|\^/| 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.
| Type ? for help.
#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(2.0) - cos(c(x)) - sin(c(x)));
> end;
exact_soln_y := proc(x) return c(2.0) - cos(c(x)) - sin(c(x)) end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]);
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if (rad_given < glob_least_given_sing) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])*
(array_x[1] - array_given_rad_poles[1, 1])
+ array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if rad_given < glob_least_given_sing then
glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if array_rad_test_poles[1, 1] < glob_least_ratio_sing then
glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_float(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if array_rad_test_poles[1, 2] < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if array_rad_test_poles[1, 3] < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_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_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g,
array_tmp3, array_tmp4, array_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,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_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_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g,
array_tmp3, array_tmp4, array_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,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_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_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g,
array_tmp3, array_tmp4, array_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,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_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_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g,
array_tmp3, array_tmp4, array_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,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_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)*22*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_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g,
array_tmp3, array_tmp4, array_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)*22*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,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_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_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g,
array_tmp3, array_tmp4, array_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,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_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_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g,
array_tmp3, array_tmp4, array_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,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre sin 1 $eq_no = 1
> array_tmp1[1] := sin(array_x[1]);
> array_tmp1_g[1] := cos(array_x[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre cos 1 $eq_no = 1
> array_tmp3[1] := cos(array_x[1]);
> array_tmp3_g[1] := sin(array_x[1]);
> #emit pre sub FULL FULL $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp2[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 sin ID_LINEAR iii = 2 $eq_no = 1
> array_tmp1[2] := array_tmp1_g[1] * array_x[2] / c(1);
> array_tmp1_g[2] := neg(array_tmp1[1]) * array_x[2] / c(1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre cos ID_LINEAR iii = 2 $eq_no = 1
> array_tmp3[2] := neg(array_tmp3_g[1]) * array_x[2] / c(1);
> array_tmp3_g[2] := array_tmp3[1] * array_x[2] / c(1);
> #emit pre sub FULL FULL $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp2[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 sin ID_LINEAR iii = 3 $eq_no = 1
> array_tmp1[3] := array_tmp1_g[2] * array_x[2] / c(2);
> array_tmp1_g[3] := neg(array_tmp1[2]) * array_x[2] / c(2);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre cos ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := neg(array_tmp3_g[2]) * array_x[2] / c(2);
> array_tmp3_g[3] := array_tmp3[2] * array_x[2] / c(2);
> #emit pre sub FULL FULL $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp2[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 sin ID_LINEAR iii = 4 $eq_no = 1
> array_tmp1[4] := array_tmp1_g[3] * array_x[2] / c(3);
> array_tmp1_g[4] := neg(array_tmp1[3]) * array_x[2] / c(3);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre cos ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := neg(array_tmp3_g[3]) * array_x[2] / c(3);
> array_tmp3_g[4] := array_tmp3[3] * array_x[2] / c(3);
> #emit pre sub FULL FULL $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp2[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 sin ID_LINEAR iii = 5 $eq_no = 1
> array_tmp1[5] := array_tmp1_g[4] * array_x[2] / c(4);
> array_tmp1_g[5] := neg(array_tmp1[4]) * array_x[2] / c(4);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre cos ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := neg(array_tmp3_g[4]) * array_x[2] / c(4);
> array_tmp3_g[5] := array_tmp3[4] * array_x[2] / c(4);
> #emit pre sub FULL FULL $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp2[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 sin LINEAR $eq_no = 1
> array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / c(kkk - 1);
> array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1]) * array_x[2] / c(kkk - 1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit cos LINEAR $eq_no = 1
> array_tmp3[kkk] := neg(array_tmp3_g[kkk - 1]) * array_x[2] / c(kkk - 1);
> array_tmp3_g[kkk] := array_tmp3[kkk - 1] * array_x[2] / c(kkk - 1);
> #emit FULL - FULL sub $eq_no = 1
> array_tmp4[kkk] := array_tmp2[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_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
array_tmp1[1] := sin(array_x[1]);
array_tmp1_g[1] := cos(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
array_tmp3[1] := cos(array_x[1]);
array_tmp3_g[1] := sin(array_x[1]);
array_tmp4[1] := array_tmp2[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_tmp1_g[1]*array_x[2]/c(1);
array_tmp1_g[2] := neg(array_tmp1[1])*array_x[2]/c(1);
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := neg(array_tmp3_g[1])*array_x[2]/c(1);
array_tmp3_g[2] := array_tmp3[1]*array_x[2]/c(1);
array_tmp4[2] := array_tmp2[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_tmp1[3] := array_tmp1_g[2]*array_x[2]/c(2);
array_tmp1_g[3] := neg(array_tmp1[2])*array_x[2]/c(2);
array_tmp2[3] := array_tmp1[3];
array_tmp3[3] := neg(array_tmp3_g[2])*array_x[2]/c(2);
array_tmp3_g[3] := array_tmp3[2]*array_x[2]/c(2);
array_tmp4[3] := array_tmp2[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_tmp1[4] := array_tmp1_g[3]*array_x[2]/c(3);
array_tmp1_g[4] := neg(array_tmp1[3])*array_x[2]/c(3);
array_tmp2[4] := array_tmp1[4];
array_tmp3[4] := neg(array_tmp3_g[3])*array_x[2]/c(3);
array_tmp3_g[4] := array_tmp3[3]*array_x[2]/c(3);
array_tmp4[4] := array_tmp2[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_tmp1[5] := array_tmp1_g[4]*array_x[2]/c(4);
array_tmp1_g[5] := neg(array_tmp1[4])*array_x[2]/c(4);
array_tmp2[5] := array_tmp1[5];
array_tmp3[5] := neg(array_tmp3_g[4])*array_x[2]/c(4);
array_tmp3_g[5] := array_tmp3[4]*array_x[2]/c(4);
array_tmp4[5] := array_tmp2[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_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/c(kkk - 1);
array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1])*array_x[2]/c(kkk - 1)
;
array_tmp2[kkk] := array_tmp1[kkk];
array_tmp3[kkk] := neg(array_tmp3_g[kkk - 1])*array_x[2]/c(kkk - 1)
;
array_tmp3_g[kkk] := array_tmp3[kkk - 1]*array_x[2]/c(kkk - 1);
array_tmp4[kkk] := array_tmp2[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,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_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 := 40;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=40;
> #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..(40),[]);
> array_norms:= Array(0..(40),[]);
> array_fact_1:= Array(0..(40),[]);
> 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..(40),[]);
> array_x:= Array(0..(40),[]);
> array_tmp0:= Array(0..(40),[]);
> array_tmp1_g:= Array(0..(40),[]);
> array_tmp1:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_tmp3_g:= Array(0..(40),[]);
> array_tmp3:= Array(0..(40),[]);
> array_tmp4:= Array(0..(40),[]);
> array_m1:= Array(0..(40),[]);
> array_y_higher := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..40+ 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..(40) ,(0..40+ 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 <= 40) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) 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 <= 40) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp1_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp3_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) 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 <= 40) 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 <= 40) 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 <= 40) 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 <= 40) 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 <=40) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1_g);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3_g);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_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_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;
> array_y_set_initial[1,31] := false;
> array_y_set_initial[1,32] := false;
> array_y_set_initial[1,33] := false;
> array_y_set_initial[1,34] := false;
> array_y_set_initial[1,35] := false;
> array_y_set_initial[1,36] := false;
> array_y_set_initial[1,37] := false;
> array_y_set_initial[1,38] := false;
> array_y_set_initial[1,39] := false;
> array_y_set_initial[1,40] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 40;
> 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/subpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( x ) - cos ( x ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=40;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := c(0.0);");
> omniout_str(ALWAYS,"x_end := c(10.0);");
> 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,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 3;");
> omniout_str(ALWAYS,"");
> 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:=false;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(c(2.0) - cos(c(x)) - sin(c(x)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> 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(0.0);
> x_end := c(10.0);
> 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:=false;
> glob_h:=c(0.001);
> glob_display_interval:=c(0.01);
> #END OVERRIDE BLOCK
> #END BLOCK 2
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
> # after second input block
> glob_check_sign := c(my_check_sign(x_start,x_end));
> glob__pi := arccos(glob__m1);
> glob_prec = expt(10.0,c(-Digits));
> if (glob_optimize) then # if number 9
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> found_h := false;
> glob_min_pole_est := glob_larger_float;
> last_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> glob_min_h := float_abs(glob_min_h) * glob_check_sign;
> glob_max_h := float_abs(glob_max_h) * glob_check_sign;
> glob_h := float_abs(glob_min_h) * glob_check_sign;
> glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign));
> display_max := c(x_end) - c(x_start)/glob__10;
> if ((glob_display_interval) > (display_max)) then # if number 10
> glob_display_interval := c(display_max);
> fi;# end if 10;
> chk_data();
> min_value := glob_larger_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := glob_small_float;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> atomall();
> if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> glob_h := glob_check_sign * float_abs(glob_min_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
> glob_h_reason := 2;
> glob_h := glob_display_interval;
> found_h := true;
> fi;# end if 10;
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if ( not found_h) then # if number 10
> est_answer := est_size_answer();
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := test_suggested_h();
> omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
> if (estimated_step_error < est_needed_step_err) then # if number 11
> omniout_str(ALWAYS,"Double H and LOOP");
> glob_h := glob_h*glob__2;
> else
> omniout_str(ALWAYS,"Found H for OPTIMAL");
> found_h := true;
> glob_h_reason := 3;
> glob_h := glob_h/glob__2;
> fi;# end if 11;
> fi;# end if 10;
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 10
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 10;
> if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MAX H");
> glob_h := glob_check_sign * float_abs(glob_max_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> else
> found_h := true;
> glob_h := glob_h * glob_check_sign;
> fi;# end if 9;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 9
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 9;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 9
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> glob_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and (glob_check_sign * array_x[1] < glob_check_sign * x_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1
> #left paren 0001C
> if (reached_interval()) then # if number 10
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 10;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> track_estimated_error();
