closed_form) = 0.083060053333333333333333333333335
y[1] (numeric) = 0.083060053333333333333333333333254
absolute error = 8.1e-32
relative error = 9.7519802539656447768554286183938e-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] = 0.35
y[1] (closed_form) = 0.084421666666666666666666666666668
y[1] (numeric) = 0.084421666666666666666666666666584
absolute error = 8.4e-32
relative error = 9.9500523167433320829960713087081e-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] = 0.36
y[1] (closed_form) = 0.085798080000000000000000000000002
y[1] (numeric) = 0.085798079999999999999999999999914
absolute error = 8.8e-32
relative error = 1.0256639775622018581301586235962e-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] = 0.37
y[1] (closed_form) = 0.087189373333333333333333333333335
y[1] (numeric) = 0.087189373333333333333333333333244
absolute error = 9.1e-32
relative error = 1.0437051732451187094207046332710e-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] = 0.38
y[1] (closed_form) = 0.088595626666666666666666666666668
y[1] (numeric) = 0.088595626666666666666666666666574
absolute error = 9.4e-32
relative error = 1.0610004526935264825712992304210e-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] = 0.39
y[1] (closed_form) = 0.090016920000000000000000000000002
y[1] (numeric) = 0.090016919999999999999999999999904
absolute error = 9.8e-32
relative error = 1.0886842162562327171380669323056e-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] = 0.4
y[1] (closed_form) = 0.091453333333333333333333333333335
y[1] (numeric) = 0.091453333333333333333333333333234
absolute error = 1.01e-31
relative error = 1.1043883948097390290129756524274e-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] = 0.41
y[1] (closed_form) = 0.092904946666666666666666666666669
y[1] (numeric) = 0.092904946666666666666666666666564
absolute error = 1.05e-31
relative error = 1.1301873987047119557753006621391e-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] = 0.42
y[1] (closed_form) = 0.094371840000000000000000000000002
y[1] (numeric) = 0.094371839999999999999999999999894
absolute error = 1.08e-31
relative error = 1.1444091796875000000000000000000e-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] = 0.43
y[1] (closed_form) = 0.095854093333333333333333333333335
y[1] (numeric) = 0.095854093333333333333333333333224
absolute error = 1.11e-31
relative error = 1.1580100143871442388062857200882e-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] = 0.44
y[1] (closed_form) = 0.097351786666666666666666666666669
y[1] (numeric) = 0.097351786666666666666666666666554
absolute error = 1.15e-31
relative error = 1.1812828910244961777109654827085e-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] = 0.45
y[1] (closed_form) = 0.098865000000000000000000000000002
y[1] (numeric) = 0.098864999999999999999999999999884
absolute error = 1.18e-31
relative error = 1.1935467556769331917260911343751e-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] = 0.46
y[1] (closed_form) = 0.10039381333333333333333333333334
y[1] (numeric) = 0.10039381333333333333333333333321
absolute error = 1.3e-31
relative error = 1.2949005091415991636138003722938e-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] = 0.47
y[1] (closed_form) = 0.10193830666666666666666666666667
y[1] (numeric) = 0.10193830666666666666666666666651
absolute error = 1.6e-31
relative error = 1.5695767884706213810627682913573e-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] = 0.48
y[1] (closed_form) = 0.10349856
y[1] (numeric) = 0.10349855999999999999999999999981
absolute error = 1.9e-31
relative error = 1.8357743334786493647834327356825e-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] = 0.49
y[1] (closed_form) = 0.10507465333333333333333333333334
y[1] (numeric) = 0.10507465333333333333333333333311
absolute error = 2.3e-31
relative error = 2.1889199031697971182139834801896e-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=88.9MB, alloc=40.3MB, time=1.11
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (closed_form) = 0.10666666666666666666666666666667
y[1] (numeric) = 0.10666666666666666666666666666641
absolute error = 2.6e-31
relative error = 2.4374999999999999999999999999999e-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] = 0.51
y[1] (closed_form) = 0.10827468
y[1] (numeric) = 0.10827467999999999999999999999971
absolute error = 2.9e-31
relative error = 2.6783731893735451353908411458709e-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] = 0.52
y[1] (closed_form) = 0.10989877333333333333333333333334
y[1] (numeric) = 0.10989877333333333333333333333301
absolute error = 3.3e-31
relative error = 3.0027632701511500037367720695212e-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] = 0.53
y[1] (closed_form) = 0.11153902666666666666666666666667
y[1] (numeric) = 0.11153902666666666666666666666631
absolute error = 3.6e-31
relative error = 3.2275698538759587526135844589881e-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] = 0.54
y[1] (closed_form) = 0.11319552
y[1] (numeric) = 0.11319551999999999999999999999961
absolute error = 3.9e-31
relative error = 3.4453660356876314539656693127078e-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] = 0.55
y[1] (closed_form) = 0.11486833333333333333333333333334
y[1] (numeric) = 0.11486833333333333333333333333291
absolute error = 4.3e-31
relative error = 3.7434163752702369379434424921285e-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] = 0.56
y[1] (closed_form) = 0.11655754666666666666666666666667
y[1] (numeric) = 0.11655754666666666666666666666621
absolute error = 4.6e-31
relative error = 3.9465484059605006556989989265387e-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] = 0.57
y[1] (closed_form) = 0.11826324
y[1] (numeric) = 0.11826323999999999999999999999951
absolute error = 4.9e-31
relative error = 4.1432993041624768609417431824124e-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] = 0.58
y[1] (closed_form) = 0.11998549333333333333333333333334
y[1] (numeric) = 0.11998549333333333333333333333281
absolute error = 5.3e-31
relative error = 4.4172006571461083295402822030039e-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] = 0.59
y[1] (closed_form) = 0.12172438666666666666666666666667
y[1] (numeric) = 0.12172438666666666666666666666611
absolute error = 5.6e-31
relative error = 4.6005571712882732126315088436400e-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] = 0.6
y[1] (closed_form) = 0.12348
y[1] (numeric) = 0.12347999999999999999999999999941
absolute error = 5.9e-31
relative error = 4.7781017168772270813087139617752e-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] = 0.61
y[1] (closed_form) = 0.12525241333333333333333333333334
y[1] (numeric) = 0.12525241333333333333333333333271
absolute error = 6.3e-31
relative error = 5.0298432040857017152883068866481e-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] = 0.62
y[1] (closed_form) = 0.12704170666666666666666666666667
y[1] (numeric) = 0.12704170666666666666666666666601
absolute error = 6.6e-31
relative error = 5.1951443137623675920390658060008e-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] = 0.63
y[1] (closed_form) = 0.12884796
y[1] (numeric) = 0.12884795999999999999999999999931
absolute error = 6.9e-31
relative error = 5.3551488126005254565147946463413e-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] = 0.64
y[1] (closed_form) = 0.13067125333333333333333333333334
y[1] (numeric) = 0.13067125333333333333333333333261
absolute error = 7.3e-31
relative error = 5.5865385949717683379277298837671e-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] = 0.65
y[1] (closed_form) = 0.13251166666666666666666666666667
y[1] (numeric) = 0.13251166666666666666666666666591
absolute error = 7.6e-31
relative error = 5.7353440577559208623140100871620e-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] = 0.66
y[1] (closed_form) = 0.13436928
y[1] (numeric) = 0.13436927999999999999999999999921
absolute error = 7.9e-31
relative error = 5.8793200350556317634506934918458e-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] = 0.67
y[1] (closed_form) = 0.13624417333333333333333333333334
y[1] (numeric) = 0.13624417333333333333333333333251
absolute error = 8.3e-31
relative error = 6.0920036409141117521062429776810e-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] = 0.68
y[1] (closed_form) = 0.13813642666666666666666666666667
y[1] (numeric) = 0.13813642666666666666666666666581
absolute error = 8.6e-31
relative error = 6.2257293079923306736760335096742e-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] = 0.69
y[1] (closed_form) = 0.14004612
y[1] (numeric) = 0.14004611999999999999999999999911
absolute error = 8.9e-31
relative error = 6.3550493223232460849325922060533e-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=131.3MB, alloc=40.3MB, time=1.61
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (closed_form) = 0.14197333333333333333333333333334
y[1] (numeric) = 0.14197333333333333333333333333241
absolute error = 9.3e-31
relative error = 6.5505259203606311044327573253190e-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] = 0.71
y[1] (closed_form) = 0.14391814666666666666666666666667
y[1] (numeric) = 0.14391814666666666666666666666571
absolute error = 9.6e-31
relative error = 6.6704583281181775455511239212732e-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] = 0.72
y[1] (closed_form) = 0.14588064
y[1] (numeric) = 0.14588063999999999999999999999901
absolute error = 9.9e-31
relative error = 6.7863700076994452450990069689851e-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] = 0.73
y[1] (closed_form) = 0.14786089333333333333333333333334
y[1] (numeric) = 0.14786089333333333333333333333231
absolute error = 1.03e-30
relative error = 6.9660068783569277321648356513826e-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] = 0.74
y[1] (closed_form) = 0.14985898666666666666666666666667
y[1] (numeric) = 0.14985898666666666666666666666561
absolute error = 1.06e-30
relative error = 7.0733162126457725947521865889211e-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] = 0.75
y[1] (closed_form) = 0.151875
y[1] (numeric) = 0.15187499999999999999999999999891
absolute error = 1.09e-30
relative error = 7.1769547325102880658436213991770e-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] = 0.76
y[1] (closed_form) = 0.15390901333333333333333333333334
y[1] (numeric) = 0.15390901333333333333333333333221
absolute error = 1.13e-30
relative error = 7.3420001566293366747591823948622e-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] = 0.77
y[1] (closed_form) = 0.15596110666666666666666666666667
y[1] (numeric) = 0.15596110666666666666666666666551
absolute error = 1.16e-30
relative error = 7.4377517882022381135536099042811e-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] = 0.78
y[1] (closed_form) = 0.15803136
y[1] (numeric) = 0.15803135999999999999999999999881
absolute error = 1.19e-30
relative error = 7.5301509776287440670003725842769e-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] = 0.79
y[1] (closed_form) = 0.16011985333333333333333333333334
y[1] (numeric) = 0.16011985333333333333333333333211
absolute error = 1.23e-30
relative error = 7.6817457323010288376481983620766e-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] = 0.8
y[1] (closed_form) = 0.16222666666666666666666666666667
y[1] (numeric) = 0.16222666666666666666666666666541
absolute error = 1.26e-30
relative error = 7.7669104956028601956110791485163e-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] = 0.81
y[1] (closed_form) = 0.16435188
y[1] (numeric) = 0.16435187999999999999999999999871
absolute error = 1.29e-30
relative error = 7.8490127402254236458992741671102e-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] = 0.82
y[1] (closed_form) = 0.16649557333333333333333333333334
y[1] (numeric) = 0.16649557333333333333333333333201
absolute error = 1.33e-30
relative error = 7.9882003669687154044856287670668e-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] = 0.83
y[1] (closed_form) = 0.16865782666666666666666666666667
y[1] (numeric) = 0.16865782666666666666666666666531
absolute error = 1.36e-30
relative error = 8.0636637319410495585657967686368e-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] = 0.84
y[1] (closed_form) = 0.17083872
y[1] (numeric) = 0.17083871999999999999999999999861
absolute error = 1.39e-30
relative error = 8.1363288135148753163217331527654e-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] = 0.85
y[1] (closed_form) = 0.17303833333333333333333333333334
y[1] (numeric) = 0.17303833333333333333333333333191
absolute error = 1.43e-30
relative error = 8.2640648025967271221213026015427e-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] = 0.86
y[1] (closed_form) = 0.17525674666666666666666666666667
y[1] (numeric) = 0.17525674666666666666666666666521
absolute error = 1.46e-30
relative error = 8.3306350697977884788610325301027e-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] = 0.87
y[1] (closed_form) = 0.17749404
y[1] (numeric) = 0.17749403999999999999999999999851
absolute error = 1.49e-30
relative error = 8.3946480681830218073801238621871e-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] = 0.88
y[1] (closed_form) = 0.17975029333333333333333333333334
y[1] (numeric) = 0.17975029333333333333333333333181
absolute error = 1.53e-30
relative error = 8.5118080845783691627911668869225e-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] = 0.89
y[1] (closed_form) = 0.18202558666666666666666666666667
y[1] (numeric) = 0.18202558666666666666666666666511
absolute error = 1.56e-30
relative error = 8.5702237172664150732215741977372e-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=173.6MB, alloc=40.3MB, time=2.11
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (closed_form) = 0.18432
y[1] (numeric) = 0.18431999999999999999999999999841