> atomall();
> track_estimated_error();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if (reached_interval()) then # if number 10
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 10;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 10
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 10;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 10;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = sin ( x ) - cos ( x ) ; ");
> 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,"2015-04-24T20:38:29-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sub")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( x ) - cos ( x ) ; ")
> ;
> 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,"sub diffeq.mxt")
> ;
> logitem_str(html_log_file,"sub 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_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g,
array_tmp3, array_tmp4, array_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 := 40;
Digits := 32;
max_terms := 40;
glob_html_log := true;
array_y_init := Array(0 .. 40, []);
array_norms := Array(0 .. 40, []);
array_fact_1 := Array(0 .. 40, []);
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 .. 40, []);
array_x := Array(0 .. 40, []);
array_tmp0 := Array(0 .. 40, []);
array_tmp1_g := Array(0 .. 40, []);
array_tmp1 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_tmp3_g := Array(0 .. 40, []);
array_tmp3 := Array(0 .. 40, []);
array_tmp4 := Array(0 .. 40, []);
array_m1 := Array(0 .. 40, []);
array_y_higher := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 41, []);
array_y_set_initial := Array(0 .. 2, 0 .. 41, []);
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 .. 40, 0 .. 41, []);
term := 1;
while term <= 40 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 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 <= 40 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp1_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp3_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 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 <= 40 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 <= 40 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 <= 40 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 <= 40 do
term := 1;
while term <= 40 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1_g);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3_g);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_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_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;
array_y_set_initial[1, 31] := false;
array_y_set_initial[1, 32] := false;
array_y_set_initial[1, 33] := false;
array_y_set_initial[1, 34] := false;
array_y_set_initial[1, 35] := false;
array_y_set_initial[1, 36] := false;
array_y_set_initial[1, 37] := false;
array_y_set_initial[1, 38] := false;
array_y_set_initial[1, 39] := false;
array_y_set_initial[1, 40] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 40;
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/subpostode.ode#################");
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = sin ( x ) - cos ( x ) ; ")
;
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=40;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := c(0.0);");
omniout_str(ALWAYS, "x_end := c(10.0);");
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, "");
omniout_str(ALWAYS, "glob_type_given_pole := 3;");
omniout_str(ALWAYS, "");
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:=false;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(c(2.0) - cos(c(x)) - sin(c(x)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
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.);
x_end := c(10.0);
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 := false;
glob_h := c(0.001);
glob_display_interval := c(0.01);
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
glob_check_sign := c(my_check_sign(x_start, x_end));
glob__pi := arccos(glob__m1);
glob_prec = expt(10.0, c(-Digits));
if glob_optimize then
omniout_str(ALWAYS, "START of Optimize");
found_h := false;
glob_min_pole_est := glob_larger_float;
last_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
glob_min_h := float_abs(glob_min_h)*glob_check_sign;
glob_max_h := float_abs(glob_max_h)*glob_check_sign;
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_display_interval :=
c(float_abs(c(glob_display_interval))*glob_check_sign);
display_max := c(x_end) - c(x_start)/glob__10;
if display_max < glob_display_interval then
glob_display_interval := c(display_max)
end if;
chk_data();
min_value := glob_larger_float;
est_answer := est_size_answer();
opt_iter := 1;
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
;
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := glob_small_float;
while opt_iter <= 100 and not found_h do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] :=
array_y_init[it]*expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
atomall();
if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if;
if
glob_check_sign*glob_display_interval <= glob_check_sign*glob_h
then
omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL");
glob_h_reason := 2;
glob_h := glob_display_interval;
found_h := true
end if;
if glob_look_poles then check_for_pole() end if;
if not found_h then
est_answer := est_size_answer();
est_needed_step_err := estimated_needed_step_error(x_start,
x_end, glob_h, est_answer);
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := test_suggested_h();
omniout_float(ALWAYS, "estimated_step_error", 32,
estimated_step_error, 32, "");
if estimated_step_error < est_needed_step_err then
omniout_str(ALWAYS, "Double H and LOOP");
glob_h := glob_h*glob__2
else
omniout_str(ALWAYS, "Found H for OPTIMAL");
found_h := true;
glob_h_reason := 3;
glob_h := glob_h/glob__2
end if
end if;
opt_iter := opt_iter + 1
end do;
if not found_h and opt_iter = 1 then
omniout_str(ALWAYS, "Beginning glob_h too large.");
found_h := false
end if;
if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then
omniout_str(ALWAYS, "SETTING H FOR MAX H");
glob_h := float_abs(glob_max_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if
else found_h := true; glob_h := glob_check_sign*glob_h
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
glob_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
glob_clock_sec - glob_orig_start_sec < glob_max_sec do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
track_estimated_error();
atomall();
track_estimated_error();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = sin ( x ) \
- cos ( x ) ; ");
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, "2015-04-24T20:38:29-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "sub");
logitem_str(html_log_file, "diff ( y , x , 1 ) = si\
n ( x ) - cos ( x ) ; ");
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,
"sub diffeq.mxt");
logitem_str(html_log_file,
"sub 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/subpostode.ode#################
diff ( y , x , 1 ) = sin ( x ) - cos ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(0.0);
x_end := c(10.0);
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:=false;
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(2.0) - cos(c(x)) - sin(c(x)));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0
y[1] (closed_form) = 1
y[1] (numeric) = 1
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 14
Correct digits = 32
h = 0.001
memory used=4.0MB, alloc=40.3MB, time=0.09
TOP MAIN SOLVE Loop
x[1] = 0.01
y[1] (closed_form) = 0.9900501662491680575371996279787
y[1] (numeric) = 0.99005016624916805753719962797869
absolute error = 1e-32
relative error = 1.0100498278673364177533130571212e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.02
y[1] (closed_form) = 0.98020132664008914222081411446952
y[1] (numeric) = 0.98020132664008914222081411446955
absolute error = 3e-32
relative error = 3.0605957352489297705151550159651e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.03
y[1] (closed_form) = 0.97045446604851682295931495160714
y[1] (numeric) = 0.97045446604851682295931495160713
absolute error = 1e-32
relative error = 1.0304450491858585356639979788752e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.04
y[1] (closed_form) = 0.96081055915238790023288243015498
y[1] (numeric) = 0.96081055915238790023288243015495
absolute error = 3e-32
relative error = 3.1223636870170881978952783575183e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.05
y[1] (closed_form) = 0.95127057033435542464226418799801
y[1] (numeric) = 0.951270570334355424642264187998
absolute error = 1e-32
relative error = 1.0512256251641601923030243401200e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.06
y[1] (closed_form) = 0.94183545358535123525324717496022
y[1] (numeric) = 0.94183545358535123525324717496019
absolute error = 3e-32
relative error = 3.1852697714655878479208085428790e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.07
y[1] (closed_form) = 0.93250615240918766140254430325241
y[1] (numeric) = 0.93250615240918766140254430325239
absolute error = 2e-32
relative error = 2.1447579673687680969400182105632e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.08
y[1] (closed_form) = 0.923283599728207927715416878052
y[1] (numeric) = 0.92328359972820792771541687805201
absolute error = 1e-32
relative error = 1.0830908296154892181054901739052e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.09
y[1] (closed_form) = 0.91416871778999469721590664556776
y[1] (numeric) = 0.91416871778999469721590664556774
absolute error = 2e-32
relative error = 2.1877799590813009997699789874950e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (closed_form) = 0.90516241807514608159762381378548
y[1] (numeric) = 0.90516241807514608159762381378552
absolute error = 4e-32
relative error = 4.4190964186362432691470777552431e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (closed_form) = 0.89626560120612834097721089849675
y[1] (numeric) = 0.89626560120612834097721089849671
absolute error = 4e-32
relative error = 4.4629627586031352002385497946687e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=44.0MB, alloc=44.3MB, time=0.55
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (closed_form) = 0.88747915685721438778455121787143
y[1] (numeric) = 0.88747915685721438778455121787141
absolute error = 2e-32
relative error = 2.2535740524684547050771561960182e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (closed_form) = 0.87880396366551710086428201813989
y[1] (numeric) = 0.8788039636655171008642820181399
absolute error = 1e-32
relative error = 1.1379102067643967806620860007662e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (closed_form) = 0.87024088914312634638306342128323
y[1] (numeric) = 0.87024088914312634638306342128325
absolute error = 2e-32
relative error = 2.2982142357954235280997659705404e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (closed_form) = 0.86179078959035849176729356265806
y[1] (numeric) = 0.86179078959035849176729356265803
absolute error = 3e-32
relative error = 3.4811233030536478583240801580004e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (closed_form) = 0.85345451001012708764758431629571
y[1] (numeric) = 0.85345451001012708764758431629568
absolute error = 3e-32
relative error = 3.5151258383582764271087599440139e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (closed_form) = 0.84523288402344328067044563311665
y[1] (numeric) = 0.84523288402344328067044563311666
absolute error = 1e-32
relative error = 1.1831058858475081722627590692914e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (closed_form) = 0.83712673378605440706548123568929
y[1] (numeric) = 0.83712673378605440706548123568926
absolute error = 3e-32
relative error = 3.5836867691848364631547410666592e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (closed_form) = 0.82913686990622910303927134282879
y[1] (numeric) = 0.82913686990622910303927134282877
absolute error = 2e-32
relative error = 2.4121469839185769006788484508972e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (closed_form) = 0.82126409136369715341639085613341
y[1] (numeric) = 0.82126409136369715341639085613344
absolute error = 3e-32
relative error = 3.6529053583951824327994283518707e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (closed_form) = 0.81350918542975218447514900567296
y[1] (numeric) = 0.813509185429752184475149005673
absolute error = 4e-32
relative error = 4.9169696810330685308463507609692e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (closed_form) = 0.80587292758852519064218601349829
y[1] (numeric) = 0.80587292758852519064218601349829
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=83.9MB, alloc=44.3MB, time=0.98
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (closed_form) = 0.79835608145943676762765213956833
y[1] (numeric) = 0.79835608145943676762765213956833
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (closed_form) = 0.79095939872083580671303266854678
y[1] (numeric) = 0.7909593987208358067130326685468
absolute error = 2e-32
relative error = 2.5285747956651913342996147878410e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (closed_form) = 0.78368361903483228625855584565641
y[1] (numeric) = 0.78368361903483228625855584565641
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (closed_form) = 0.77652946997333167708839388918468
y[1] (numeric) = 0.77652946997333167708839388918471
absolute error = 3e-32
relative error = 3.8633433964882606312622881552082e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (closed_form) = 0.76949766694527835825148076948726
y[1] (numeric) = 0.76949766694527835825148076948725
absolute error = 1e-32
relative error = 1.2995490993101522427969375383627e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (closed_form) = 0.76258891312511531875574038794565
y[1] (numeric) = 0.76258891312511531875574038794566
absolute error = 1e-32
relative error = 1.3113224999586814966271286491260e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (closed_form) = 0.75580389938246729924593501656373
y[1] (numeric) = 0.75580389938246729924593501656375
absolute error = 2e-32
relative error = 2.6461890467012782928419196795625e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (closed_form) = 0.74914330421305440525236902674697
y[1] (numeric) = 0.7491433042130544052523690267469
absolute error = 7e-32
relative error = 9.3440066281487022744123521215372e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (closed_form) = 0.74260779367084310059155123983884
y[1] (numeric) = 0.74260779367084310059155123983882
absolute error = 2e-32
relative error = 2.6932117021202301215282500153118e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (closed_form) = 0.73619802130144136576293518281675
y[1] (numeric) = 0.73619802130144136576293518281674
absolute error = 1e-32
relative error = 1.3583301925101793931781037123669e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (closed_form) = 0.72991462807674468177039372546358
y[1] (numeric) = 0.72991462807674468177039372546356
absolute error = 2e-32
relative error = 2.7400464699136239336066412218297e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=123.9MB, alloc=44.3MB, time=1.44
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (closed_form) = 0.72375824233083937471558445294261
y[1] (numeric) = 0.72375824233083937471558445294262
absolute error = 1e-32
relative error = 1.3816768383590813722827019178294e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (closed_form) = 0.71772947969716973077533273577867
y[1] (numeric) = 0.71772947969716973077533273577869
absolute error = 2e-32
relative error = 2.7865652123469364717569004911159e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (closed_form) = 0.71182894304697516479917419595457
y[1] (numeric) = 0.71182894304697516479917419595452
absolute error = 5e-32
relative error = 7.0241594540923843160846759663437e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (closed_form) = 0.70605722242900359875889462638195
y[1] (numeric) = 0.70605722242900359875889462638197
absolute error = 2e-32
relative error = 2.8326316004806630948045569354413e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (closed_form) = 0.7004148950105070786619837259262
y[1] (numeric) = 0.70041489501050707866198372592623
absolute error = 3e-32
relative error = 4.2831756168677656931760135062886e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (closed_form) = 0.69490252501952553031814114927174
y[1] (numeric) = 0.69490252501952553031814114927172
absolute error = 2e-32
relative error = 2.8781015005576552508456836684567e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (closed_form) = 0.68952066368846442553516151115249
y[1] (numeric) = 0.68952066368846442553516151115247
absolute error = 2e-32
relative error = 2.9005657195266150975074209357512e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (closed_form) = 0.68426984919897200093056030167186
y[1] (numeric) = 0.68426984919897200093056030167181
absolute error = 5e-32
relative error = 7.3070587661478270049896291066928e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (closed_form) = 0.67915060662812154159112405224796
y[1] (numeric) = 0.67915060662812154159112405224796
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (closed_form) = 0.67416344789590411130717084971203
y[1] (numeric) = 0.67416344789590411130717084971195
absolute error = 8e-32
relative error = 1.1866558510355874342598517125897e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (closed_form) = 0.66930887171403698006474186022168
y[1] (numeric) = 0.66930887171403698006474186022168
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=163.9MB, alloc=44.3MB, time=1.87
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (closed_form) = 0.6645873635360928679103151422817
y[1] (numeric) = 0.66458736353609286791031514228164
absolute error = 6e-32
relative error = 9.0281584170899570087576188779765e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (closed_form) = 0.6599993955089549922220964525707
y[1] (numeric) = 0.65999939550895499222209645257068
absolute error = 2e-32
relative error = 3.0303058057465503164676245801618e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (closed_form) = 0.65554542642560277284270592307019
y[1] (numeric) = 0.65554542642560277284270592307018
absolute error = 1e-32
relative error = 1.5254472988280226362122123031876e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (closed_form) = 0.65122590167923291646340222625266
y[1] (numeric) = 0.65122590167923291646340222625259
absolute error = 7e-32
relative error = 1.0748958206284479106739602127863e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (closed_form) = 0.64704125321872046811317350367534
y[1] (numeric) = 0.64704125321872046811317350367535
absolute error = 1e-32
relative error = 1.5454965120469193320782298104001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (closed_form) = 0.64299189950542428361043048218063
y[1] (numeric) = 0.64299189950542428361043048218057
absolute error = 6e-32
relative error = 9.3313772764712473071777688592128e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (closed_form) = 0.63907824547134124239406128874993
y[1] (numeric) = 0.6390782454713412423940612887499
absolute error = 3e-32
relative error = 4.6942608690856019513594403203764e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (closed_form) = 0.63530068247861338527769348546375
y[1] (numeric) = 0.63530068247861338527769348546372
absolute error = 3e-32
relative error = 4.7221734254960308557562394849936e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (closed_form) = 0.63165958828039202637964395896972
y[1] (numeric) = 0.63165958828039202637964395896971
absolute error = 1e-32
relative error = 1.5831311968561500497458974086669e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (closed_form) = 0.62815532698306275278475053812396
y[1] (numeric) = 0.62815532698306275278475053812396
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (closed_form) = 0.62478824900983508940664009462491
y[1] (numeric) = 0.62478824900983508940664009462494
absolute error = 3e-32
relative error = 4.8016267987664658704821651377512e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=203.9MB, alloc=44.3MB, time=2.33
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (closed_form) = 0.62155869106570047005360505502167
y[1] (numeric) = 0.62155869106570047005360505502165
absolute error = 2e-32
relative error = 3.2177170535108718753074835019641e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (closed_form) = 0.61846697610376201887178014300517
y[1] (numeric) = 0.61846697610376201887178014300515
absolute error = 2e-32
relative error = 3.2338024135090668655877658861939e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (closed_form) = 0.61551341329293950915941661237354
y[1] (numeric) = 0.61551341329293950915941661237353
absolute error = 1e-32
relative error = 1.6246599641916705193534696674766e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (closed_form) = 0.61269829798705272902946009863353
y[1] (numeric) = 0.61269829798705272902946009863356
absolute error = 3e-32
relative error = 4.8963739737096424586619595212475e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (closed_form) = 0.61002191169528634555810205538594
y[1] (numeric) = 0.61002191169528634555810205538597
absolute error = 3e-32
relative error = 4.9178561334999027288355138404427e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (closed_form) = 0.60748452205403922090827738918248
y[1] (numeric) = 0.60748452205403922090827738918247
absolute error = 1e-32
relative error = 1.6461324753078141528724439770216e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (closed_form) = 0.60508638280016099547303711805709
y[1] (numeric) = 0.60508638280016099547303711805709
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (closed_form) = 0.60282773374557861435817894342828
y[1] (numeric) = 0.60282773374557861435817894342834
absolute error = 6e-32
relative error = 9.9530921756368287839031131446441e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (closed_form) = 0.60070880075331533453034298153177
y[1] (numeric) = 0.60070880075331533453034298153178
absolute error = 1e-32
relative error = 1.6647000988598067618365664632282e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (closed_form) = 0.59872979571490461070987375071416
y[1] (numeric) = 0.59872979571490461070987375071419
absolute error = 3e-32
relative error = 5.0106074918451212230426693531184e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (closed_form) = 0.5968909165292011186010374293735
y[1] (numeric) = 0.59689091652920111860103742937351
absolute error = 1e-32
relative error = 1.6753479945963928310371272312506e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (closed_form) = 0.59519234708259103433961394103531
y[1] (numeric) = 0.59519234708259103433961394103535
absolute error = 4e-32
relative error = 6.7205165180743588920436470425970e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=243.9MB, alloc=44.3MB, time=2.77
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (closed_form) = 0.59363425723060354911342772853545
y[1] (numeric) = 0.59363425723060354911342772853549
absolute error = 4e-32
relative error = 6.7381556089108203236772016740630e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (closed_form) = 0.59221680278092545778903147749348
y[1] (numeric) = 0.59221680278092545778903147749357
absolute error = 9e-32
relative error = 1.5197137193233785826108981086723e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (closed_form) = 0.59094012547782052007152565840938
y[1] (numeric) = 0.59094012547782052007152565840947
absolute error = 9e-32
relative error = 1.5229969352178967578937796774080e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (closed_form) = 0.58980435298795515224841408300756
y[1] (numeric) = 0.58980435298795515224841408300767
absolute error = 1.1e-31
relative error = 1.8650252315490522413402306749502e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (closed_form) = 0.58880959888763186693650920509983
y[1] (numeric) = 0.58880959888763186693650920509995
absolute error = 1.2e-31
relative error = 2.0380102536830541843299943611348e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (closed_form) = 0.58795596265143173747727371068817
y[1] (numeric) = 0.58795596265143173747727371068819
absolute error = 2e-32
relative error = 3.4016153029231121785742080766685e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (closed_form) = 0.58724352964226702272469428169303
y[1] (numeric) = 0.58724352964226702272469428169305
absolute error = 2e-32
relative error = 3.4057420798120096002470083651664e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (closed_form) = 0.58667237110284494695491929422001
y[1] (numeric) = 0.58667237110284494695491929422007
absolute error = 6e-32
relative error = 1.0227173283652362258839022481981e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (closed_form) = 0.58624254414854348851255599456327
y[1] (numeric) = 0.5862425441485434885125559945633
absolute error = 3e-32
relative error = 5.1173358705264029386130163469900e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (closed_form) = 0.58595409176169988960882570022349
y[1] (numeric) = 0.58595409176169988960882570022346
absolute error = 3e-32
relative error = 5.1198550230792859062184040072948e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (closed_form) = 0.58580704278731245841583765111748
y[1] (numeric) = 0.58580704278731245841583765111754
absolute error = 6e-32
relative error = 1.0242280412764524309767484771113e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=283.9MB, alloc=44.3MB, time=3.22
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (closed_form) = 0.5858014119301560932731902639458
y[1] (numeric) = 0.58580141193015609327319026394589
absolute error = 9e-32
relative error = 1.5363568295859709588830756802058e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (closed_form) = 0.58593719975331181745207540777631
y[1] (numeric) = 0.58593719975331181745207540777633
absolute error = 2e-32
relative error = 3.4133350823979590780442391413599e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (closed_form) = 0.58621439267811047152218390680536
y[1] (numeric) = 0.58621439267811047152218390680538
absolute error = 2e-32
relative error = 3.4117210784659074197197630734523e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (closed_form) = 0.58663296298549056895212865687538
y[1] (numeric) = 0.58663296298549056895212865687537
absolute error = 1e-32
relative error = 1.7046433853815565520163306470571e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (closed_form) = 0.58719286881877017915895685599752
y[1] (numeric) = 0.58719286881877017915895685599748
absolute error = 4e-32
relative error = 6.8120718292213295886706325276142e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (closed_form) = 0.58789405418783256082075629249945
y[1] (numeric) = 0.58789405418783256082075629249951
absolute error = 6e-32
relative error = 1.0205920534931955291370556899733e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (closed_form) = 0.58873644897472512689251244630303
y[1] (numeric) = 0.58873644897472512689251244630308