absolute error = 1.59e-30
relative error = 8.6263020833333333333333333333333e-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] = 0.91
y[1] (closed_form) = 0.18663361333333333333333333333334
y[1] (numeric) = 0.18663361333333333333333333333171
absolute error = 1.63e-30
relative error = 8.7336893439916968154575370881741e-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] = 0.92
y[1] (closed_form) = 0.18896650666666666666666666666667
y[1] (numeric) = 0.18896650666666666666666666666501
absolute error = 1.66e-30
relative error = 8.7846255364619112748587262871556e-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] = 0.93
y[1] (closed_form) = 0.19131876
y[1] (numeric) = 0.19131875999999999999999999999831
absolute error = 1.69e-30
relative error = 8.8334254309404890560653853286526e-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] = 0.94
y[1] (closed_form) = 0.19369045333333333333333333333334
y[1] (numeric) = 0.19369045333333333333333333333161
absolute error = 1.73e-30
relative error = 8.9317773293799921579339239848266e-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] = 0.95
y[1] (closed_form) = 0.19608166666666666666666666666667
y[1] (numeric) = 0.19608166666666666666666666666491
absolute error = 1.76e-30
relative error = 8.9758518984436756793512907037032e-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] = 0.96
y[1] (closed_form) = 0.19849248
y[1] (numeric) = 0.19849247999999999999999999999821
absolute error = 1.79e-30
relative error = 9.0179738799172643719298585014405e-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] = 0.97
y[1] (closed_form) = 0.20092297333333333333333333333334
y[1] (numeric) = 0.20092297333333333333333333333151
absolute error = 1.83e-30
relative error = 9.1079679423418181547913916994921e-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] = 0.98
y[1] (closed_form) = 0.20337322666666666666666666666667
y[1] (numeric) = 0.20337322666666666666666666666481
absolute error = 1.86e-30
relative error = 9.1457466181061394380853277835586e-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] = 0.99
y[1] (closed_form) = 0.20584332
y[1] (numeric) = 0.20584331999999999999999999999811
absolute error = 1.89e-30
relative error = 9.1817407531126101153051748290885e-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] = 1
y[1] (closed_form) = 0.20833333333333333333333333333334
y[1] (numeric) = 0.20833333333333333333333333333141
absolute error = 1.93e-30
relative error = 9.2639999999999999999999999999997e-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] = 1.01
y[1] (closed_form) = 0.21084334666666666666666666666667
y[1] (numeric) = 0.21084334666666666666666666666471
absolute error = 1.96e-30
relative error = 9.2960011828054838312501331952549e-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] = 1.02
y[1] (closed_form) = 0.21337344
y[1] (numeric) = 0.21337343999999999999999999999801
absolute error = 1.99e-30
relative error = 9.3263716421312793194879362679816e-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] = 1.03
y[1] (closed_form) = 0.21592369333333333333333333333334
y[1] (numeric) = 0.21592369333333333333333333333131
absolute error = 2.03e-30
relative error = 9.4014694203390494061574962562389e-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] = 1.04
y[1] (closed_form) = 0.21849418666666666666666666666667
y[1] (numeric) = 0.21849418666666666666666666666461
absolute error = 2.06e-30
relative error = 9.4281684626361378707009382522701e-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] = 1.05
y[1] (closed_form) = 0.221085
y[1] (numeric) = 0.22108499999999999999999999999791
absolute error = 2.09e-30
relative error = 9.4533776601759504263066241490829e-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] = 1.06
y[1] (closed_form) = 0.22369621333333333333333333333334
y[1] (numeric) = 0.22369621333333333333333333333121
absolute error = 2.13e-30
relative error = 9.5218420028686523437499999999997e-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] = 1.07
y[1] (closed_form) = 0.22632790666666666666666666666667
y[1] (numeric) = 0.22632790666666666666666666666451
absolute error = 2.16e-30
relative error = 9.5436750677910215579248350755743e-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] = 1.08
y[1] (closed_form) = 0.22898016
y[1] (numeric) = 0.22898015999999999999999999999781
absolute error = 2.19e-30
relative error = 9.5641473916342795812528037363586e-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] = 1.09
y[1] (closed_form) = 0.23165305333333333333333333333334
y[1] (numeric) = 0.23165305333333333333333333333111
absolute error = 2.23e-30
relative error = 9.6264649565882403794778386689655e-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=216.1MB, alloc=40.3MB, time=2.61
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (closed_form) = 0.23434666666666666666666666666667
y[1] (numeric) = 0.23434666666666666666666666666441
absolute error = 2.26e-30
relative error = 9.6438324988620846609012289485661e-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] = 1.11
y[1] (closed_form) = 0.23706108
y[1] (numeric) = 0.23706107999999999999999999999771
absolute error = 2.29e-30
relative error = 9.6599576784177309915233660455778e-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] = 1.12
y[1] (closed_form) = 0.23979637333333333333333333333334
y[1] (numeric) = 0.23979637333333333333333333333101
absolute error = 2.33e-30
relative error = 9.7165773093704836681433269382776e-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] = 1.13
y[1] (closed_form) = 0.24255262666666666666666666666667
y[1] (numeric) = 0.24255262666666666666666666666431
absolute error = 2.36e-30
relative error = 9.7298472188605997093029487978608e-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] = 1.14
y[1] (closed_form) = 0.24532992
y[1] (numeric) = 0.24532991999999999999999999999761
absolute error = 2.39e-30
relative error = 9.7419833667251022622923449369730e-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] = 1.15
y[1] (closed_form) = 0.24812833333333333333333333333334
y[1] (numeric) = 0.24812833333333333333333333333091
absolute error = 2.43e-30
relative error = 9.7933193172887685807747335048393e-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] = 1.16
y[1] (closed_form) = 0.25094794666666666666666666666667
y[1] (numeric) = 0.25094794666666666666666666666421
absolute error = 2.46e-30
relative error = 9.8028297608173296602918342268695e-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] = 1.17
y[1] (closed_form) = 0.25378884000000000000000000000001
y[1] (numeric) = 0.25378883999999999999999999999751
absolute error = 2.50e-30
relative error = 9.8507089594640962147902169378287e-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] = 1.18
y[1] (closed_form) = 0.25665109333333333333333333333334
y[1] (numeric) = 0.25665109333333333333333333333081
absolute error = 2.53e-30
relative error = 9.8577409787773097089735107044414e-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] = 1.19
y[1] (closed_form) = 0.25953478666666666666666666666667
y[1] (numeric) = 0.25953478666666666666666666666411
absolute error = 2.56e-30
relative error = 9.8638029717686142934005661103669e-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] = 1.2
y[1] (closed_form) = 0.26244000000000000000000000000001
y[1] (numeric) = 0.26243999999999999999999999999741
absolute error = 2.60e-30
relative error = 9.9070263679317177259564090839807e-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] = 1.21
y[1] (closed_form) = 0.26536681333333333333333333333334
y[1] (numeric) = 0.26536681333333333333333333333071
absolute error = 2.63e-30
relative error = 9.9108097465691640617608501761408e-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] = 1.22
y[1] (closed_form) = 0.26831530666666666666666666666667
y[1] (numeric) = 0.26831530666666666666666666666401
absolute error = 2.66e-30
relative error = 9.9137094824954203134541013637288e-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] = 1.23
y[1] (closed_form) = 0.27128556000000000000000000000001
y[1] (numeric) = 0.27128555999999999999999999999731
absolute error = 2.70e-30
relative error = 9.9526122953245281466510786641202e-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] = 1.24
y[1] (closed_form) = 0.27427765333333333333333333333334
y[1] (numeric) = 0.27427765333333333333333333333061
absolute error = 2.73e-30
relative error = 9.9534175198815565190776995612813e-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] = 1.25
y[1] (closed_form) = 0.27729166666666666666666666666667
y[1] (numeric) = 0.27729166666666666666666666666391
absolute error = 2.76e-30
relative error = 9.9534184823441021788129226145754e-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] = 1.26
y[1] (closed_form) = 0.28032768000000000000000000000001
y[1] (numeric) = 0.28032767999999999999999999999721
absolute error = 2.80e-30
relative error = 9.9883108225345424326274166004581e-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] = 1.27
y[1] (closed_form) = 0.28338577333333333333333333333334
y[1] (numeric) = 0.28338577333333333333333333333051
absolute error = 2.83e-30
relative error = 9.9863869901161352113041854418189e-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] = 1.28
y[1] (closed_form) = 0.28646602666666666666666666666667
y[1] (numeric) = 0.28646602666666666666666666666381
absolute error = 2.86e-30
relative error = 9.9837318696360131500410147530233e-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=258.5MB, alloc=40.3MB, time=3.11
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (closed_form) = 0.28956852000000000000000000000001
y[1] (numeric) = 0.28956851999999999999999999999711
absolute error = 2.90e-30
relative error = 1.0014900791011398614738922587303e-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] = 1.3
y[1] (closed_form) = 0.29269333333333333333333333333334
y[1] (numeric) = 0.29269333333333333333333333333041
absolute error = 2.93e-30
relative error = 1.0010477405247813411078717201166e-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] = 1.31
y[1] (closed_form) = 0.29584054666666666666666666666667
y[1] (numeric) = 0.29584054666666666666666666666371
absolute error = 2.96e-30
relative error = 1.0005389840409975806336395358202e-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] = 1.32
y[1] (closed_form) = 0.29901024000000000000000000000001
y[1] (numeric) = 0.29901023999999999999999999999701
absolute error = 3.00e-30
relative error = 1.0033101207503796525496919436605e-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] = 1.33
y[1] (closed_form) = 0.30220249333333333333333333333334
y[1] (numeric) = 0.30220249333333333333333333333031
absolute error = 3.03e-30
relative error = 1.0026389810946629295403563182602e-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] = 1.34
y[1] (closed_form) = 0.30541738666666666666666666666667
y[1] (numeric) = 0.30541738666666666666666666666361
absolute error = 3.06e-30
relative error = 1.0019075971400711350028359005451e-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] = 1.35
y[1] (closed_form) = 0.30865500000000000000000000000001
y[1] (numeric) = 0.30865499999999999999999999999691
absolute error = 3.10e-30
relative error = 1.0043576161086002170708396105684e-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] = 1.36
y[1] (closed_form) = 0.31191541333333333333333333333334
y[1] (numeric) = 0.31191541333333333333333333333021
absolute error = 3.13e-30
relative error = 1.0034771820189200012174240742875e-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] = 1.37
y[1] (closed_form) = 0.31519870666666666666666666666667
y[1] (numeric) = 0.31519870666666666666666666666351
absolute error = 3.16e-30
relative error = 1.0025421847120100281291340324027e-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] = 1.38
y[1] (closed_form) = 0.31850496000000000000000000000001
y[1] (numeric) = 0.31850495999999999999999999999681
absolute error = 3.20e-30
relative error = 1.0046939300411522633744855967078e-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] = 1.39
y[1] (closed_form) = 0.32183425333333333333333333333334
y[1] (numeric) = 0.32183425333333333333333333333011
absolute error = 3.23e-30
relative error = 1.0036221957563332082033613244150e-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] = 1.4
y[1] (closed_form) = 0.32518666666666666666666666666667
y[1] (numeric) = 0.32518666666666666666666666666341
absolute error = 3.26e-30
relative error = 1.0025011275575054327770716306532e-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] = 1.41
y[1] (closed_form) = 0.32856228000000000000000000000001
y[1] (numeric) = 0.32856227999999999999999999999671
absolute error = 3.30e-30
relative error = 1.0043757914024701800827532606603e-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] = 1.42
y[1] (closed_form) = 0.33196117333333333333333333333334
y[1] (numeric) = 0.33196117333333333333333333333001
absolute error = 3.33e-30
relative error = 1.0031293619559042406887102620194e-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] = 1.43
y[1] (closed_form) = 0.33538342666666666666666666666667
y[1] (numeric) = 0.33538342666666666666666666666331
absolute error = 3.36e-30
relative error = 1.0018384132437949527778295703501e-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] = 1.44
y[1] (closed_form) = 0.33882912000000000000000000000001
y[1] (numeric) = 0.33882911999999999999999999999661
absolute error = 3.40e-30
relative error = 1.0034556652037463604072755021764e-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] = 1.45
y[1] (closed_form) = 0.34229833333333333333333333333334
y[1] (numeric) = 0.34229833333333333333333333332991
absolute error = 3.43e-30
relative error = 1.0020498687791838503449719786346e-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] = 1.46
y[1] (closed_form) = 0.34579114666666666666666666666667
y[1] (numeric) = 0.34579114666666666666666666666321