absolute error = 5e-32
relative error = 8.4927644767152059655826656074348e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (closed_form) = 0.58971996894067118143338060624745
y[1] (numeric) = 0.5897199689406711814333806062475
absolute error = 5e-32
relative error = 8.4786004601160544190374552232370e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (closed_form) = 0.59084451573449372707753337079435
y[1] (numeric) = 0.5908445157344937270775333707943
absolute error = 5e-32
relative error = 8.4624632485322705049210485709364e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (closed_form) = 0.59210997690245050077485626352191
y[1] (numeric) = 0.59210997690245050077485626352192
absolute error = 1e-32
relative error = 1.6888754437670097793219826197199e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (closed_form) = 0.59351622589947925430611322964662
y[1] (numeric) = 0.59351622589947925430611322964656
absolute error = 6e-32
relative error = 1.0109243417746406627732002867178e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=323.8MB, alloc=44.3MB, time=3.66
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (closed_form) = 0.59506312210185215505390153287935
y[1] (numeric) = 0.59506312210185215505390153287931
absolute error = 4e-32
relative error = 6.7219759575612757641228365531012e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (closed_form) = 0.59675051082123804159986425595375
y[1] (numeric) = 0.59675051082123804159986425595375
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (closed_form) = 0.59857822332017112793431919084398
y[1] (numeric) = 0.59857822332017112793431919084395
absolute error = 3e-32
relative error = 5.0118762813650538000412511408889e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (closed_form) = 0.60054607682892460942077369965635
y[1] (numeric) = 0.60054607682892460942077369965631
absolute error = 4e-32
relative error = 6.6606046635443520586175874862001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (closed_form) = 0.60265387456378748316879038614185
y[1] (numeric) = 0.6026538745637874831687903861418
absolute error = 5e-32
relative error = 8.2966362800191014999119629521542e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (closed_form) = 0.60490140574674275514839692413694
y[1] (numeric) = 0.60490140574674275514839692413695
absolute error = 1e-32
relative error = 1.6531619706942378077254283204761e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (closed_form) = 0.60728844562654506624172705321767
y[1] (numeric) = 0.60728844562654506624172705321767
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (closed_form) = 0.60981475550119562948685220729376
y[1] (numeric) = 0.60981475550119562948685220729375
absolute error = 1e-32
relative error = 1.6398422487794973604136956635491e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (closed_form) = 0.61248008274181223103880844492095
y[1] (numeric) = 0.61248008274181223103880844492088
absolute error = 7e-32
relative error = 1.1428943074628621538413069981790e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (closed_form) = 0.61528416081789190786761417979929
y[1] (numeric) = 0.61528416081789190786761417979924
absolute error = 5e-32
relative error = 8.1263265307423862330795245408963e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (closed_form) = 0.6182267093239637759465610709267
y[1] (numeric) = 0.61822670932396377594656107092669
absolute error = 1e-32
relative error = 1.6175295970203367645896586495765e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=363.9MB, alloc=44.3MB, time=4.11
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (closed_form) = 0.62130743400762934367016985943879
y[1] (numeric) = 0.62130743400762934367016985943878
absolute error = 1e-32
relative error = 1.6095091500027352023512826041291e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (closed_form) = 0.62452602679898750649383620651082
y[1] (numeric) = 0.62452602679898750649383620651078
absolute error = 4e-32
relative error = 6.4048571690471057183033749789774e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (closed_form) = 0.62788216584144128032022331486818
y[1] (numeric) = 0.6278821658414412803202233148682
absolute error = 2e-32
relative error = 3.1853110484827161687998422223332e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (closed_form) = 0.63137551552388319298473488689163
y[1] (numeric) = 0.63137551552388319298473488689164
absolute error = 1e-32
relative error = 1.5838434899874934416442581808790e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (closed_form) = 0.63500572651425611532774094218763
y[1] (numeric) = 0.63500572651425611532774094218762
absolute error = 1e-32
relative error = 1.5747889479506128944195658914403e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (closed_form) = 0.63877243579448617579841653804618
y[1] (numeric) = 0.63877243579448617579841653804616
absolute error = 2e-32
relative error = 3.1310054847818525951136239348387e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (closed_form) = 0.64267526669678426532784367404728
y[1] (numeric) = 0.64267526669678426532784367404725
absolute error = 3e-32
relative error = 4.6679873265068518758589319706099e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (closed_form) = 0.64671382894131250235114022384924
y[1] (numeric) = 0.6467138289413125023511402238492
absolute error = 4e-32
relative error = 6.1851159214394794951839581287304e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (closed_form) = 0.65088771867521189136350229748885
y[1] (numeric) = 0.6508877186752118913635022974888
absolute error = 5e-32
relative error = 7.6818164739331372197259624326541e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (closed_form) = 0.6551965185129872722768273703436
y[1] (numeric) = 0.65519651851298727227682737034358
absolute error = 2e-32
relative error = 3.0525192724453649566797706618982e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (closed_form) = 0.65963979757824552211563652872703
y[1] (numeric) = 0.65963979757824552211563652872706
absolute error = 3e-32
relative error = 4.5479366330139356450836254570644e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=404.1MB, alloc=44.3MB, time=4.55
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (closed_form) = 0.66421711154678283526690795869975
y[1] (numeric) = 0.66421711154678283526690795869973
absolute error = 2e-32
relative error = 3.0110636495686454553257250528822e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (closed_form) = 0.6689280026910167735917026419351
y[1] (numeric) = 0.66892800269101677359170264193506
absolute error = 4e-32
relative error = 5.9797167765566426475769697726677e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (closed_form) = 0.6737719999257586432305976810752
y[1] (numeric) = 0.67377199992575864323059768107521
absolute error = 1e-32
relative error = 1.4841815927497545981992637111734e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (closed_form) = 0.67874861885532162090339023143642
y[1] (numeric) = 0.67874861885532162090339023143641
absolute error = 1e-32
relative error = 1.4732994988431123178704677247712e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (closed_form) = 0.68385736182195991892969870973167
y[1] (numeric) = 0.68385736182195991892969870973167
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (closed_form) = 0.68909771795563414509432505598747
y[1] (numeric) = 0.68909771795563414509432505598748
absolute error = 1e-32
relative error = 1.4511729961415755705489808734586e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (closed_form) = 0.69446916322509788086286250741244
y[1] (numeric) = 0.69446916322509788086286250741248
absolute error = 4e-32
relative error = 5.7597949798434496591646152204256e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (closed_form) = 0.69997116049030036933229933004683
y[1] (numeric) = 0.69997116049030036933229933004688
absolute error = 5e-32
relative error = 7.1431514356930222852083891089645e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (closed_form) = 0.70560315955610007269149220888207
y[1] (numeric) = 0.70560315955610007269149220888211
absolute error = 4e-32
relative error = 5.6689088559586782874932325360269e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (closed_form) = 0.71136459722728372788052439779159
y[1] (numeric) = 0.7113645972272837278805243977916
absolute error = 1e-32
relative error = 1.4057488999280296620671033802987e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (closed_form) = 0.71725489736488539858923175367643
y[1] (numeric) = 0.71725489736488539858923175367641
absolute error = 2e-32
relative error = 2.7884089845155149582133300811527e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=444.2MB, alloc=44.3MB, time=4.98
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (closed_form) = 0.72327347094379989173662918911306
y[1] (numeric) = 0.72327347094379989173662918911307
absolute error = 1e-32
relative error = 1.3826029021845630956206094961136e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (closed_form) = 0.72941971611168477713760062122081
y[1] (numeric) = 0.72941971611168477713760062122081
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (closed_form) = 0.73569301824914512020397060052595
y[1] (numeric) = 0.7356930182491451202039706005259
absolute error = 5e-32
relative error = 6.7963129674648234717611149369548e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (closed_form) = 0.74209275003119490925684128939808
y[1] (numeric) = 0.74209275003119490925684128939809
absolute error = 1e-32
relative error = 1.3475404522655201763817989422268e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (closed_form) = 0.74861827148998903135868124172911
y[1] (numeric) = 0.74861827148998903135868124172915
absolute error = 4e-32
relative error = 5.3431770934988331744558942758465e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (closed_form) = 0.75526893007881952351985924724711
y[1] (numeric) = 0.75526893007881952351985924724712
absolute error = 1e-32
relative error = 1.3240316927847680068734085551357e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (closed_form) = 0.76204406073736969970783261865343
y[1] (numeric) = 0.76204406073736969970783261865344
absolute error = 1e-32
relative error = 1.3122600798599219826936422505230e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (closed_form) = 0.76894298595821962830066726066755
y[1] (numeric) = 0.76894298595821962830066726066758
absolute error = 3e-32
relative error = 3.9014596072575456622490773130695e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (closed_form) = 0.7759650158545963094925652154463
y[1] (numeric) = 0.77596501585459630949256521544632
absolute error = 2e-32
relative error = 2.5774357852941770705133202216139e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (closed_form) = 0.78310944822936177769011742459983
y[1] (numeric) = 0.7831094482293617776901174245999
absolute error = 7e-32
relative error = 8.9387249966492527165697514063344e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (closed_form) = 0.7903755686452322301465319762256
y[1] (numeric) = 0.79037556864523223014653197622565
absolute error = 5e-32
relative error = 6.3261064718516099336496401041171e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=484.4MB, alloc=44.3MB, time=5.44
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (closed_form) = 0.79776265049622115997949015961035
y[1] (numeric) = 0.79776265049622115997949015961034
absolute error = 1e-32
relative error = 1.2535056628409263907557163925598e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (closed_form) = 0.80526995508029934931886428772418
y[1] (numeric) = 0.80526995508029934931886428772419
absolute error = 1e-32
relative error = 1.2418195832232219510732298943898e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (closed_form) = 0.81289673167326445664553230818147
y[1] (numeric) = 0.81289673167326445664553230818155
absolute error = 8e-32
relative error = 9.8413484619784623971955983202946e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (closed_form) = 0.82064221760381281142411310546277
y[1] (numeric) = 0.82064221760381281142411310546279
absolute error = 2e-32
relative error = 2.4371156602688383766239252507984e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (closed_form) = 0.82850563832980590891271884119575
y[1] (numeric) = 0.82850563832980590891271884119578
absolute error = 3e-32
relative error = 3.6209771680585477608255551469801e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (closed_form) = 0.83648620751572397856379855775309
y[1] (numeric) = 0.83648620751572397856379855775304
absolute error = 5e-32
relative error = 5.9773848690816718917041868172683e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (closed_form) = 0.8445831271112988807237773859903
y[1] (numeric) = 0.84458312711129888072377738599026
absolute error = 4e-32
relative error = 4.7360643039141383935539130642181e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (closed_form) = 0.85279558743131846840734858869686
y[1] (numeric) = 0.85279558743131846840734858869685
absolute error = 1e-32
relative error = 1.1726139472790563915365359321524e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (closed_form) = 0.8611227672365944337767444236884
y[1] (numeric) = 0.86112276723659443377674442368839
absolute error = 1e-32
relative error = 1.1612746033983896430294294573374e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (closed_form) = 0.86956383381608554260881087994327
y[1] (numeric) = 0.86956383381608554260881087994325
absolute error = 2e-32
relative error = 2.3000036595622765114287691845228e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (closed_form) = 0.87811794307016804449487537991282
y[1] (numeric) = 0.87811794307016804449487537991286
absolute error = 4e-32
relative error = 4.5551967495559656862566186023716e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=524.5MB, alloc=44.3MB, time=5.87
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (closed_form) = 0.88678423959504493180177923842899
y[1] (numeric) = 0.88678423959504493180177923842898
absolute error = 1e-32
relative error = 1.1276700186469886849886734351772e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (closed_form) = 0.89556185676828560653851958962657
y[1] (numeric) = 0.8955618567682856065385195896266
absolute error = 3e-32
relative error = 3.3498523606462719279620449819829e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (closed_form) = 0.90444991683548740123309693580203
y[1] (numeric) = 0.90444991683548740123309693580202
absolute error = 1e-32
relative error = 1.1056444158885277847506688142278e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (closed_form) = 0.91344753099805028773969832678951
y[1] (numeric) = 0.91344753099805028773969832678946
absolute error = 5e-32
relative error = 5.4737681479492359292042417358720e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (closed_form) = 0.9225537995020559965784807983926
y[1] (numeric) = 0.92255379950205599657848079839257
absolute error = 3e-32
relative error = 3.2518428753089908250652731210648e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (closed_form) = 0.93176781172824265897008677742421
y[1] (numeric) = 0.93176781172824265897008677742422
absolute error = 1e-32
relative error = 1.0732287458451696228885741169597e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (closed_form) = 0.94108864628306597417566662024709
y[1] (numeric) = 0.94108864628306597417566662024707
absolute error = 2e-32
relative error = 2.1251983093189168815624634705694e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (closed_form) = 0.95051537109083779610155833573045
y[1] (numeric) = 0.95051537109083779610155833573039
absolute error = 6e-32
relative error = 6.3123650416239283219654117536836e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (closed_form) = 0.96004704348693292538674592421492
y[1] (numeric) = 0.96004704348693292538674592421486
absolute error = 6e-32
relative error = 6.2496937423063531515793936270579e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (closed_form) = 0.96968271031205478637155965448357
y[1] (numeric) = 0.96968271031205478637155965448352
absolute error = 5e-32
relative error = 5.1563258237232505121349278226731e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (closed_form) = 0.97942140800755056245847587766993
y[1] (numeric) = 0.97942140800755056245847587766992
absolute error = 1e-32
relative error = 1.0210109681330253227570074395674e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=564.6MB, alloc=44.3MB, time=6.33
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (closed_form) = 0.98926216271176625843090931282562
y[1] (numeric) = 0.98926216271176625843090931282556
absolute error = 6e-32
relative error = 6.0651263397690204168870741973008e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (closed_form) = 0.99920399035743205430406154253127
y[1] (numeric) = 0.99920399035743205430406154253127
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (closed_form) = 1.009245896770068212253594824731
y[1] (numeric) = 1.009245896770068212253594824731
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (closed_form) = 1.0193868777674016961134430024979
y[1] (numeric) = 1.0193868777674016961134430024979
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (closed_form) = 1.0296259192597835618636566374003
y[1] (numeric) = 1.0296259192597835618636566374003
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (closed_form) = 1.0399619973515970774529144617567
y[1] (numeric) = 1.0399619973515970774529144617567
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (closed_form) = 1.0503940784436464312282253834655
y[1] (numeric) = 1.0503940784436464312282253834655
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (closed_form) = 1.0609211193365157901863017124867
y[1] (numeric) = 1.0609211193365157901863017124867
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (closed_form) = 1.0715420673348883722269107330887
y[1] (numeric) = 1.0715420673348883722269107330886
absolute error = 1e-31
relative error = 9.3323447626015659293682456143318e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (closed_form) = 1.0822558603528151005879115571391
y[1] (numeric) = 1.0822558603528151005879115571391
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (closed_form) = 1.0930614270199223136842573410376
y[1] (numeric) = 1.0930614270199223136842573410376
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=604.7MB, alloc=44.3MB, time=6.76
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (closed_form) = 1.1039576867885479096684850959144
y[1] (numeric) = 1.1039576867885479096684850959144
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (closed_form) = 1.1149435500417952121875168649792
y[1] (numeric) = 1.1149435500417952121875168649793
absolute error = 1e-31
relative error = 8.9690639491345871897483168168759e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (closed_form) = 1.1260179182024937520392411758875
y[1] (numeric) = 1.1260179182024937520392411758877
absolute error = 2e-31
relative error = 1.7761706698172955155467105550124e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (closed_form) = 1.137179683843056068741509458687
y[1] (numeric) = 1.1371796838430560687415094586872
absolute error = 2e-31
relative error = 1.7587370126426063559661203215939e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (closed_form) = 1.14842773079621954642493755919
y[1] (numeric) = 1.1484277307962195464249375591901
absolute error = 1e-31
relative error = 8.7075570641845028105388523373559e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (closed_form) = 1.1597609342666622099582076232457
y[1] (numeric) = 1.1597609342666622099582076232459
absolute error = 2e-31
relative error = 1.7244933338478383309106515412901e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (closed_form) = 1.1711781609434813198192706751205
y[1] (numeric) = 1.1711781609434813198192706751207
absolute error = 2e-31
relative error = 1.7076821159206331370108850634445e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (closed_form) = 1.1826782691135235179466946196796
y[1] (numeric) = 1.1826782691135235179466946196798
absolute error = 2e-31
relative error = 1.6910769836830602927850142990352e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (closed_form) = 1.1942601087755551916510140069746
y[1] (numeric) = 1.1942601087755551916510140069749
absolute error = 3e-31
relative error = 2.5120155801534930573966090761655e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (closed_form) = 1.2059225217552616386448320770481
y[1] (numeric) = 1.2059225217552616386448320770484
absolute error = 3e-31
relative error = 2.4877220102278187721668081277940e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (closed_form) = 1.217664341821063533371004392832
y[1] (numeric) = 1.2176643418210635333710043928323
absolute error = 3e-31
relative error = 2.4637331462900403335567809166697e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=644.9MB, alloc=44.3MB, time=7.20
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (closed_form) = 1.229484394800739113078784643007
y[1] (numeric) = 1.2294843948007391130787846430074
absolute error = 4e-31
relative error = 3.2533963154922959679624149023594e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (closed_form) = 1.241381498698840421526509831356
y[1] (numeric) = 1.2413814986988404215265098313563
absolute error = 3e-31
relative error = 2.4166624064757396804469083841236e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (closed_form) = 1.2533544638148918687843011276872
y[1] (numeric) = 1.2533544638148918687843011276876
absolute error = 4e-31
relative error = 3.1914355559280639955124290737998e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (closed_form) = 1.2654020928623592873792985817516
y[1] (numeric) = 1.2654020928623592873792985817521
absolute error = 5e-31
relative error = 3.9513132056624957434893179495707e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (closed_form) = 1.2775231810883775879769557263328
y[1] (numeric) = 1.2775231810883775879769557263334
absolute error = 6e-31
relative error = 4.6965879671070539139950719185512e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (closed_form) = 1.2897165163942250419325986538757
y[1] (numeric) = 1.2897165163942250419325986538763
absolute error = 6e-31
relative error = 4.6521851303996111048406558326333e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (closed_form) = 1.3019808794565321433853893115545
y[1] (numeric) = 1.301980879456532143385389311555
absolute error = 5e-31
relative error = 3.8403021725534715920483164189011e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (closed_form) = 1.3143150438492129301094906668387
y[1] (numeric) = 1.3143150438492129301094906668393
absolute error = 6e-31
relative error = 4.5651155163132716849709725284206e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (closed_form) = 1.3267177761661065700919577223859
y[1] (numeric) = 1.3267177761661065700919577223866
absolute error = 7e-31
relative error = 5.2761786460932984905638385872885e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (closed_form) = 1.3391878361443169497808975726373
y[1] (numeric) = 1.3391878361443169497808975726379
absolute error = 6e-31
relative error = 4.4803274328377433162954577908993e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=684.7MB, alloc=44.3MB, time=7.66
x[1] = 1.88
y[1] (closed_form) = 1.3517239767882379301478563337071
y[1] (numeric) = 1.3517239767882379301478563337079
absolute error = 8e-31
relative error = 5.9183680524839028352463645795795e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (closed_form) = 1.3643249444942518681421807434129
y[1] (numeric) = 1.3643249444942518681421807434138
absolute error = 9e-31
relative error = 6.5966689506921336824908874048007e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (closed_form) = 1.3769894791760889337891240834453
y[1] (numeric) = 1.3769894791760889337891240834462
absolute error = 9e-31
relative error = 6.5359976500220472218723445477034e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (closed_form) = 1.3897163143908346871044523624493
y[1] (numeric) = 1.3897163143908346871044523624502
absolute error = 9e-31
relative error = 6.4761418620497673179806491749987e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (closed_form) = 1.402504177465573314172865263472
y[1] (numeric) = 1.4025041774655733141728652634729
absolute error = 9e-31
relative error = 6.4170931856072273631600981320483e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.93
y[1] (closed_form) = 1.4153517896246538581721596919631
y[1] (numeric) = 1.4153517896246538581721596919639
absolute error = 8e-31
relative error = 5.6523050019398858250727471594508e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (closed_form) = 1.428257866117566718826088346975
y[1] (numeric) = 1.4282578661175667188260883469759
absolute error = 9e-31
relative error = 6.3013831140063660347592670313226e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (closed_form) = 1.4412211163474176327425314240392
y[1] (numeric) = 1.4412211163474176327425314240399
absolute error = 7e-31
relative error = 4.8569923938809367266232894923243e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (closed_form) = 1.4542402439999862873460089259574
y[1] (numeric) = 1.4542402439999862873460089259581
absolute error = 7e-31
relative error = 4.8135100296399622991024301603375e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (closed_form) = 1.4673139471733566626506888167261
y[1] (numeric) = 1.4673139471733566626506888167268
absolute error = 7e-31
relative error = 4.7706218655420310774305141767859e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (closed_form) = 1.4804409185081061379477386425052
y[1] (numeric) = 1.4804409185081061379477386425059
absolute error = 7e-31
relative error = 4.7283210781921329183248823166511e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=724.5MB, alloc=44.3MB, time=8.09
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (closed_form) = 1.4936198453180403446048424450727
y[1] (numeric) = 1.4936198453180403446048424450733
absolute error = 6e-31
relative error = 4.0170864218280418268641684357715e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (closed_form) = 1.5068494097214606916015483635891
y[1] (numeric) = 1.5068494097214606916015483635895
absolute error = 4e-31
relative error = 2.6545452877997909615773234638178e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (closed_form) = 1.5201282887729514371572826298917
y[1] (numeric) = 1.5201282887729514371572826298922
absolute error = 5e-31
relative error = 3.2891960743892236332153285253399e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (closed_form) = 1.5334551545956731278546893495365
y[1] (numeric) = 1.5334551545956731278546893495369
absolute error = 4e-31
relative error = 2.6084884112927853833229981466121e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (closed_form) = 1.5468286745141491760246278997285
y[1] (numeric) = 1.5468286745141491760246278997289
absolute error = 4e-31
relative error = 2.5859360289247153699168879340919e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (closed_form) = 1.5602475111875322968457445567072