absolute error = 3.46e-30
relative error = 1.0006039869306852506268138116202e-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] = 1.47
y[1] (closed_form) = 0.34930764000000000000000000000001
y[1] (numeric) = 0.34930763999999999999999999999651
absolute error = 3.50e-30
relative error = 1.0019820923470210957882283937448e-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] = 1.48
y[1] (closed_form) = 0.35284789333333333333333333333334
y[1] (numeric) = 0.35284789333333333333333333332981
absolute error = 3.53e-30
relative error = 1.0004310828250375081357058406886e-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=300.9MB, alloc=40.3MB, time=3.62
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (closed_form) = 0.35641198666666666666666666666667
y[1] (numeric) = 0.35641198666666666666666666666311
absolute error = 3.56e-30
relative error = 9.9884407179870755562691699968638e-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] = 1.5
y[1] (closed_form) = 0.36000000000000000000000000000001
y[1] (numeric) = 0.35999999999999999999999999999641
absolute error = 3.60e-30
relative error = 9.9999999999999999999999999999997e-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] = 1.51
y[1] (closed_form) = 0.36361201333333333333333333333334
y[1] (numeric) = 0.36361201333333333333333333332971
absolute error = 3.63e-30
relative error = 9.9831685062404062117346251229468e-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] = 1.52
y[1] (closed_form) = 0.36724810666666666666666666666667
y[1] (numeric) = 0.36724810666666666666666666666301
absolute error = 3.66e-30
relative error = 9.9660146194354784601930146551606e-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] = 1.53
y[1] (closed_form) = 0.37090836000000000000000000000001
y[1] (numeric) = 0.37090835999999999999999999999631
absolute error = 3.70e-30
relative error = 9.9755098537007901358707579413953e-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] = 1.54
y[1] (closed_form) = 0.37459285333333333333333333333334
y[1] (numeric) = 0.37459285333333333333333333332961
absolute error = 3.73e-30
relative error = 9.9574777436579676337658550809154e-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] = 1.55
y[1] (closed_form) = 0.37830166666666666666666666666667
y[1] (numeric) = 0.37830166666666666666666666666291
absolute error = 3.76e-30
relative error = 9.9391579030843991347293385789999e-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] = 1.56
y[1] (closed_form) = 0.38203488000000000000000000000001
y[1] (numeric) = 0.38203487999999999999999999999621
absolute error = 3.80e-30
relative error = 9.9467357535521363913158924127553e-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] = 1.57
y[1] (closed_form) = 0.38579257333333333333333333333334
y[1] (numeric) = 0.38579257333333333333333333332951
absolute error = 3.83e-30
relative error = 9.9276146425213715017773108678814e-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] = 1.58
y[1] (closed_form) = 0.38957482666666666666666666666667
y[1] (numeric) = 0.38957482666666666666666666666281
absolute error = 3.86e-30
relative error = 9.9082377396595645878830226949639e-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] = 1.59
y[1] (closed_form) = 0.39338172000000000000000000000001
y[1] (numeric) = 0.39338171999999999999999999999611
absolute error = 3.90e-30
relative error = 9.9140346429925620336399973033823e-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] = 1.6
y[1] (closed_form) = 0.39721333333333333333333333333334
y[1] (numeric) = 0.39721333333333333333333333332941
absolute error = 3.93e-30
relative error = 9.8939276962841126514719210499814e-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] = 1.61
y[1] (closed_form) = 0.40106974666666666666666666666667
y[1] (numeric) = 0.40106974666666666666666666666271
absolute error = 3.96e-30
relative error = 9.8735943882877761144852910205376e-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] = 1.62
y[1] (closed_form) = 0.40495104000000000000000000000001
y[1] (numeric) = 0.40495103999999999999999999999601
absolute error = 4.00e-30
relative error = 9.8777373185657209325848379102815e-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] = 1.63
y[1] (closed_form) = 0.40885729333333333333333333333334
y[1] (numeric) = 0.40885729333333333333333333332931
absolute error = 4.03e-30
relative error = 9.8567399083044362634499659326935e-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] = 1.64
y[1] (closed_form) = 0.41278858666666666666666666666667
y[1] (numeric) = 0.41278858666666666666666666666261
absolute error = 4.06e-30
relative error = 9.8355432566223407210483597350107e-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] = 1.65
y[1] (closed_form) = 0.41674500000000000000000000000001
y[1] (numeric) = 0.41674499999999999999999999999591
absolute error = 4.10e-30
relative error = 9.8381504277195887173211436249983e-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] = 1.66
y[1] (closed_form) = 0.42072661333333333333333333333334
y[1] (numeric) = 0.42072661333333333333333333332921
absolute error = 4.13e-30
relative error = 9.8163507349317193974513172385956e-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] = 1.67
y[1] (closed_form) = 0.42473350666666666666666666666668
y[1] (numeric) = 0.42473350666666666666666666666251
absolute error = 4.17e-30
relative error = 9.8179209658460977554772933227178e-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] = 1.68
y[1] (closed_form) = 0.42876576000000000000000000000001
y[1] (numeric) = 0.42876575999999999999999999999581
absolute error = 4.20e-30
relative error = 9.7955583020435213856628850214157e-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=343.3MB, alloc=40.3MB, time=4.13
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (closed_form) = 0.43282345333333333333333333333334
y[1] (numeric) = 0.43282345333333333333333333332911
absolute error = 4.23e-30
relative error = 9.7730378689583642094071365633635e-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] = 1.7
y[1] (closed_form) = 0.43690666666666666666666666666668
y[1] (numeric) = 0.43690666666666666666666666666241
absolute error = 4.27e-30
relative error = 9.7732543945312499999999999999997e-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] = 1.71
y[1] (closed_form) = 0.44101548000000000000000000000001
y[1] (numeric) = 0.44101547999999999999999999999571
absolute error = 4.30e-30
relative error = 9.7502246406407321575197315069301e-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] = 1.72
y[1] (closed_form) = 0.44514997333333333333333333333334
y[1] (numeric) = 0.44514997333333333333333333332901
absolute error = 4.33e-30
relative error = 9.7270588776552549420947211558482e-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] = 1.73
y[1] (closed_form) = 0.44931022666666666666666666666668
y[1] (numeric) = 0.44931022666666666666666666666231
absolute error = 4.37e-30
relative error = 9.7260194418899939275809049765078e-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] = 1.74
y[1] (closed_form) = 0.45349632000000000000000000000001
y[1] (numeric) = 0.45349631999999999999999999999561
absolute error = 4.40e-30
relative error = 9.7023940569131850948647168735568e-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] = 1.75
y[1] (closed_form) = 0.45770833333333333333333333333334
y[1] (numeric) = 0.45770833333333333333333333332891
absolute error = 4.43e-30
relative error = 9.6786527082385070550751024123804e-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] = 1.76
y[1] (closed_form) = 0.46194634666666666666666666666668
y[1] (numeric) = 0.46194634666666666666666666666221
absolute error = 4.47e-30
relative error = 9.6764484279501896555028497393172e-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] = 1.77
y[1] (closed_form) = 0.46621044000000000000000000000001
y[1] (numeric) = 0.46621043999999999999999999999551
absolute error = 4.50e-30
relative error = 9.6522935007633033700403620305026e-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] = 1.78
y[1] (closed_form) = 0.47050069333333333333333333333334
y[1] (numeric) = 0.47050069333333333333333333332881
absolute error = 4.53e-30
relative error = 9.6280410723872259543535352069760e-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] = 1.79
y[1] (closed_form) = 0.47481718666666666666666666666668
y[1] (numeric) = 0.47481718666666666666666666666211
absolute error = 4.57e-30
relative error = 9.6247569134607848651589107038498e-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] = 1.8
y[1] (closed_form) = 0.47916000000000000000000000000001
y[1] (numeric) = 0.47915999999999999999999999999541
absolute error = 4.60e-30
relative error = 9.6001335670757158360464145588111e-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] = 1.81
y[1] (closed_form) = 0.48352921333333333333333333333334
y[1] (numeric) = 0.48352921333333333333333333332871
absolute error = 4.63e-30
relative error = 9.5754297203304448395823915885564e-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] = 1.82
y[1] (closed_form) = 0.48792490666666666666666666666668
y[1] (numeric) = 0.48792490666666666666666666666201
absolute error = 4.67e-30
relative error = 9.5711449368383681335882067972861e-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] = 1.83
y[1] (closed_form) = 0.49234716000000000000000000000001
y[1] (numeric) = 0.49234715999999999999999999999531
absolute error = 4.70e-30
relative error = 9.5461097003179626343330588115912e-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] = 1.84
y[1] (closed_form) = 0.49679605333333333333333333333334
y[1] (numeric) = 0.49679605333333333333333333332861
absolute error = 4.73e-30
relative error = 9.5210096140323605361974963622898e-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] = 1.85
y[1] (closed_form) = 0.50127166666666666666666666666668
y[1] (numeric) = 0.50127166666666666666666666666191
absolute error = 4.77e-30
relative error = 9.5157981533632793927444532738399e-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] = 1.86
y[1] (closed_form) = 0.50577408000000000000000000000001
y[1] (numeric) = 0.50577407999999999999999999999521
absolute error = 4.80e-30
relative error = 9.4904033041788143828960155490766e-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] = 1.87
y[1] (closed_form) = 0.51030337333333333333333333333334
y[1] (numeric) = 0.51030337333333333333333333332851
absolute error = 4.83e-30
relative error = 9.4649580081161133091209822298384e-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=385.5MB, alloc=40.3MB, time=4.63
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (closed_form) = 0.51485962666666666666666666666668
y[1] (numeric) = 0.51485962666666666666666666666181
absolute error = 4.87e-30
relative error = 9.4588888849755604582654917565619e-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] = 1.89
y[1] (closed_form) = 0.51944292000000000000000000000001
y[1] (numeric) = 0.51944291999999999999999999999511
absolute error = 4.90e-30
relative error = 9.4331827643352998246660095011015e-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] = 1.9
y[1] (closed_form) = 0.52405333333333333333333333333334
y[1] (numeric) = 0.52405333333333333333333333332841
absolute error = 4.93e-30
relative error = 9.4074394463667820069204152249134e-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] = 1.91
y[1] (closed_form) = 0.52869094666666666666666666666668
y[1] (numeric) = 0.52869094666666666666666666666171
absolute error = 4.97e-30
relative error = 9.4005770882502470693590591968018e-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] = 1.92
y[1] (closed_form) = 0.53335584000000000000000000000001
y[1] (numeric) = 0.53335583999999999999999999999501
absolute error = 5.00e-30
relative error = 9.3746043916946704849055369863390e-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] = 1.93
y[1] (closed_form) = 0.53804809333333333333333333333334
y[1] (numeric) = 0.53804809333333333333333333332831
absolute error = 5.03e-30
relative error = 9.3486066809343709968727206963183e-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] = 1.94
y[1] (closed_form) = 0.54276778666666666666666666666668
y[1] (numeric) = 0.54276778666666666666666666666161
absolute error = 5.07e-30
relative error = 9.3410112474373325619127875532970e-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] = 1.95
y[1] (closed_form) = 0.54751500000000000000000000000001
y[1] (numeric) = 0.54751499999999999999999999999491
absolute error = 5.10e-30
relative error = 9.3148132927864990000273965096845e-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] = 1.96
y[1] (closed_form) = 0.55228981333333333333333333333334
y[1] (numeric) = 0.55228981333333333333333333332821
absolute error = 5.13e-30
relative error = 9.2886015207088375050239323624677e-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] = 1.97
y[1] (closed_form) = 0.55709230666666666666666666666668
y[1] (numeric) = 0.55709230666666666666666666666151
absolute error = 5.17e-30
relative error = 9.2803291988260090374490422568629e-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] = 1.98
y[1] (closed_form) = 0.56192256000000000000000000000001
y[1] (numeric) = 0.56192255999999999999999999999481
absolute error = 5.20e-30
relative error = 9.2539441733750643505040979312165e-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] = 1.99
y[1] (closed_form) = 0.56678065333333333333333333333334
y[1] (numeric) = 0.56678065333333333333333333332811
absolute error = 5.23e-30
relative error = 9.2275556147541051095392599733290e-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
y[1] (closed_form) = 0.57166666666666666666666666666668
y[1] (numeric) = 0.57166666666666666666666666666141
absolute error = 5.27e-30
relative error = 9.2186588921282798833819241982505e-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] = 2.01
y[1] (closed_form) = 0.57658068000000000000000000000001
y[1] (numeric) = 0.57658067999999999999999999999471
absolute error = 5.30e-30
relative error = 9.1921220808161660914479479263854e-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] = 2.02
y[1] (closed_form) = 0.58152277333333333333333333333334
y[1] (numeric) = 0.58152277333333333333333333332801
absolute error = 5.33e-30
relative error = 9.1655911761598422238918106686701e-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] = 2.03
y[1] (closed_form) = 0.58649302666666666666666666666668
y[1] (numeric) = 0.58649302666666666666666666666131
absolute error = 5.37e-30
relative error = 9.1561190940673190612757953336959e-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] = 2.04
y[1] (closed_form) = 0.59149152000000000000000000000001
y[1] (numeric) = 0.59149151999999999999999999999461
absolute error = 5.40e-30
relative error = 9.1294630901893572371079808549071e-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] = 2.05
y[1] (closed_form) = 0.59651833333333333333333333333335
y[1] (numeric) = 0.59651833333333333333333333332791
absolute error = 5.44e-30
relative error = 9.1195855953016252643813685525170e-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] = 2.06
y[1] (closed_form) = 0.60157354666666666666666666666668
y[1] (numeric) = 0.60157354666666666666666666666121
absolute error = 5.47e-30
relative error = 9.0928200388953273122647946221747e-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] = 2.07
y[1] (closed_form) = 0.60665724000000000000000000000001
y[1] (numeric) = 0.60665723999999999999999999999451
absolute error = 5.50e-30
relative error = 9.0660749387908071450692651422077e-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=427.9MB, alloc=40.3MB, time=5.13
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (closed_form) = 0.61176949333333333333333333333335
y[1] (numeric) = 0.61176949333333333333333333332781
absolute error = 5.54e-30
relative error = 9.0556983641245966454642001109261e-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] = 2.09
y[1] (closed_form) = 0.61691038666666666666666666666668
y[1] (numeric) = 0.61691038666666666666666666666111
absolute error = 5.57e-30
relative error = 9.0288640301490358005319367941045e-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] = 2.1
y[1] (closed_form) = 0.62208000000000000000000000000001
y[1] (numeric) = 0.62207999999999999999999999999441
absolute error = 5.60e-30
relative error = 9.0020576131687242798353909465019e-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] = 2.11
y[1] (closed_form) = 0.62727841333333333333333333333335
y[1] (numeric) = 0.62727841333333333333333333332771
absolute error = 5.64e-30
relative error = 8.9912228447799712795260439484594e-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] = 2.12
y[1] (closed_form) = 0.63250570666666666666666666666668
y[1] (numeric) = 0.63250570666666666666666666666101
absolute error = 5.67e-30
relative error = 8.9643459975739243923132561776305e-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] = 2.13
y[1] (closed_form) = 0.63776196000000000000000000000001
y[1] (numeric) = 0.63776195999999999999999999999431
absolute error = 5.70e-30
relative error = 8.9375038925181426625068701181236e-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] = 2.14
y[1] (closed_form) = 0.64304725333333333333333333333335
y[1] (numeric) = 0.64304725333333333333333333332761
absolute error = 5.74e-30
relative error = 8.9262491523691861815276861768829e-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] = 2.15
y[1] (closed_form) = 0.64836166666666666666666666666668
y[1] (numeric) = 0.64836166666666666666666666666091
absolute error = 5.77e-30
relative error = 8.8993540128066382703069531665709e-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] = 2.16
y[1] (closed_form) = 0.65370528000000000000000000000001
y[1] (numeric) = 0.65370527999999999999999999999421
absolute error = 5.80e-30
relative error = 8.8724998519210369541454522135723e-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] = 2.17
y[1] (closed_form) = 0.65907817333333333333333333333335
y[1] (numeric) = 0.65907817333333333333333333332751
absolute error = 5.84e-30
relative error = 8.8608608755222420454200850185438e-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) = 0.66448042666666666666666666666668
y[1] (numeric) = 0.66448042666666666666666666666081
absolute error = 5.87e-30
relative error = 8.8339697670954220432316922824030e-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) = 0.66991212000000000000000000000001
y[1] (numeric) = 0.66991211999999999999999999999411
absolute error = 5.90e-30
relative error = 8.8071253286177297404322226622798e-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) = 0.67537333333333333333333333333335
y[1] (numeric) = 0.67537333333333333333333333332741
absolute error = 5.94e-30
relative error = 8.7951355299784810376483130318044e-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) = 0.68086414666666666666666666666668
y[1] (numeric) = 0.68086414666666666666666666666071
absolute error = 5.97e-30
relative error = 8.7682690140574494635846199450340e-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) = 0.68638464000000000000000000000001
y[1] (numeric) = 0.68638463999999999999999999999401
absolute error = 6.00e-30
relative error = 8.7414543542233112908820337238315e-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) = 0.69193489333333333333333333333335
y[1] (numeric) = 0.69193489333333333333333333332731
absolute error = 6.04e-30
relative error = 8.7291449790931196860005152315195e-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) = 0.69751498666666666666666666666668
y[1] (numeric) = 0.69751498666666666666666666666061
absolute error = 6.07e-30
relative error = 8.7023219802168551733292268186198e-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) = 0.70312500000000000000000000000001
y[1] (numeric) = 0.70312499999999999999999999999391
absolute error = 6.10e-30
relative error = 8.6755555555555555555555555555554e-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) = 0.70876501333333333333333333333335
y[1] (numeric) = 0.70876501333333333333333333332721
absolute error = 6.14e-30
relative error = 8.6629558238540593124837463760436e-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) = 0.71443510666666666666666666666668
y[1] (numeric) = 0.71443510666666666666666666666051
absolute error = 6.17e-30
relative error = 8.6361937458355209980069475122656e-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=470.3MB, alloc=40.3MB, time=5.63
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (closed_form) = 0.72013536000000000000000000000001
y[1] (numeric) = 0.72013535999999999999999999999381
absolute error = 6.20e-30
relative error = 8.6094925265161260794081823728249e-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) = 0.72586585333333333333333333333335
y[1] (numeric) = 0.72586585333333333333333333332711
absolute error = 6.24e-30
relative error = 8.5966297647761875706730678004615e-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] = 2.3
y[1] (closed_form) = 0.73162666666666666666666666666668
y[1] (numeric) = 0.73162666666666666666666666666041
absolute error = 6.27e-30
relative error = 8.5699445983379501385041551246536e-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) = 0.73741788000000000000000000000001
y[1] (numeric) = 0.73741787999999999999999999999371
absolute error = 6.30e-30
relative error = 8.5433241732625197533859634648402e-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) = 0.74323957333333333333333333333335
y[1] (numeric) = 0.74323957333333333333333333332701
absolute error = 6.34e-30
relative error = 8.5302239378427069043040549975737e-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) = 0.74909182666666666666666666666668
y[1] (numeric) = 0.74909182666666666666666666666031
absolute error = 6.37e-30
relative error = 8.5036303604398335712718228919579e-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) = 0.75497472000000000000000000000002
y[1] (numeric) = 0.75497471999999999999999999999361
absolute error = 6.41e-30
relative error = 8.4903505113389756944444444444442e-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) = 0.76088833333333333333333333333335
y[1] (numeric) = 0.76088833333333333333333333332691
absolute error = 6.44e-30
relative error = 8.4637912264830800840245940600130e-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) = 0.76683274666666666666666666666668
y[1] (numeric) = 0.76683274666666666666666666666021
absolute error = 6.47e-30
relative error = 8.4373026949153414696809331182099e-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) = 0.77280804000000000000000000000002
y[1] (numeric) = 0.77280803999999999999999999999351
absolute error = 6.51e-30
relative error = 8.4238254043009179873439204902680e-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) = 0.77881429333333333333333333333335
y[1] (numeric) = 0.77881429333333333333333333332681
absolute error = 6.54e-30
relative error = 8.3973805514132663067714285401232e-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) = 0.78485158666666666666666666666668
y[1] (numeric) = 0.78485158666666666666666666666011
absolute error = 6.57e-30
relative error = 8.3710093877791145532754566302801e-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) = 0.79092000000000000000000000000002
y[1] (numeric) = 0.79091999999999999999999999999341
absolute error = 6.61e-30
relative error = 8.3573559904920851666413796591309e-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) = 0.79701961333333333333333333333335
y[1] (numeric) = 0.79701961333333333333333333332671
absolute error = 6.64e-30
relative error = 8.3310371400145050382783553749767e-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) = 0.80315050666666666666666666666668
y[1] (numeric) = 0.80315050666666666666666666666001
absolute error = 6.67e-30
relative error = 8.3047946115139100204846620030768e-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) = 0.80931276000000000000000000000002
y[1] (numeric) = 0.80931275999999999999999999999331
absolute error = 6.71e-30
relative error = 8.2909850574949541139077060888053e-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) = 0.81550645333333333333333333333335
y[1] (numeric) = 0.81550645333333333333333333332661
absolute error = 6.74e-30
relative error = 8.2648027767906157096586392841786e-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) = 0.82173166666666666666666666666668
y[1] (numeric) = 0.82173166666666666666666666665991
absolute error = 6.77e-30
relative error = 8.2386991698425479525960420980895e-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) = 0.82798848000000000000000000000002
y[1] (numeric) = 0.82798847999999999999999999999321
absolute error = 6.81e-30
relative error = 8.2247521124931593251152479802616e-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) = 0.83427697333333333333333333333335
y[1] (numeric) = 0.83427697333333333333333333332651
absolute error = 6.84e-30
relative error = 8.1987160363193850905437911083501e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=512.7MB, alloc=40.3MB, time=6.12
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.84059722666666666666666666666668
y[1] (numeric) = 0.84059722666666666666666666665981
absolute error = 6.87e-30
relative error = 8.1727607254220142402880796244041e-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) = 0.84694932000000000000000000000002
y[1] (numeric) = 0.84694931999999999999999999999311
absolute error = 6.91e-30
relative error = 8.1586936040045465766475850054403e-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) = 0.85333333333333333333333333333335
y[1] (numeric) = 0.85333333333333333333333333332641
absolute error = 6.94e-30
relative error = 8.1328124999999999999999999999998e-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) = 0.85974934666666666666666666666668
y[1] (numeric) = 0.85974934666666666666666666665971
absolute error = 6.97e-30
relative error = 8.1070140117272319416010877340822e-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) = 0.86619744000000000000000000000002
y[1] (numeric) = 0.86619743999999999999999999999301
absolute error = 7.01e-30
relative error = 8.0928431282364445685731881174803e-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) = 0.87267769333333333333333333333335
y[1] (numeric) = 0.87267769333333333333333333332631
absolute error = 7.04e-30
relative error = 8.0671249577946509369545475720267e-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) = 0.87919018666666666666666666666668
y[1] (numeric) = 0.87919018666666666666666666665961
absolute error = 7.07e-30
relative error = 8.0414910302911479266738555043622e-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) = 0.88573500000000000000000000000002
y[1] (numeric) = 0.88573499999999999999999999999291
absolute error = 7.11e-30
relative error = 8.0272316211959559010313468475332e-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) = 0.89231221333333333333333333333335
y[1] (numeric) = 0.89231221333333333333333333332621
absolute error = 7.14e-30
relative error = 8.0016835960674810741878448045747e-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] = 2.57
y[1] (closed_form) = 0.89892190666666666666666666666668
y[1] (numeric) = 0.89892190666666666666666666665951
absolute error = 7.17e-30
relative error = 7.9762212343755244708465072004845e-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) = 0.90556416000000000000000000000002
y[1] (numeric) = 0.90556415999999999999999999999281
absolute error = 7.21e-30
relative error = 7.9618875375986611484270755591739e-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) = 0.91223905333333333333333333333335
y[1] (numeric) = 0.91223905333333333333333333332611
absolute error = 7.24e-30
relative error = 7.9365161725371722374116293406073e-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) = 0.91894666666666666666666666666669
y[1] (numeric) = 0.91894666666666666666666666665941