y[1] (numeric) = 1.5602475111875322968457445567074
absolute error = 2e-31
relative error = 1.2818479027585592595050688480979e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (closed_form) = 1.5737103227433374786259633894871
y[1] (numeric) = 1.5737103227433374786259633894871
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (closed_form) = 1.587215762911628113080312041288
y[1] (numeric) = 1.587215762911628113080312041288
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (closed_form) = 1.6007624811596418671038760185679
y[1] (numeric) = 1.6007624811596418671038760185679
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (closed_form) = 1.6143491228268428335648920447478
y[1] (numeric) = 1.6143491228268428335648920447477
absolute error = 1e-31
relative error = 6.1944469499195267202933663818424e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (closed_form) = 1.6279743292603864560154442531429
y[1] (numeric) = 1.627974329260386456015444253143
absolute error = 1e-31
relative error = 6.1426030007138702086587275361294e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=764.5MB, alloc=44.3MB, time=8.53
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (closed_form) = 1.6416367379509836809401792104502
y[1] (numeric) = 1.6416367379509836809401792104502
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (closed_form) = 1.655334982669150751241034648761
y[1] (numeric) = 1.6553349826691507512410346487611
absolute error = 1e-31
relative error = 6.0410733203230349235763747258174e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (closed_form) = 1.6690676936018310160921745493298
y[1] (numeric) = 1.6690676936018310160921745493298
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (closed_form) = 1.6828334974893750950979962132938
y[1] (numeric) = 1.6828334974893750950979962132938
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (closed_form) = 1.6966310177628656988519432749397
y[1] (numeric) = 1.6966310177628656988519432749397
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (closed_form) = 1.7104588746817733735285057452202
y[1] (numeric) = 1.7104588746817733735285057452202
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (closed_form) = 1.7243156854719294040486606236371
y[1] (numeric) = 1.7243156854719294040486606236371
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (closed_form) = 1.7382000644638020786434135704731
y[1] (numeric) = 1.7382000644638020786434135704731
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (closed_form) = 1.7521106232310624873042151215786
y[1] (numeric) = 1.7521106232310624873042151215788
absolute error = 2e-31
relative error = 1.1414804370695529371273074556472e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (closed_form) = 1.766045970729425997655877517892
y[1] (numeric) = 1.7660459707294259976558775178922
absolute error = 2e-31
relative error = 1.1324733518538843558558584940540e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (closed_form) = 1.7800047134357555242201057022388
y[1] (numeric) = 1.780004713435755524220105702239
absolute error = 2e-31
relative error = 1.1235925303476364154596318019398e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=804.4MB, alloc=44.3MB, time=8.98
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (closed_form) = 1.7939854554874126808586351349626
y[1] (numeric) = 1.7939854554874126808586351349627
absolute error = 1e-31
relative error = 5.5741812005287821006656160831340e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (closed_form) = 1.807986798821842881396857687891
y[1] (numeric) = 1.807986798821842881396857687891
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (closed_form) = 1.8220073433163804300341937834971
y[1] (numeric) = 1.8220073433163804300341937834972
absolute error = 1e-31
relative error = 5.4884520837321132407350386105454e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (closed_form) = 1.8360456869282596211486735957059
y[1] (numeric) = 1.8360456869282596211486735957061
absolute error = 2e-31
relative error = 1.0892975127138797697270488864649e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (closed_form) = 1.8501004258348178475024223818086
y[1] (numeric) = 1.8501004258348178475024223818088
absolute error = 2e-31
relative error = 1.0810223986071151830003511597215e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (closed_form) = 1.8641701545738766966540649310045
y[1] (numeric) = 1.8641701545738766966540649310048
absolute error = 3e-31
relative error = 1.6092951561526089167532896773320e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (closed_form) = 1.8782534661842869975853917461896
y[1] (numeric) = 1.8782534661842869975853917461899
absolute error = 3e-31
relative error = 1.5972285178818626771972565790576e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (closed_form) = 1.8923489523466237631547447741598
y[1] (numeric) = 1.8923489523466237631547447741601
absolute error = 3e-31
relative error = 1.5853312869594288778231469657976e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (closed_form) = 1.9064552035240169590001227402154
y[1] (numeric) = 1.9064552035240169590001227402158
absolute error = 4e-31
relative error = 2.0981347962470544263285668198787e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (closed_form) = 1.9205708091031040159324743595225
y[1] (numeric) = 1.9205708091031040159324743595229
absolute error = 4e-31
relative error = 2.0827141498979555755114735771654e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (closed_form) = 1.9346943575350899906854001313727
y[1] (numeric) = 1.934694357535089990685400131373
absolute error = 3e-31
relative error = 1.5506325266912803921184354311885e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=844.2MB, alloc=44.3MB, time=9.42
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (closed_form) = 1.9488244364769012691227374882835
y[1] (numeric) = 1.9488244364769012691227374882837
absolute error = 2e-31
relative error = 1.0262597094767624527574428059977e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (closed_form) = 1.9629596329324186966513362353406
y[1] (numeric) = 1.9629596329324186966513362353406
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (closed_form) = 1.9770985333937760126436768852674
y[1] (numeric) = 1.9770985333937760126436768852673
absolute error = 1e-31
relative error = 5.0579168569988077917246479543899e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (closed_form) = 1.9912397239827094591446379302457
y[1] (numeric) = 1.9912397239827094591446379302456
absolute error = 1e-31
relative error = 5.0219970401147104902762630848625e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (closed_form) = 2.0053817905919444290193323217124
y[1] (numeric) = 2.0053817905919444290193323217122
absolute error = 2e-31
relative error = 9.9731632618926102682035409101823e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (closed_form) = 2.0195233190266050149950201885332
y[1] (numeric) = 2.019523319026605014995020188533
absolute error = 2e-31
relative error = 9.9033270928705338877018382943843e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (closed_form) = 2.0336628951456323187600345003473
y[1] (numeric) = 2.033662895145632318760034500347
absolute error = 3e-31
relative error = 1.4751707410117090543757531103491e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (closed_form) = 2.047799105003197378406657981605
y[1] (numeric) = 2.0477991050031973784066579816048
absolute error = 2e-31
relative error = 9.7665830359705975837380568920863e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (closed_form) = 2.0619305349900945730430507019935
y[1] (numeric) = 2.0619305349900945730430507019933
absolute error = 2e-31
relative error = 9.6996478109268987341997287752460e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (closed_form) = 2.0760557719751013653515945949133
y[1] (numeric) = 2.076055771975101365351594594913
absolute error = 3e-31
relative error = 1.4450478838272653685282913768053e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (closed_form) = 2.0901734034462902462371984623505
y[1] (numeric) = 2.0901734034462902462371984623502
absolute error = 3e-31
relative error = 1.4352876153976422676272016600518e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=884.2MB, alloc=44.3MB, time=9.88
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (closed_form) = 2.104282017652278750488858196988
y[1] (numeric) = 2.1042820176522787504888581969876
absolute error = 4e-31
relative error = 1.9008858919313249663099395366463e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (closed_form) = 2.1183802037434034185706140195549
y[1] (numeric) = 2.1183802037434034185706140195545
absolute error = 4e-31
relative error = 1.8882351680456482820565743495054e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (closed_form) = 2.1324665519128035872633702117027
y[1] (numeric) = 2.1324665519128035872633702117023
absolute error = 4e-31
relative error = 1.8757621292638965287831788878745e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (closed_form) = 2.1465396535374009008960825960703
y[1] (numeric) = 2.14653965353740090089608259607
absolute error = 3e-31
relative error = 1.3975982204922861759109947009798e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (closed_form) = 2.1605981013187604453326731792058
y[1] (numeric) = 2.1605981013187604453326731792055
absolute error = 3e-31
relative error = 1.3885044137402950141395876702204e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (closed_form) = 2.1746404894238194187186571529247
y[1] (numeric) = 2.1746404894238194187186571529245
absolute error = 2e-31
relative error = 9.1969224785744185880142684679950e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (closed_form) = 2.1886654136254692662376810927798
y[1] (numeric) = 2.1886654136254692662376810927795
absolute error = 3e-31
relative error = 1.3706983174877220619411919422211e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (closed_form) = 2.2026714714429772207816480882812
y[1] (numeric) = 2.2026714714429772207816480882809
absolute error = 3e-31
relative error = 1.3619825012010031054080610847566e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (closed_form) = 2.2166572622822332074973803528544
y[1] (numeric) = 2.2166572622822332074973803528541
absolute error = 3e-31
relative error = 1.3533892005078178951006289256439e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (closed_form) = 2.2306213875758080876362366781547
y[1] (numeric) = 2.2306213875758080876362366781544
absolute error = 3e-31
relative error = 1.3449167199371006817406695786482e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (closed_form) = 2.2445624509228092359990145851528
y[1] (numeric) = 2.2445624509228092359990145851525
absolute error = 3e-31
relative error = 1.3365633906807123849825071044416e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=924.0MB, alloc=44.3MB, time=10.31
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (closed_form) = 2.2584790582285194665349386078246
y[1] (numeric) = 2.2584790582285194665349386078242
absolute error = 4e-31
relative error = 1.7711034270724986238358961438746e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (closed_form) = 2.2723698178438053423185401940661
y[1] (numeric) = 2.2723698178438053423185401940656
absolute error = 5e-31
relative error = 2.2003460707572565995517349505624e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (closed_form) = 2.2862333407042809291896047402451
y[1] (numeric) = 2.2862333407042809291896047402449
absolute error = 2e-31
relative error = 8.7480134437366489298428299727635e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (closed_form) = 2.3000682404692130767967911728213
y[1] (numeric) = 2.300068240469213076796791172821
absolute error = 3e-31
relative error = 1.3043091275361469715240388601914e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (closed_form) = 2.3138731336601543366325737300976
y[1] (numeric) = 2.3138731336601543366325737300974
absolute error = 2e-31
relative error = 8.6435162365031640966455585864638e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (closed_form) = 2.3276466397992896538832294965324
y[1] (numeric) = 2.3276466397992896538832294965322
absolute error = 2e-31
relative error = 8.5923695023247074378844613403058e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (closed_form) = 2.3413873815474829985399752164358
y[1] (numeric) = 2.3413873815474829985399752164356
absolute error = 2e-31
relative error = 8.5419440446379645287244004630221e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (closed_form) = 2.3550939848420101312231807491671
y[1] (numeric) = 2.355093984842010131223180749167
absolute error = 1e-31
relative error = 4.2461150443942232558821304874149e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (closed_form) = 2.3687650790339637305578536667508
y[1] (numeric) = 2.3687650790339637305578536667506
absolute error = 2e-31
relative error = 8.4432180198115951785077393058611e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (closed_form) = 2.3823992970253171417021613365833
y[1] (numeric) = 2.3823992970253171417021613365831
absolute error = 2e-31
relative error = 8.3948983803731642757149654666691e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (closed_form) = 2.3959952754056330397683570467331
y[1] (numeric) = 2.3959952754056330397683570467328
absolute error = 3e-31
relative error = 1.2520892803063274902192659405602e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=964.0MB, alloc=44.3MB, time=10.75
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (closed_form) = 2.4095516545884033373836915876564