absolute error = 7.28e-30
relative error = 7.9221137244091060779733317856674e-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) = 0.92568708000000000000000000000002
y[1] (numeric) = 0.92568707999999999999999999999271
absolute error = 7.31e-30
relative error = 7.8968370175372870063175128251761e-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) = 0.93246037333333333333333333333335
y[1] (numeric) = 0.93246037333333333333333333332601
absolute error = 7.34e-30
relative error = 7.8716481792799116339213728589116e-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) = 0.93926662666666666666666666666669
y[1] (numeric) = 0.93926662666666666666666666665931
absolute error = 7.38e-30
relative error = 7.8571938898655925842398715695876e-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) = 0.94610592000000000000000000000002
y[1] (numeric) = 0.94610591999999999999999999999261
absolute error = 7.41e-30
relative error = 7.8321040417969269233618155565498e-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) = 0.95297833333333333333333333333335
y[1] (numeric) = 0.95297833333333333333333333332591
absolute error = 7.44e-30
relative error = 7.8071029946466079151852000832476e-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) = 0.95988394666666666666666666666669
y[1] (numeric) = 0.95988394666666666666666666665921
absolute error = 7.48e-30
relative error = 7.7926087064747382794720072826580e-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=555.2MB, alloc=40.3MB, time=6.64
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (closed_form) = 0.96682284000000000000000000000002
y[1] (numeric) = 0.96682283999999999999999999999251
absolute error = 7.51e-30
relative error = 7.7677105766347017619070728614560e-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) = 0.97379509333333333333333333333335
y[1] (numeric) = 0.97379509333333333333333333332581
absolute error = 7.54e-30
relative error = 7.7429020248914241123307090805906e-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) = 0.98080078666666666666666666666669
y[1] (numeric) = 0.98080078666666666666666666665911
absolute error = 7.58e-30
relative error = 7.7283787931708972664092072030555e-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) = 0.98784000000000000000000000000002
y[1] (numeric) = 0.98783999999999999999999999999241
absolute error = 7.61e-30
relative error = 7.7036767087787495950761256883704e-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) = 0.99491281333333333333333333333335
y[1] (numeric) = 0.99491281333333333333333333332571
absolute error = 7.64e-30
relative error = 7.6790648362474267594449582657567e-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) = 1.0020193066666666666666666666667
y[1] (numeric) = 1.002019306666666666666666666659
absolute error = 7.7e-30
relative error = 7.6844826729087109539126910768237e-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) = 1.00915956
y[1] (numeric) = 1.009159559999999999999999999992
absolute error = 8.0e-30
relative error = 7.9273886083980614522444795548486e-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) = 1.0163336533333333333333333333334
y[1] (numeric) = 1.016333653333333333333333333325
absolute error = 8.4e-30
relative error = 8.2650023173492211691530592368191e-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) = 1.0235416666666666666666666666667
y[1] (numeric) = 1.023541666666666666666666666658
absolute error = 8.7e-30
relative error = 8.4998982291878689191939751679216e-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) = 1.03078368
y[1] (numeric) = 1.030783679999999999999999999991
absolute error = 9.0e-30
relative error = 8.7312208901095523747523825755565e-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) = 1.0380597733333333333333333333334
y[1] (numeric) = 1.038059773333333333333333333324
absolute error = 9.4e-30
relative error = 9.0553552324019671416994702797006e-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) = 1.0453700266666666666666666666667
y[1] (numeric) = 1.045370026666666666666666666657
absolute error = 9.7e-30
relative error = 9.2790110224702316571744828548872e-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) = 1.05271452
y[1] (numeric) = 1.05271451999999999999999999999
absolute error = 1.00e-29
relative error = 9.4992515159760501831018726710448e-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) = 1.0600933333333333333333333333334
y[1] (numeric) = 1.060093333333333333333333333323
absolute error = 1.04e-29
relative error = 9.8104569408982856855371225175136e-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) = 1.0675065466666666666666666666667
y[1] (numeric) = 1.067506546666666666666666666656
absolute error = 1.07e-29
relative error = 1.0023357733412682521441148757482e-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] = 2.82
y[1] (closed_form) = 1.07495424
y[1] (numeric) = 1.074954239999999999999999999989
absolute error = 1.10e-29
relative error = 1.0232993731900624904740131077580e-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] = 2.83
y[1] (closed_form) = 1.0824364933333333333333333333334
y[1] (numeric) = 1.082436493333333333333333333322
absolute error = 1.14e-29
relative error = 1.0531795694446714699949079075764e-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] = 2.84
y[1] (closed_form) = 1.0899533866666666666666666666667
y[1] (numeric) = 1.089953386666666666666666666655
absolute error = 1.17e-29
relative error = 1.0734404005827576430669132957661e-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] = 2.85
y[1] (closed_form) = 1.097505
y[1] (numeric) = 1.097504999999999999999999999988
absolute error = 1.20e-29
relative error = 1.0933890961772383724903303401807e-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] = 2.86
y[1] (closed_form) = 1.1050914133333333333333333333334
y[1] (numeric) = 1.105091413333333333333333333321
absolute error = 1.24e-29
relative error = 1.1220791194637340167671920860459e-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=597.6MB, alloc=40.3MB, time=7.14
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (closed_form) = 1.1127127066666666666666666666667
y[1] (numeric) = 1.112712706666666666666666666654
absolute error = 1.27e-29
relative error = 1.1413548100879660425794484501438e-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] = 2.88
y[1] (closed_form) = 1.12036896
y[1] (numeric) = 1.120368959999999999999999999987
absolute error = 1.30e-29
relative error = 1.1603320391882331334848834084086e-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] = 2.89
y[1] (closed_form) = 1.1280602533333333333333333333334
y[1] (numeric) = 1.12806025333333333333333333332
absolute error = 1.34e-29
relative error = 1.1878798105335248108910116255137e-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] = 2.9
y[1] (closed_form) = 1.1357866666666666666666666666667
y[1] (numeric) = 1.135786666666666666666666666653
absolute error = 1.37e-29
relative error = 1.2062124342599549211119459053343e-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] = 2.91
y[1] (closed_form) = 1.14354828
y[1] (numeric) = 1.143548279999999999999999999986
absolute error = 1.40e-29
relative error = 1.2242596351069672370982010484070e-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] = 2.92
y[1] (closed_form) = 1.1513451733333333333333333333334
y[1] (numeric) = 1.151345173333333333333333333319
absolute error = 1.44e-29
relative error = 1.2507109365221582897908357352387e-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] = 2.93
y[1] (closed_form) = 1.1591774266666666666666666666667
y[1] (numeric) = 1.159177426666666666666666666652
absolute error = 1.47e-29
relative error = 1.2681406367851170600780160119750e-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] = 2.94
y[1] (closed_form) = 1.16704512
y[1] (numeric) = 1.167045119999999999999999999985
absolute error = 1.50e-29
relative error = 1.2852973499430767509657210168532e-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] = 2.95
y[1] (closed_form) = 1.1749483333333333333333333333334
y[1] (numeric) = 1.174948333333333333333333333318
absolute error = 1.54e-29
relative error = 1.3106959313104547859551271048797e-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] = 2.96
y[1] (closed_form) = 1.1828871466666666666666666666667
y[1] (numeric) = 1.182887146666666666666666666651
absolute error = 1.57e-29
relative error = 1.3272610192985893858615038801785e-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] = 2.97
y[1] (closed_form) = 1.19086164
y[1] (numeric) = 1.190861639999999999999999999984
absolute error = 1.60e-29
relative error = 1.3435649837541160533141364768455e-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] = 2.98
y[1] (closed_form) = 1.1988718933333333333333333333334
y[1] (numeric) = 1.198871893333333333333333333317
absolute error = 1.64e-29
relative error = 1.3679526637663994169096209912536e-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] = 2.99
y[1] (closed_form) = 1.2069179866666666666666666666667
y[1] (numeric) = 1.20691798666666666666666666665
absolute error = 1.67e-29
relative error = 1.3836897108579009881135364414543e-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
y[1] (closed_form) = 1.215
y[1] (numeric) = 1.214999999999999999999999999983
absolute error = 1.70e-29
relative error = 1.3991769547325102880658436213992e-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] = 3.01
y[1] (closed_form) = 1.2231180133333333333333333333334
y[1] (numeric) = 1.223118013333333333333333333316
absolute error = 1.74e-29
relative error = 1.4225937162498497964508216274491e-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] = 3.02
y[1] (closed_form) = 1.2312721066666666666666666666667
y[1] (numeric) = 1.231272106666666666666666666649
absolute error = 1.77e-29
relative error = 1.4375376412869387073366983228879e-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] = 3.03
y[1] (closed_form) = 1.23946236
y[1] (numeric) = 1.239462359999999999999999999982
absolute error = 1.80e-29
relative error = 1.4522425674951516881884174360890e-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] = 3.04
y[1] (closed_form) = 1.2476888533333333333333333333334
y[1] (numeric) = 1.247688853333333333333333333315
absolute error = 1.84e-29
relative error = 1.4747266476607885914804571361936e-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] = 3.05
y[1] (closed_form) = 1.2559516666666666666666666666667
y[1] (numeric) = 1.255951666666666666666666666648
absolute error = 1.87e-29
relative error = 1.4889107993805494107390013681524e-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] = 3.06
y[1] (closed_form) = 1.26425088
y[1] (numeric) = 1.264250879999999999999999999981
absolute error = 1.90e-29
relative error = 1.5028662665435518621114188981225e-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=639.9MB, alloc=40.3MB, time=7.64
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (closed_form) = 1.2725865733333333333333333333334
y[1] (numeric) = 1.272586573333333333333333333314
absolute error = 1.94e-29
relative error = 1.5244542419762341669841914514200e-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] = 3.08
y[1] (closed_form) = 1.2809588266666666666666666666667
y[1] (numeric) = 1.280958826666666666666666666647
absolute error = 1.97e-29
relative error = 1.5379104768936002855860722330580e-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] = 3.09
y[1] (closed_form) = 1.28936772
y[1] (numeric) = 1.28936771999999999999999999998
absolute error = 2.00e-29
relative error = 1.5511478757976041156048175302543e-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] = 3.1
y[1] (closed_form) = 1.2978133333333333333333333333334
y[1] (numeric) = 1.297813333333333333333333333313
absolute error = 2.04e-29
relative error = 1.5718747431577217062546231610092e-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] = 3.11
y[1] (closed_form) = 1.3062957466666666666666666666667
y[1] (numeric) = 1.306295746666666666666666666646
absolute error = 2.07e-29
relative error = 1.5846334991766693445356697734431e-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] = 3.12
y[1] (closed_form) = 1.31481504
y[1] (numeric) = 1.314815039999999999999999999979
absolute error = 2.10e-29
relative error = 1.5971828250458710907353174177259e-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] = 3.13
y[1] (closed_form) = 1.3233712933333333333333333333334
y[1] (numeric) = 1.323371293333333333333333333312
absolute error = 2.14e-29
relative error = 1.6170820772526555333974450123329e-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] = 3.14
y[1] (closed_form) = 1.3319645866666666666666666666667
y[1] (numeric) = 1.331964586666666666666666666645
absolute error = 2.17e-29
relative error = 1.6291724432633564311779900774939e-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] = 3.15
y[1] (closed_form) = 1.340595
y[1] (numeric) = 1.340594999999999999999999999978
absolute error = 2.20e-29
relative error = 1.6410623640995229730082537977540e-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] = 3.16
y[1] (closed_form) = 1.3492626133333333333333333333334
y[1] (numeric) = 1.349262613333333333333333333311
absolute error = 2.24e-29
relative error = 1.6601660624584513797047228641311e-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] = 3.17
y[1] (closed_form) = 1.3579675066666666666666666666667
y[1] (numeric) = 1.357967506666666666666666666644
absolute error = 2.27e-29
relative error = 1.6716158441611410967192214505908e-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] = 3.18
y[1] (closed_form) = 1.36670976
y[1] (numeric) = 1.366709759999999999999999999977
absolute error = 2.30e-29
relative error = 1.6828737653852709736996390513813e-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] = 3.19
y[1] (closed_form) = 1.3754894533333333333333333333334
y[1] (numeric) = 1.37548945333333333333333333331
absolute error = 2.34e-29
relative error = 1.7012126078679057168391810957687e-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] = 3.2
y[1] (closed_form) = 1.3843066666666666666666666666667
y[1] (numeric) = 1.384306666666666666666666666643
absolute error = 2.37e-29
relative error = 1.7120483900484478391107943326623e-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] = 3.21
y[1] (closed_form) = 1.39316148
y[1] (numeric) = 1.393161479999999999999999999976
absolute error = 2.40e-29
relative error = 1.7227005156645588564507252956779e-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] = 3.22
y[1] (closed_form) = 1.4020539733333333333333333333334
y[1] (numeric) = 1.402053973333333333333333333309
absolute error = 2.44e-29
relative error = 1.7403039015673462233237088504666e-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] = 3.23
y[1] (closed_form) = 1.4109842266666666666666666666667
y[1] (numeric) = 1.410984226666666666666666666642
absolute error = 2.47e-29
relative error = 1.7505511070348180693576758812243e-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] = 3.24
y[1] (closed_form) = 1.41995232
y[1] (numeric) = 1.419952319999999999999999999975
absolute error = 2.50e-29
relative error = 1.7606224975216069226887843670695e-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] = 3.25
y[1] (closed_form) = 1.4289583333333333333333333333334
y[1] (numeric) = 1.428958333333333333333333333308
absolute error = 2.54e-29
relative error = 1.7775185887155562035282111094911e-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=682.1MB, alloc=40.3MB, time=8.14
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (closed_form) = 1.4380023466666666666666666666667
y[1] (numeric) = 1.438002346666666666666666666641
absolute error = 2.57e-29
relative error = 1.7872015340985628062396486028914e-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] = 3.27
y[1] (closed_form) = 1.44708444
y[1] (numeric) = 1.447084439999999999999999999974
absolute error = 2.60e-29
relative error = 1.7967161612213866386401058945807e-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] = 3.28
y[1] (closed_form) = 1.4562046933333333333333333333334
y[1] (numeric) = 1.456204693333333333333333333307
absolute error = 2.64e-29
relative error = 1.8129319401909724193353330033674e-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] = 3.29
y[1] (closed_form) = 1.4653631866666666666666666666667
y[1] (numeric) = 1.46536318666666666666666666664
absolute error = 2.67e-29
relative error = 1.8220738887767336569002929958506e-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] = 3.3
y[1] (closed_form) = 1.47456
y[1] (numeric) = 1.474559999999999999999999999973
absolute error = 2.70e-29
relative error = 1.8310546875000000000000000000000e-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] = 3.31
y[1] (closed_form) = 1.4837952133333333333333333333334
y[1] (numeric) = 1.483795213333333333333333333306
absolute error = 2.74e-29
relative error = 1.8466160123569972248012194243408e-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] = 3.32
y[1] (closed_form) = 1.4930689066666666666666666666667
y[1] (numeric) = 1.493068906666666666666666666639
absolute error = 2.77e-29
relative error = 1.8552392241454754738356884765523e-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] = 3.33
y[1] (closed_form) = 1.50238116
y[1] (numeric) = 1.502381159999999999999999999972
absolute error = 2.80e-29
relative error = 1.8637081418140254101695471207852e-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] = 3.34
y[1] (closed_form) = 1.5117320533333333333333333333334
y[1] (numeric) = 1.511732053333333333333333333305
absolute error = 2.84e-29
relative error = 1.8786397984602280135993059228555e-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] = 3.35
y[1] (closed_form) = 1.5211216666666666666666666666667
y[1] (numeric) = 1.521121666666666666666666666638
absolute error = 2.87e-29
relative error = 1.8867655775946039819300012162077e-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] = 3.36
y[1] (closed_form) = 1.53055008
y[1] (numeric) = 1.530550079999999999999999999971
absolute error = 2.90e-29
relative error = 1.8947436205419688064045575039270e-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] = 3.37
y[1] (closed_form) = 1.5400173733333333333333333333334
y[1] (numeric) = 1.540017373333333333333333333304
absolute error = 2.94e-29
relative error = 1.9090693721437930444819310826302e-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] = 3.38
y[1] (closed_form) = 1.5495236266666666666666666666667
y[1] (numeric) = 1.549523626666666666666666666637
absolute error = 2.97e-29
relative error = 1.9167181118683942708861094100387e-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] = 3.39
y[1] (closed_form) = 1.55906892
y[1] (numeric) = 1.55906891999999999999999999997
absolute error = 3.00e-29
relative error = 1.9242253895998388576689733510947e-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] = 3.4
y[1] (closed_form) = 1.5686533333333333333333333333334
y[1] (numeric) = 1.568653333333333333333333333303
absolute error = 3.04e-29
relative error = 1.9379680235276117944053923110268e-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] = 3.41
y[1] (closed_form) = 1.5782769466666666666666666666667
y[1] (numeric) = 1.578276946666666666666666666636
absolute error = 3.07e-29
relative error = 1.9451592488148953595985279169973e-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] = 3.42
y[1] (closed_form) = 1.58793984
y[1] (numeric) = 1.587939839999999999999999999969
absolute error = 3.10e-29
relative error = 1.9522150159038770637557654577141e-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] = 3.43
y[1] (closed_form) = 1.5976420933333333333333333333334
y[1] (numeric) = 1.597642093333333333333333333302
absolute error = 3.14e-29
relative error = 1.9653963882791036794331833536984e-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] = 3.44
y[1] (closed_form) = 1.6073837866666666666666666666667
y[1] (numeric) = 1.607383786666666666666666666635
absolute error = 3.17e-29
relative error = 1.9721487962584401332437644595212e-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] = 3.45
y[1] (closed_form) = 1.617165
y[1] (numeric) = 1.617164999999999999999999999968
absolute error = 3.20e-29
relative error = 1.9787714920864599468823527593041e-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=724.5MB, alloc=40.3MB, time=8.66
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (closed_form) = 1.6269858133333333333333333333334
y[1] (numeric) = 1.626985813333333333333333333301
absolute error = 3.24e-29
relative error = 1.9914125700714981034540633077103e-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] = 3.47
y[1] (closed_form) = 1.6368463066666666666666666666667
y[1] (numeric) = 1.636846306666666666666666666634
absolute error = 3.27e-29
relative error = 1.9977440683842497678442186137891e-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] = 3.48
y[1] (closed_form) = 1.64674656
y[1] (numeric) = 1.646746559999999999999999999967
absolute error = 3.30e-29
relative error = 2.0039513548460061759594627603169e-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] = 3.49
y[1] (closed_form) = 1.6566866533333333333333333333334
y[1] (numeric) = 1.6566866533333333333333333333
absolute error = 3.34e-29
relative error = 2.0160722568023102884255746483991e-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] = 3.5
y[1] (closed_form) = 1.6666666666666666666666666666667
y[1] (numeric) = 1.666666666666666666666666666633
absolute error = 3.37e-29
relative error = 2.0220000000000000000000000000000e-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] = 3.51
y[1] (closed_form) = 1.67668668
y[1] (numeric) = 1.676686679999999999999999999966
absolute error = 3.40e-29
relative error = 2.0278087972882327663031234911462e-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] = 3.52
y[1] (closed_form) = 1.6867467733333333333333333333334
y[1] (numeric) = 1.686746773333333333333333333299
absolute error = 3.44e-29
relative error = 2.0394288309216112486926312622242e-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] = 3.53
y[1] (closed_form) = 1.6968470266666666666666666666667
y[1] (numeric) = 1.696847026666666666666666666632
absolute error = 3.47e-29
relative error = 2.0449692550167967606304043420075e-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] = 3.54
y[1] (closed_form) = 1.70698752
y[1] (numeric) = 1.706987519999999999999999999965
absolute error = 3.50e-29
relative error = 2.0503957755941882926009910136894e-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] = 3.55
y[1] (closed_form) = 1.7171683333333333333333333333334
y[1] (numeric) = 1.717168333333333333333333333298
absolute error = 3.54e-29
relative error = 2.0615334741983168025654638790023e-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] = 3.56
y[1] (closed_form) = 1.7273895466666666666666666666667
y[1] (numeric) = 1.727389546666666666666666666631
absolute error = 3.57e-29
relative error = 2.0667023294710841366984151252939e-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] = 3.57
y[1] (closed_form) = 1.73765124
y[1] (numeric) = 1.737651239999999999999999999964
absolute error = 3.60e-29
relative error = 2.0717621103300337759376847105406e-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] = 3.58
y[1] (closed_form) = 1.7479534933333333333333333333334
y[1] (numeric) = 1.747953493333333333333333333297
absolute error = 3.64e-29
relative error = 2.0824352672327391898878285945547e-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] = 3.59
y[1] (closed_form) = 1.7582963866666666666666666666667
y[1] (numeric) = 1.75829638666666666666666666663
absolute error = 3.67e-29
relative error = 2.0872476493894707732588640781980e-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] = 3.6
y[1] (closed_form) = 1.76868
y[1] (numeric) = 1.768679999999999999999999999963
absolute error = 3.70e-29
relative error = 2.0919555826944387905104371621774e-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] = 3.61
y[1] (closed_form) = 1.7791044133333333333333333333334
y[1] (numeric) = 1.779104413333333333333333333296
absolute error = 3.74e-29
relative error = 2.1021812840049837509630594587324e-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] = 3.62
y[1] (closed_form) = 1.7895697066666666666666666666667
y[1] (numeric) = 1.789569706666666666666666666629
absolute error = 3.77e-29
relative error = 2.1066516637802124023437500000000e-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] = 3.63
y[1] (closed_form) = 1.80007596
y[1] (numeric) = 1.800075959999999999999999999962
absolute error = 3.80e-29
relative error = 2.1110220259816146869713209213682e-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] = 3.64
y[1] (closed_form) = 1.8106232533333333333333333333334
y[1] (numeric) = 1.810623253333333333333333333295
absolute error = 3.84e-29
relative error = 2.1208166817313381239832966834609e-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] = 3.65
y[1] (closed_form) = 1.8212116666666666666666666666667
y[1] (numeric) = 1.821211666666666666666666666628
absolute error = 3.87e-29
relative error = 2.1249589330180365269641914220111e-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=766.9MB, alloc=40.3MB, time=9.16
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (closed_form) = 1.83184128
y[1] (numeric) = 1.831841279999999999999999999961
absolute error = 3.90e-29
relative error = 2.1290054125213293588405213796689e-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] = 3.67
y[1] (closed_form) = 1.8425121733333333333333333333334
y[1] (numeric) = 1.842512173333333333333333333294
absolute error = 3.94e-29
relative error = 2.1383847862845056336235658195162e-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] = 3.68
y[1] (closed_form) = 1.8532244266666666666666666666667
y[1] (numeric) = 1.853224426666666666666666666627
absolute error = 3.97e-29
relative error = 2.1422122128730557346707970580602e-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] = 3.69
y[1] (closed_form) = 1.86397812
y[1] (numeric) = 1.86397811999999999999999999996
absolute error = 4.00e-29
relative error = 2.1459479363416561992691201761531e-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] = 3.7
y[1] (closed_form) = 1.8747733333333333333333333333334
y[1] (numeric) = 1.874773333333333333333333333293
absolute error = 4.04e-29
relative error = 2.1549271734182976786527082385070e-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] = 3.71
y[1] (closed_form) = 1.8856101466666666666666666666667
y[1] (numeric) = 1.885610146666666666666666666626
absolute error = 4.07e-29
relative error = 2.1584525344196104276372830436119e-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] = 3.72
y[1] (closed_form) = 1.89648864
y[1] (numeric) = 1.896488639999999999999999999959
absolute error = 4.10e-29
relative error = 2.1618900917856275690636354141304e-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] = 3.73
y[1] (closed_form) = 1.9074088933333333333333333333334
y[1] (numeric) = 1.907408893333333333333333333292
absolute error = 4.14e-29
relative error = 2.1704837460231477582779017066132e-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] = 3.74
y[1] (closed_form) = 1.9183709866666666666666666666667
y[1] (numeric) = 1.918370986666666666666666666625
absolute error = 4.17e-29
relative error = 2.1737192800469376017251970672005e-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] = 3.75
y[1] (closed_form) = 1.929375
y[1] (numeric) = 1.929374999999999999999999999958
absolute error = 4.20e-29
relative error = 2.1768707482993197278911564625850e-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] = 3.76
y[1] (closed_form) = 1.9404210133333333333333333333334
y[1] (numeric) = 1.940421013333333333333333333291
absolute error = 4.24e-29
relative error = 2.1850928076254736635298995181636e-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] = 3.77