y[1] (numeric) = 2.4095516545884033373836915876561
absolute error = 3e-31
relative error = 1.2450449004847984160966231104610e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (closed_form) = 2.4230670789470067025141704100862
y[1] (numeric) = 2.4230670789470067025141704100858
absolute error = 4e-31
relative error = 1.6508003574289332971581944716309e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (closed_form) = 2.4365401969502700909126715372384
y[1] (numeric) = 2.436540196950270090912671537238
absolute error = 4e-31
relative error = 1.6416720746108175957261261912542e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (closed_form) = 2.4499696612976207371511469866912
y[1] (numeric) = 2.4499696612976207371511469866909
absolute error = 3e-31
relative error = 1.2245049591393948006181853690080e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (closed_form) = 2.4633541290538150891504307655679
y[1] (numeric) = 2.4633541290538150891504307655675
absolute error = 4e-31
relative error = 1.6238022592133016603142914512646e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (closed_form) = 2.4766922617832312134264741960854
y[1] (numeric) = 2.476692261783231213426474196085
absolute error = 4e-31
relative error = 1.6150573334129042546387176250345e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (closed_form) = 2.4899827256837112419243939126075
y[1] (numeric) = 2.489982725683711241924393912607
absolute error = 5e-31
relative error = 2.0080460592862451826705007274644e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (closed_form) = 2.5032241917199404763071841259797
y[1] (numeric) = 2.5032241917199404763071841259791
absolute error = 6e-31
relative error = 2.3969087626456101005920872077266e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (closed_form) = 2.5164153357563498118998131669984
y[1] (numeric) = 2.5164153357563498118998131669978
absolute error = 6e-31
relative error = 2.3843440765697773043423355281677e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (closed_form) = 2.529554838689528191157061550139
y[1] (numeric) = 2.5295548386895281911570615501384
absolute error = 6e-31
relative error = 2.3719588554594788748738925433413e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (closed_form) = 2.5426413865801318455200981171489
y[1] (numeric) = 2.5426413865801318455200981171485
absolute error = 4e-31
relative error = 1.5731671879139922156383057875042e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1003.9MB, alloc=44.3MB, time=11.20
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (closed_form) = 2.5556736707842771348475326046904
y[1] (numeric) = 2.5556736707842771348475326046898
absolute error = 6e-31
relative error = 2.3477175777918230008834577907783e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (closed_form) = 2.5686503880844038452464951986566
y[1] (numeric) = 2.5686503880844038452464951986563
absolute error = 3e-31
relative error = 1.1679285020322595740715097308078e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (closed_form) = 2.5815702408195958590830123518903
y[1] (numeric) = 2.5815702408195958590830123518898
absolute error = 5e-31
relative error = 1.9368057165132962080076487524872e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (closed_form) = 2.5944319370153461652132780240618
y[1] (numeric) = 2.5944319370153461652132780240615
absolute error = 3e-31
relative error = 1.1563224909462155160072369223686e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (closed_form) = 2.6072341905127532330429343646538
y[1] (numeric) = 2.6072341905127532330429343646532
absolute error = 6e-31
relative error = 2.3012892443006842050571195363759e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (closed_form) = 2.6199757210971358308846191971525
y[1] (numeric) = 2.6199757210971358308846191971518
absolute error = 7e-31
relative error = 2.6717804839308563893184513580270e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (closed_form) = 2.6326552546260534272391232077354
y[1] (numeric) = 2.6326552546260534272391232077348
absolute error = 6e-31
relative error = 2.2790678686306952934344169146421e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (closed_form) = 2.6452715231567193730667120348564
y[1] (numeric) = 2.6452715231567193730667120348557
absolute error = 7e-31
relative error = 2.6462311859943174187118744125453e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (closed_form) = 2.6578232650727941238365634254889
y[1] (numeric) = 2.6578232650727941238365634254883
absolute error = 6e-31
relative error = 2.2574864472170493443257290875785e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (closed_form) = 2.6703092252105458221377751804832
y[1] (numeric) = 2.6703092252105458221377751804825
absolute error = 7e-31
relative error = 2.6214192475959675154652244387956e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (closed_form) = 2.6827281549843656248988162566396
y[1] (numeric) = 2.6827281549843656248988162566388
absolute error = 8e-31
relative error = 2.9820390057548049688181438750298e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1043.8MB, alloc=44.3MB, time=11.64
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (closed_form) = 2.6950788125116252237872948377508
y[1] (numeric) = 2.6950788125116252237872948377501
absolute error = 7e-31
relative error = 2.5973266412481974482320586495683e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (closed_form) = 2.7073599627368640731420509846478
y[1] (numeric) = 2.7073599627368640731420509846472
absolute error = 6e-31
relative error = 2.2161811072712376037108785592409e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (closed_form) = 2.7195703775552939068182696666288
y[1] (numeric) = 2.7195703775552939068182696666283
absolute error = 5e-31
relative error = 1.8385256881988304904287180027505e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (closed_form) = 2.7317088359356081935968497506059
y[1] (numeric) = 2.7317088359356081935968497506054
absolute error = 5e-31
relative error = 1.8303561251569125638908041229142e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (closed_form) = 2.7437741240420842503148288827758
y[1] (numeric) = 2.7437741240420842503148288827752
absolute error = 6e-31
relative error = 2.1867689280343878150269744274670e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (closed_form) = 2.7557650353559658026073026420937
y[1] (numeric) = 2.7557650353559658026073026420932
absolute error = 5e-31
relative error = 1.8143781983771861770433824922791e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (closed_form) = 2.7676803707961138551059155704172
y[1] (numeric) = 2.7676803707961138551059155704167
absolute error = 5e-31
relative error = 1.8065669911738279908924270939916e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (closed_form) = 2.7795189388389138061074462869052
y[1] (numeric) = 2.7795189388389138061074462869046
absolute error = 6e-31
relative error = 2.1586469212929252922456724077108e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (closed_form) = 2.7912795556374268161009420906446
y[1] (numeric) = 2.791279555637426816100942090644
absolute error = 6e-31
relative error = 2.1495518024635185774187487803061e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (closed_form) = 2.8029610451397735151158428141748
y[1] (numeric) = 2.8029610451397735151158428141742
absolute error = 6e-31
relative error = 2.1405934307948263803801545540110e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (closed_form) = 2.8145622392067382106190118761381
y[1] (numeric) = 2.8145622392067382106190118761376
absolute error = 5e-31
relative error = 1.7764751940284716856025054601447e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1083.7MB, alloc=44.3MB, time=12.08
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (closed_form) = 2.8260819777285818356378880098541
y[1] (numeric) = 2.8260819777285818356378880098535
absolute error = 6e-31
relative error = 2.1230806633650464673262340651704e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (closed_form) = 2.8375191087410519559122891516003
y[1] (numeric) = 2.8375191087410519559122891515997
absolute error = 6e-31
relative error = 2.1145232049774899500445967607625e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (closed_form) = 2.8488724885405782351708279919232
y[1] (numeric) = 2.8488724885405782351708279919225
absolute error = 7e-31
relative error = 2.4571124289195419052951195117390e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (closed_form) = 2.8601409817986418390814074494976
y[1] (numeric) = 2.860140981798641839081407449497
absolute error = 6e-31
relative error = 2.0977986883103963320139640451544e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (closed_form) = 2.8713234616753073410307085369239
y[1] (numeric) = 2.8713234616753073410307085369234
absolute error = 5e-31
relative error = 1.7413572753947726158215223266762e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (closed_form) = 2.8824188099319057766367022757911
y[1] (numeric) = 2.8824188099319057766367022757907
absolute error = 4e-31
relative error = 1.3877233891956512545900160900929e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (closed_form) = 2.8934259170428575787826366422344
y[1] (numeric) = 2.8934259170428575787826366422339
absolute error = 5e-31
relative error = 1.7280553030748081647558278815438e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (closed_form) = 2.9043436823066242109721806128685
y[1] (numeric) = 2.9043436823066242109721806128681
absolute error = 4e-31
relative error = 1.3772474739708516975644409089911e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (closed_form) = 2.9151710139557774039348491829575
y[1] (numeric) = 2.9151710139557774039348491829571
absolute error = 4e-31
relative error = 1.3721321942523538167199994320579e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (closed_form) = 2.9259068292661749886497728724079
y[1] (numeric) = 2.9259068292661749886497728724075
absolute error = 4e-31
relative error = 1.3670975302392695671190252711762e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1123.5MB, alloc=44.3MB, time=12.53
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (closed_form) = 2.9365500546652324082954889002241
y[1] (numeric) = 2.9365500546652324082954889002237
absolute error = 4e-31
relative error = 1.3621426250321488921938616098291e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (closed_form) = 2.9470996258392790820647850075112
y[1] (numeric) = 2.9470996258392790820647850075108
absolute error = 4e-31
relative error = 1.3572666376559545394502750523682e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (closed_form) = 2.9575544878399888852976777829448
y[1] (numeric) = 2.9575544878399888852976777829445
absolute error = 3e-31
relative error = 1.0143515571173840444066195287555e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (closed_form) = 2.9679135951898741029732039640134
y[1] (numeric) = 2.9679135951898741029732039640132
absolute error = 2e-31
relative error = 6.7387406535062849979116160449458e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (closed_form) = 2.9781759119868323072525868697737
y[1] (numeric) = 2.9781759119868323072525868697734
absolute error = 3e-31
relative error = 1.0073280050131787465971144323283e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (closed_form) = 2.9883404120077357044731457560209
y[1] (numeric) = 2.9883404120077357044731457560207
absolute error = 2e-31
relative error = 6.6926779558433476825730718059629e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (closed_form) = 2.9984060788110525927445728700206
y[1] (numeric) = 2.9984060788110525927445728700204
absolute error = 2e-31
relative error = 6.6702105966682570209957684495449e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (closed_form) = 3.0083719058384906680873361733658
y[1] (numeric) = 3.0083719058384906680873361733654
absolute error = 4e-31
relative error = 1.3296228409250230834769730658929e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (closed_form) = 3.0182368965156520148672963654614
y[1] (numeric) = 3.018236896515652014867296365461
absolute error = 4e-31
relative error = 1.3252770200436308742139157221162e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (closed_form) = 3.028000064351689715111373625032
y[1] (numeric) = 3.0280000643516897151113736250315
absolute error = 5e-31
relative error = 1.6512549186720461800082622634785e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (closed_form) = 3.0376604330379561111263794005864
y[1] (numeric) = 3.037660433037956111126379400586
absolute error = 4e-31
relative error = 1.3168028777988231720298842479693e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1163.4MB, alloc=44.3MB, time=12.97
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (closed_form) = 3.0472170365456328566769579781507
y[1] (numeric) = 3.0472170365456328566769579781501
absolute error = 6e-31
relative error = 1.9690097318442674902363211043186e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (closed_form) = 3.0566689192223329937988781369027
y[1] (numeric) = 3.0566689192223329937988781369021
absolute error = 6e-31
relative error = 1.9629211270700848413434075107234e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (closed_form) = 3.0660151358876653951204950258811
y[1] (numeric) = 3.0660151358876653951204950258806
absolute error = 5e-31
relative error = 1.6307812513627438163817135536933e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (closed_form) = 3.0752547519277520153277868853919
y[1] (numeric) = 3.0752547519277520153277868853916
absolute error = 3e-31