y[1] (closed_form) = 1.9515091066666666666666666666667
y[1] (numeric) = 1.951509106666666666666666666624
absolute error = 4.27e-29
relative error = 2.1880502557805127810044961921879e-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] = 3.78
y[1] (closed_form) = 1.96263936
y[1] (numeric) = 1.962639359999999999999999999957
absolute error = 4.30e-29
relative error = 2.1909272215961265548042407546540e-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] = 3.79
y[1] (closed_form) = 1.9738118533333333333333333333334
y[1] (numeric) = 1.97381185333333333333333333329
absolute error = 4.34e-29
relative error = 2.1987911323314307924343940677790e-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] = 3.8
y[1] (closed_form) = 1.9850266666666666666666666666667
y[1] (numeric) = 1.985026666666666666666666666623
absolute error = 4.37e-29
relative error = 2.2014817601106954062749786736702e-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) = 1.99628388
y[1] (numeric) = 1.996283879999999999999999999956
absolute error = 4.40e-29
relative error = 2.2040953413900231464074137592094e-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) = 2.0075835733333333333333333333334
y[1] (numeric) = 2.007583573333333333333333333289
absolute error = 4.44e-29
relative error = 2.2116140314039097404316943072815e-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) = 2.0189258266666666666666666666667
y[1] (numeric) = 2.018925826666666666666666666622
absolute error = 4.47e-29
relative error = 2.2140486495138665718325184368503e-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) = 2.03031072
y[1] (numeric) = 2.030310719999999999999999999955
absolute error = 4.50e-29
relative error = 2.2164095158794216483277988110115e-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=809.2MB, alloc=40.3MB, time=9.66
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (closed_form) = 2.0417383333333333333333333333334
y[1] (numeric) = 2.041738333333333333333333333288
absolute error = 4.54e-29
relative error = 2.2235954166506808332442208151060e-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) = 2.0532087466666666666666666666667
y[1] (numeric) = 2.053208746666666666666666666621
absolute error = 4.57e-29
relative error = 2.2257844008405289214431296402815e-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) = 2.06472204
y[1] (numeric) = 2.064722039999999999999999999954
absolute error = 4.60e-29
relative error = 2.2279027931527286840024238807467e-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) = 2.0762782933333333333333333333334
y[1] (numeric) = 2.076278293333333333333333333287
absolute error = 4.64e-29
relative error = 2.2347678607913266758485657593800e-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) = 2.0878775866666666666666666666667
y[1] (numeric) = 2.08787758666666666666666666662
absolute error = 4.67e-29
relative error = 2.2367211707347925678835615515875e-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] = 3.9
y[1] (closed_form) = 2.09952
y[1] (numeric) = 2.099519999999999999999999999953
absolute error = 4.70e-29
relative error = 2.2386069196768785246151501295534e-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) = 2.1112056133333333333333333333334
y[1] (numeric) = 2.111205613333333333333333333286
absolute error = 4.74e-29
relative error = 2.2451626549609843465049268752417e-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) = 2.1229345066666666666666666666667
y[1] (numeric) = 2.122934506666666666666666666619
absolute error = 4.77e-29
relative error = 2.2468898522402524987927402728228e-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) = 2.13470676
y[1] (numeric) = 2.134706759999999999999999999952
absolute error = 4.80e-29
relative error = 2.2485523960208942234295449553924e-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) = 2.1465224533333333333333333333334
y[1] (numeric) = 2.146522453333333333333333333285
absolute error = 4.84e-29
relative error = 2.2548098634998982291878689191939e-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) = 2.1583816666666666666666666666667
y[1] (numeric) = 2.158381666666666666666666666618
absolute error = 4.87e-29
relative error = 2.2563201287384297957806350282503e-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) = 2.17028448
y[1] (numeric) = 2.170284479999999999999999999951
absolute error = 4.90e-29
relative error = 2.2577685299578790703051058080644e-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) = 2.1822309733333333333333333333334
y[1] (numeric) = 2.182230973333333333333333333284
absolute error = 4.94e-29
relative error = 2.2637383761693224492955139249146e-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) = 2.1942212266666666666666666666667
y[1] (numeric) = 2.194221226666666666666666666617
absolute error = 4.97e-29
relative error = 2.2650405253576619001747329129839e-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) = 2.20625532
y[1] (numeric) = 2.20625531999999999999999999995
absolute error = 5.00e-29
relative error = 2.2662834870807246370741895820108e-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) = 2.2183333333333333333333333333334
y[1] (numeric) = 2.218333333333333333333333333283
absolute error = 5.04e-29
relative error = 2.2719759579263711495116453794139e-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) = 2.2304553466666666666666666666667
y[1] (numeric) = 2.230455346666666666666666666616
absolute error = 5.07e-29
relative error = 2.2730784579825497037074360977568e-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) = 2.24262144
y[1] (numeric) = 2.242621439999999999999999999949
absolute error = 5.10e-29
relative error = 2.2741243390592038574285636009972e-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) = 2.2548316933333333333333333333334
y[1] (numeric) = 2.254831693333333333333333333282
absolute error = 5.14e-29
relative error = 2.2795492963829607811615113185949e-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) = 2.2670861866666666666666666666667
y[1] (numeric) = 2.267086186666666666666666666615
absolute error = 5.17e-29
relative error = 2.2804602799867676255495865165285e-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=851.7MB, alloc=40.3MB, time=10.16
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (closed_form) = 2.279385
y[1] (numeric) = 2.279384999999999999999999999948
absolute error = 5.20e-29
relative error = 2.2813171096589650278474237568467e-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) = 2.2917282133333333333333333333334
y[1] (numeric) = 2.291728213333333333333333333281
absolute error = 5.24e-29
relative error = 2.2864840470669890256212813507798e-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) = 2.3041159066666666666666666666667
y[1] (numeric) = 2.304115906666666666666666666614
absolute error = 5.27e-29
relative error = 2.2872113268051856627374642547640e-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) = 2.31654816
y[1] (numeric) = 2.316548159999999999999999999947
absolute error = 5.30e-29
relative error = 2.2878868186362246835394952462374e-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) = 2.3290250533333333333333333333334
y[1] (numeric) = 2.32902505333333333333333333328
absolute error = 5.34e-29
relative error = 2.2928048765973200150891177761425e-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) = 2.3415466666666666666666666666667
y[1] (numeric) = 2.341546666666666666666666666613
absolute error = 5.37e-29
relative error = 2.2933559584548104956268221574344e-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) = 2.35411308
y[1] (numeric) = 2.354113079999999999999999999946
absolute error = 5.40e-29
relative error = 2.2938575236156455152103398533430e-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) = 2.3667243733333333333333333333334
y[1] (numeric) = 2.366724373333333333333333333279
absolute error = 5.44e-29
relative error = 2.2985355038779674149691719066140e-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) = 2.3793806266666666666666666666667
y[1] (numeric) = 2.379380626666666666666666666612
absolute error = 5.47e-29
relative error = 2.2989176001079989740971637845898e-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) = 2.39208192
y[1] (numeric) = 2.392081919999999999999999999945
absolute error = 5.50e-29
relative error = 2.2992523600529533704263773708887e-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) = 2.4048283333333333333333333333334
y[1] (numeric) = 2.404828333333333333333333333278
absolute error = 5.54e-29
relative error = 2.3036987394110598330996599202853e-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) = 2.4176199466666666666666666666667
y[1] (numeric) = 2.417619946666666666666666666611
absolute error = 5.57e-29
relative error = 2.3039187808157064841335745431970e-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] = 4.17
y[1] (closed_form) = 2.43045684
y[1] (numeric) = 2.430456839999999999999999999944
absolute error = 5.60e-29
relative error = 2.3040935793782703008213056768373e-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) = 2.4433390933333333333333333333334
y[1] (numeric) = 2.443339093333333333333333333277
absolute error = 5.64e-29
relative error = 2.3083165228227129090751611434127e-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) = 2.4562667866666666666666666666667
y[1] (numeric) = 2.45626678666666666666666666661
absolute error = 5.67e-29
relative error = 2.3083811704731813361272824603976e-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) = 2.46924
y[1] (numeric) = 2.469239999999999999999999999943
absolute error = 5.70e-29
relative error = 2.3084025854108956602031394275162e-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) = 2.4822588133333333333333333333334
y[1] (numeric) = 2.482258813333333333333333333276
absolute error = 5.74e-29
relative error = 2.3124099586907969537487552130677e-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) = 2.4953233066666666666666666666667
y[1] (numeric) = 2.495323306666666666666666666609
absolute error = 5.77e-29
relative error = 2.3123256151154825906647511615969e-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) = 2.5084335600000000000000000000001
y[1] (numeric) = 2.508433559999999999999999999942
absolute error = 5.81e-29
relative error = 2.3161865208022491933172828384579e-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) = 2.5215896533333333333333333333334
y[1] (numeric) = 2.521589653333333333333333333275
absolute error = 5.84e-29
relative error = 2.3159993507587573434628729229557e-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=894.1MB, alloc=40.3MB, time=10.66
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (closed_form) = 2.5347916666666666666666666666667
y[1] (numeric) = 2.534791666666666666666666666608
absolute error = 5.87e-29
relative error = 2.3157721706254623161009287416783e-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) = 2.5480396800000000000000000000001
y[1] (numeric) = 2.548039679999999999999999999941
absolute error = 5.91e-29
relative error = 2.3194301275559413580246913580246e-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) = 2.5613337733333333333333333333334
y[1] (numeric) = 2.561333773333333333333333333274
absolute error = 5.94e-29
relative error = 2.3191042346150976455063909333112e-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) = 2.5746740266666666666666666666667
y[1] (numeric) = 2.574674026666666666666666666607
absolute error = 5.97e-29
relative error = 2.3187401349323952217391900567948e-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) = 2.5880605200000000000000000000001
y[1] (numeric) = 2.58806051999999999999999999994
absolute error = 6.01e-29
relative error = 2.3222022644199989573659583509275e-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) = 2.6014933333333333333333333333334
y[1] (numeric) = 2.601493333333333333333333333273
absolute error = 6.04e-29
relative error = 2.3217434089138546065849358317274e-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) = 2.6149725466666666666666666666667
y[1] (numeric) = 2.614972546666666666666666666606
absolute error = 6.07e-29
relative error = 2.3212480787752412911246318705775e-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) = 2.6284982400000000000000000000001
y[1] (numeric) = 2.628498239999999999999999999939
absolute error = 6.11e-29
relative error = 2.3245212444958684849642509176646e-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) = 2.6420704933333333333333333333334
y[1] (numeric) = 2.642070493333333333333333333272
absolute error = 6.14e-29
relative error = 2.3239349652073628497230053720443e-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) = 2.6556893866666666666666666666667
y[1] (numeric) = 2.655689386666666666666666666605
absolute error = 6.17e-29
relative error = 2.3233138751005740109044077765239e-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) = 2.6693550000000000000000000000001
y[1] (numeric) = 2.669354999999999999999999999938
absolute error = 6.21e-29
relative error = 2.3264046932685985940423810246295e-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) = 2.6830674133333333333333333333334
y[1] (numeric) = 2.683067413333333333333333333271
absolute error = 6.24e-29
relative error = 2.3256963164588097118056757883126e-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) = 2.6968267066666666666666666666667
y[1] (numeric) = 2.696826706666666666666666666604
absolute error = 6.27e-29
relative error = 2.3249547271614827229808457894091e-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) = 2.7106329600000000000000000000001
y[1] (numeric) = 2.710632959999999999999999999937
absolute error = 6.31e-29
relative error = 2.3278695762631027699154075068872e-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) = 2.7244862533333333333333333333334
y[1] (numeric) = 2.72448625333333333333333333327
absolute error = 6.34e-29
relative error = 2.3270442242985024861127457380111e-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) = 2.7383866666666666666666666666667
y[1] (numeric) = 2.738386666666666666666666666603
absolute error = 6.37e-29
relative error = 2.3261871953802482240151135218303e-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) = 2.7523342800000000000000000000001
y[1] (numeric) = 2.752334279999999999999999999936
absolute error = 6.41e-29
relative error = 2.3289322254853432992158205434261e-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) = 2.7663291733333333333333333333334
y[1] (numeric) = 2.766329173333333333333333333269
absolute error = 6.44e-29
relative error = 2.3279948250843977651866621917754e-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) = 2.7803714266666666666666666666667
y[1] (numeric) = 2.780371426666666666666666666602
absolute error = 6.47e-29
relative error = 2.3270272230342826570168991858004e-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] = 4.44
y[1] (closed_form) = 2.7944611200000000000000000000001
y[1] (numeric) = 2.794461119999999999999999999935
absolute error = 6.51e-29
relative error = 2.3296083647068240477076310154567e-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=936.6MB, alloc=40.3MB, time=11.16
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (closed_form) = 2.8085983333333333333333333333334
y[1] (numeric) = 2.808598333333333333333333333268
absolute error = 6.54e-29
relative error = 2.3285636548242628737110266746342e-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) = 2.8227831466666666666666666666667
y[1] (numeric) = 2.822783146666666666666666666601
absolute error = 6.57e-29
relative error = 2.3274901608217055341542448205822e-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) = 2.8370156400000000000000000000001
y[1] (numeric) = 2.837015639999999999999999999934
absolute error = 6.61e-29
relative error = 2.3299131336477228585176217075771e-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) = 2.8512958933333333333333333333334
y[1] (numeric) = 2.851295893333333333333333333267
absolute error = 6.64e-29
relative error = 2.3287656730138406493548907576957e-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) = 2.8656239866666666666666666666667
y[1] (numeric) = 2.8656239866666666666666666666
absolute error = 6.67e-29
relative error = 2.3275907903599857732439695426149e-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) = 2.8800000000000000000000000000001
y[1] (numeric) = 2.879999999999999999999999999933
absolute error = 6.71e-29
relative error = 2.3298611111111111111111111111110e-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) = 2.8944240133333333333333333333334
y[1] (numeric) = 2.894424013333333333333333333266
absolute error = 6.74e-29
relative error = 2.3286152854425599684424950942801e-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) = 2.9088961066666666666666666666667
y[1] (numeric) = 2.908896106666666666666666666599
absolute error = 6.77e-29
relative error = 2.3273433466683040652012194243234e-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) = 2.9234163600000000000000000000001
y[1] (numeric) = 2.923416359999999999999999999932
absolute error = 6.81e-29
relative error = 2.3294663371179875315468235253359e-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) = 2.9379848533333333333333333333334
y[1] (numeric) = 2.937984853333333333333333333265
absolute error = 6.84e-29
relative error = 2.3281263660156650501270567022301e-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) = 2.9526016666666666666666666666667
y[1] (numeric) = 2.952601666666666666666666666598
absolute error = 6.87e-29
relative error = 2.3267615396816705718854727553835e-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) = 2.9672668800000000000000000000001
y[1] (numeric) = 2.967266879999999999999999999931
absolute error = 6.91e-29
relative error = 2.3287423340902858053671262626703e-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) = 2.9819805733333333333333333333334
y[1] (numeric) = 2.981980573333333333333333333264
absolute error = 6.94e-29
relative error = 2.3273122776391170140553967302170e-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) = 2.9967428266666666666666666666667
y[1] (numeric) = 2.996742826666666666666666666597
absolute error = 6.97e-29
relative error = 2.3258585748423604023910190989940e-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) = 3.0115537200000000000000000000001
y[1] (numeric) = 3.01155371999999999999999999993
absolute error = 7.01e-29
relative error = 2.3277021271265916518334595738175e-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) = 3.0264133333333333333333333333334
y[1] (numeric) = 3.026413333333333333333333333263
absolute error = 7.04e-29
relative error = 2.3261858922112423506813345610425e-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) = 3.0413217466666666666666666666667
y[1] (numeric) = 3.041321746666666666666666666596
absolute error = 7.07e-29
relative error = 2.3246471728118946669726681247198e-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) = 3.0562790400000000000000000000001
y[1] (numeric) = 3.056279039999999999999999999929
absolute error = 7.11e-29
relative error = 2.3263582634130161099426314162727e-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) = 3.0712852933333333333333333333334
y[1] (numeric) = 3.071285293333333333333333333262
absolute error = 7.14e-29
relative error = 2.3247596097628564166341182232600e-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=978.9MB, alloc=40.3MB, time=11.66
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (closed_form) = 3.0863405866666666666666666666667
y[1] (numeric) = 3.086340586666666666666666666595
absolute error = 7.17e-29
relative error = 2.3231395883445898716626409570075e-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) = 3.1014450000000000000000000000001
y[1] (numeric) = 3.101444999999999999999999999928
absolute error = 7.21e-29
relative error = 2.3247228308095097607728010653098e-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) = 3.1165986133333333333333333333334
y[1] (numeric) = 3.116598613333333333333333333261
absolute error = 7.24e-29
relative error = 2.3230453767854678632212786370317e-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) = 3.1318015066666666666666666666667
y[1] (numeric) = 3.131801506666666666666666666594
absolute error = 7.27e-29
relative error = 2.3213476283616152378290573059860e-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) = 3.1470537600000000000000000000001
y[1] (numeric) = 3.147053759999999999999999999927
absolute error = 7.31e-29
relative error = 2.3228074756498598867278327015296e-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) = 3.1623554533333333333333333333334
y[1] (numeric) = 3.16235545333333333333333333326
absolute error = 7.34e-29
relative error = 2.3210547037851646270133183721084e-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) = 3.1777066666666666666666666666667
y[1] (numeric) = 3.177706666666666666666666666593
absolute error = 7.37e-29
relative error = 2.3192826692625289516968211876070e-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] = 4.71
y[1] (closed_form) = 3.1931074800000000000000000000001
y[1] (numeric) = 3.193107479999999999999999999926
absolute error = 7.41e-29
relative error = 2.3206234197916820513664638686073e-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) = 3.2085579733333333333333333333334
y[1] (numeric) = 3.208557973333333333333333333259
absolute error = 7.44e-29
relative error = 2.3187986820978868147654850123990e-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) = 3.2240582266666666666666666666667
y[1] (numeric) = 3.224058226666666666666666666592
absolute error = 7.47e-29
relative error = 2.3169556735094035749982960398726e-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) = 3.2396083200000000000000000000001
y[1] (numeric) = 3.239608319999999999999999999925
absolute error = 7.51e-29
relative error = 2.3181814769508926313660041470692e-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) = 3.2552083333333333333333333333334
y[1] (numeric) = 3.255208333333333333333333333258
absolute error = 7.54e-29
relative error = 2.3162880000000000000000000000000e-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) = 3.2708583466666666666666666666667
y[1] (numeric) = 3.270858346666666666666666666591
absolute error = 7.57e-29
relative error = 2.3143772055168915171934318272485e-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) = 3.2865584400000000000000000000001
y[1] (numeric) = 3.286558439999999999999999999924
absolute error = 7.61e-29
relative error = 2.3154920683534232240823930092659e-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) = 3.3023086933333333333333333333334
y[1] (numeric) = 3.302308693333333333333333333257
absolute error = 7.64e-29
relative error = 2.3135329581463880267490599869298e-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) = 3.3181091866666666666666666666667
y[1] (numeric) = 3.31810918666666666666666666659
absolute error = 7.67e-29
relative error = 2.3115574468799176224817741480872e-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) = 3.3339600000000000000000000000001
y[1] (numeric) = 3.333959999999999999999999999923
absolute error = 7.71e-29
relative error = 2.3125652377353057625166468703883e-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) = 3.3498612133333333333333333333334
y[1] (numeric) = 3.349861213333333333333333333256
absolute error = 7.74e-29
relative error = 2.3105434843666816827448186699205e-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) = 3.3658129066666666666666666666667
y[1] (numeric) = 3.365812906666666666666666666589
absolute error = 7.77e-29
relative error = 2.3085062109691119769430004522969e-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) = 3.3818151600000000000000000000001
y[1] (numeric) = 3.381815159999999999999999999922
absolute error = 7.81e-29
relative error = 2.3094106657207131332393695934581e-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=1021.4MB, alloc=40.3MB, time=12.17
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (closed_form) = 3.3978680533333333333333333333334
y[1] (numeric) = 3.397868053333333333333333333255
absolute error = 7.84e-29
relative error = 2.3073291478487232135174454331567e-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) = 3.4139716666666666666666666666667
y[1] (numeric) = 3.413971666666666666666666666588
absolute error = 7.87e-29
relative error = 2.3052329569226067585993439703415e-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) = 3.4301260800000000000000000000001
y[1] (numeric) = 3.430126079999999999999999999921
absolute error = 7.91e-29
relative error = 2.3060376836060789928748041821249e-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) = 3.4463313733333333333333333333334
y[1] (numeric) = 3.446331373333333333333333333254
absolute error = 7.94e-29
relative error = 2.3038991727369315884667511543182e-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) = 3.4625876266666666666666666666667
y[1] (numeric) = 3.462587626666666666666666666587
absolute error = 7.97e-29
relative error = 2.3017468030614114287522127189719e-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) = 3.4788949200000000000000000000001
y[1] (numeric) = 3.47889491999999999999999999992
absolute error = 8.01e-29
relative error = 2.3024552865770375151198875532578e-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) = 3.4952533333333333333333333333334
y[1] (numeric) = 3.495253333333333333333333333253
absolute error = 8.04e-29
relative error = 2.3002624511718750000000000000000e-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) = 3.5116629466666666666666666666667
y[1] (numeric) = 3.511662946666666666666666666586
absolute error = 8.07e-29
relative error = 2.2980565397542461943414835169393e-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) = 3.5281238400000000000000000000001
y[1] (numeric) = 3.528123839999999999999999999919
absolute error = 8.11e-29
relative error = 2.2986721463836144708571227477094e-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) = 3.5446360933333333333333333333334
y[1] (numeric) = 3.544636093333333333333333333252
absolute error = 8.14e-29
relative error = 2.2964275557960708684991591821403e-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) = 3.5611997866666666666666666666667
y[1] (numeric) = 3.561199786666666666666666666585
absolute error = 8.17e-29
relative error = 2.2941706417564501407885066929353e-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) = 3.5778150000000000000000000000001
y[1] (numeric) = 3.577814999999999999999999999918
absolute error = 8.21e-29
relative error = 2.2946966234978611247367457512476e-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) = 3.5944818133333333333333333333334
y[1] (numeric) = 3.594481813333333333333333333251
absolute error = 8.24e-29
relative error = 2.2924027517498155023817693651724e-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) = 3.6112003066666666666666666666667
y[1] (numeric) = 3.611200306666666666666666666584
absolute error = 8.27e-29
relative error = 2.2900972800463836912316315967821e-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] = 4.98
y[1] (closed_form) = 3.6279705600000000000000000000001
y[1] (numeric) = 3.627970559999999999999999999917
absolute error = 8.31e-29
relative error = 2.2905367787769479584751646937289e-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) = 3.6447926533333333333333333333334
y[1] (numeric) = 3.64479265333333333333333333325
absolute error = 8.34e-29
relative error = 2.2881960081796916410963353968422e-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 ) = expt ( ( 0.2 * x + 0.3 ) , 2.0 ) ;
Iterations = 4900
Total Elapsed Time = 12 Seconds
Elapsed Time(since restart) = 12 Seconds
Time to Timeout = 2 Minutes 47 Seconds
Percent Done = 100 %
> quit
memory used=1056.7MB, alloc=40.3MB, time=12.58