relative error = 9.7552893727565891091015283598245e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (closed_form) = 3.0843868433886885001265842231147
y[1] (numeric) = 3.0843868433886885001265842231143
absolute error = 4e-31
relative error = 1.2968541895365385236751140771109e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (closed_form) = 3.0934104970689388067189788031801
y[1] (numeric) = 3.0934104970689388067189788031797
absolute error = 4e-31
relative error = 1.2930711923910747675315308281045e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (closed_form) = 3.1023248106106545964088600677324
y[1] (numeric) = 3.1023248106106545964088600677319
absolute error = 5e-31
relative error = 1.6116945533552340423653129883344e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (closed_form) = 3.1111288925899102674734176775078
y[1] (numeric) = 3.1111288925899102674734176775071
absolute error = 7e-31
relative error = 2.2499871402540108853455391665732e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (closed_form) = 3.1198218626058446048725186312483
y[1] (numeric) = 3.1198218626058446048725186312477
absolute error = 6e-31
relative error = 1.9231867280359636433168182142752e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (closed_form) = 3.128402851368700132705272486717
y[1] (numeric) = 3.1284028513687001327052724867162
absolute error = 8e-31
relative error = 2.5572154163265574701537789993227e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (closed_form) = 3.1368710007867513655519049092821
y[1] (numeric) = 3.1368710007867513655519049092813
absolute error = 8e-31
relative error = 2.5503120778615182103946686079939e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1203.2MB, alloc=44.3MB, time=13.41
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (closed_form) = 3.1452254640521132659482453287053
y[1] (numeric) = 3.1452254640521132659482453287044
absolute error = 9e-31
relative error = 2.8614800760276684977876564873717e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (closed_form) = 3.1534654057254213272185880649025
y[1] (numeric) = 3.1534654057254213272185880649015
absolute error = 1.0e-30
relative error = 3.1711145401639837813638803171833e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (closed_form) = 3.1615900018193748137292101370396
y[1] (numeric) = 3.1615900018193748137292101370386
absolute error = 1.0e-30
relative error = 3.1629654680857986932744207984064e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (closed_form) = 3.1695984398811348043081395389952
y[1] (numeric) = 3.1695984398811348043081395389942
absolute error = 1.0e-30
relative error = 3.1549737891639726377615412111293e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (closed_form) = 3.1774899190735687990954968116626
y[1] (numeric) = 3.1774899190735687990954968116616
absolute error = 1.0e-30
relative error = 3.1471382300767792993982191143252e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (closed_form) = 3.185263650255333765431428491297
y[1] (numeric) = 3.185263650255333765431428491296
absolute error = 1.0e-30
relative error = 3.1394575451229572420454572127086e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (closed_form) = 3.1929188560597896145437792896838
y[1] (numeric) = 3.1929188560597896145437792896828
absolute error = 1.0e-30
relative error = 3.1319305158730106737413601429584e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (closed_form) = 3.2004547709727352177535952502794
y[1] (numeric) = 3.2004547709727352177535952502784
absolute error = 1.0e-30
relative error = 3.1245559508283987987081116103383e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (closed_form) = 3.2078706414089591886616171275802
y[1] (numeric) = 3.2078706414089591886616171275791
absolute error = 1.1e-30
relative error = 3.4290659535973638937486218966801e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (closed_form) = 3.2151657257875977763013374462304
y[1] (numeric) = 3.2151657257875977763013374462292
absolute error = 1.2e-30
relative error = 3.7323114960304075041925041069459e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (closed_form) = 3.2223392946062923335321039691294
y[1] (numeric) = 3.2223392946062923335321039691284
absolute error = 1.0e-30
relative error = 3.1033355229657176703404104053729e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1243.1MB, alloc=44.3MB, time=13.84
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (closed_form) = 3.2293906305141389449872279485271
y[1] (numeric) = 3.229390630514138944987227948526
absolute error = 1.1e-30
relative error = 3.4062153695691908363189916968760e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (closed_form) = 3.2363190283834229196750935032676
y[1] (numeric) = 3.2363190283834229196750935032665
absolute error = 1.1e-30
relative error = 3.3989232530930739015348664877431e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (closed_form) = 3.243123795380130974843786555817
y[1] (numeric) = 3.2431237953801309748437865558158
absolute error = 1.2e-30
relative error = 3.7001362751228136792979583509326e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (closed_form) = 3.2498042510332340599496168235328
y[1] (numeric) = 3.2498042510332340599496168235318
absolute error = 1.0e-30
relative error = 3.0771084125515026888140386959904e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (closed_form) = 3.2563597273027338925048715061677
y[1] (numeric) = 3.2563597273027338925048715061665
absolute error = 1.2e-30
relative error = 3.6850965510311374689378925901293e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (closed_form) = 3.2627895686464664012079211517569
y[1] (numeric) = 3.2627895686464664012079211517557
absolute error = 1.2e-30
relative error = 3.6778344871863963170640584119340e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (closed_form) = 3.269093132085655396067034040684
y[1] (numeric) = 3.2690931320856553960670340406827
absolute error = 1.3e-30
relative error = 3.9766380077725419467887529512031e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (closed_form) = 3.275269787269209910205514582825
y[1] (numeric) = 3.2752697872692099102055145828237
absolute error = 1.3e-30
relative error = 3.9691386799738669993022472755392e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (closed_form) = 3.2813189165367587836675661535043
y[1] (numeric) = 3.2813189165367587836675661535029
absolute error = 1.4e-30
relative error = 4.2665770551727369158412932042240e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (closed_form) = 3.2872399149804161858190264267154
y[1] (numeric) = 3.2872399149804161858190264267139
absolute error = 1.5e-30
relative error = 4.5630986444411566096301151818797e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (closed_form) = 3.293032190505271899842206229175
y[1] (numeric) = 3.2930321905052718998422062291735
absolute error = 1.5e-30
relative error = 4.5550723868564582483398877318273e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1282.9MB, alloc=44.3MB, time=14.30
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (closed_form) = 3.2986951638886003203467908337052
y[1] (numeric) = 3.2986951638886003203467908337038
absolute error = 1.4e-30
relative error = 4.2441023812265156749973808888131e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (closed_form) = 3.3042282688377822432463832686906
y[1] (numeric) = 3.3042282688377822432463832686893
absolute error = 1.3e-30
relative error = 3.9343528782811893248746700996281e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (closed_form) = 3.3096309520469336557699699866143
y[1] (numeric) = 3.309630952046933655769969986613
absolute error = 1.3e-30
relative error = 3.9279303911391652549223170457738e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (closed_form) = 3.3149026732522358637764982461474
y[1] (numeric) = 3.314902673252235863776498246146
absolute error = 1.4e-30
relative error = 4.2233517481418734925782391644495e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (closed_form) = 3.3200429052859614234059420357896
y[1] (numeric) = 3.320042905285961423405942035788
absolute error = 1.6e-30
relative error = 4.8192148283764093307638924412652e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (closed_form) = 3.325051134129190474518712892103
y[1] (numeric) = 3.3250511341291904745187128921015
absolute error = 1.5e-30
relative error = 4.5112088190272007985357116425464e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (closed_form) = 3.3299268589632122043340018028928
y[1] (numeric) = 3.3299268589632122043340018028913
absolute error = 1.5e-30
relative error = 4.5046034448547371025261512046511e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (closed_form) = 3.3346695922196063011635227713918
y[1] (numeric) = 3.3346695922196063011635227713903
absolute error = 1.5e-30
relative error = 4.4981967733768112534169848869434e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (closed_form) = 3.3392788596289993901370190727586
y[1] (numeric) = 3.3392788596289993901370190727571
absolute error = 1.5e-30
relative error = 4.4919878304702381832829459907608e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (closed_form) = 3.3437542002684915753165898799309
y[1] (numeric) = 3.3437542002684915753165898799293
absolute error = 1.6e-30
relative error = 4.7850407182188382386514527473906e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (closed_form) = 3.3480951666077483455851478128628
y[1] (numeric) = 3.3480951666077483455851478128613
absolute error = 1.5e-30
relative error = 4.4801593902116671622233973901352e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1322.8MB, alloc=44.3MB, time=14.73
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (closed_form) = 3.3523013245537532351568283589299
y[1] (numeric) = 3.3523013245537532351568283589285
absolute error = 1.4e-30
relative error = 4.1762355601680978388623893609534e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (closed_form) = 3.356372253494216763480593883007
y[1] (numeric) = 3.3563722534942167634805938830056
absolute error = 1.4e-30
relative error = 4.1711702226786754909516042038780e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (closed_form) = 3.3603075463396373136792158628236
y[1] (numeric) = 3.3603075463396373136792158628222
absolute error = 1.4e-30
relative error = 4.1662853197023931112509920738767e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (closed_form) = 3.3641068095640097434708420665702
y[1] (numeric) = 3.3641068095640097434708420665689
absolute error = 1.3e-30
relative error = 3.8643243915566425736603359342592e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (closed_form) = 3.3677696632441776577459802453937
y[1] (numeric) = 3.3677696632441776577459802453921
absolute error = 1.6e-30
relative error = 4.7509187384826002544509028699038e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (closed_form) = 3.3712957410978254076054340935802
y[1] (numeric) = 3.3712957410978254076054340935786
absolute error = 1.6e-30
relative error = 4.7459496967150606133797393480166e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (closed_form) = 3.3746846905201060166909475764969
y[1] (numeric) = 3.3746846905201060166909475764951
absolute error = 1.8e-30
relative error = 5.3338316467207020957338619148211e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (closed_form) = 3.3779361726189013720464477320556
y[1] (numeric) = 3.3779361726189013720464477320538
absolute error = 1.8e-30
relative error = 5.3286974886931231846341013873085e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (closed_form) = 3.3810498622487111535201832158602
y[1] (numeric) = 3.3810498622487111535201832158584
absolute error = 1.8e-30
relative error = 5.3237901638127080680298870470698e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (closed_form) = 3.3840254480431671128430590565459
y[1] (numeric) = 3.3840254480431671128430590565439
absolute error = 2.0e-30
relative error = 5.9101210398890821633546328031976e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (closed_form) = 3.3868626324461694509823549300873
y[1] (numeric) = 3.3868626324461694509823549300854
absolute error = 1.9e-30
relative error = 5.6099116090448597849518319519260e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1362.7MB, alloc=44.3MB, time=15.17
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (closed_form) = 3.389561131741642180159038475882
y[1] (numeric) = 3.3895611317416421801590384758799
absolute error = 2.1e-30
relative error = 6.1954923318375642418403056062179e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (closed_form) = 3.392120676081904495017267975641
y[1] (numeric) = 3.3921206760819044950172679756389
absolute error = 2.1e-30
relative error = 6.1908174871467763253512185509960e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (closed_form) = 3.394541009514655315832610175317
y[1] (numeric) = 3.3945410095146553158326101753149
absolute error = 2.1e-30
relative error = 6.1864033874207158269682468430489e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (closed_form) = 3.3968218900085683053271394726706
y[1] (numeric) = 3.3968218900085683053271394726684
absolute error = 2.2e-30
relative error = 6.4766422003788094265173608885300e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (closed_form) = 3.3989630894774947996110660701379
y[1] (numeric) = 3.3989630894774947996110660701358
absolute error = 2.1e-30
relative error = 6.1783548238613625325703721672600e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (closed_form) = 3.4009643938032722329779679720729
y[1] (numeric) = 3.4009643938032722329779679720708
absolute error = 2.1e-30
relative error = 6.1747191585607463763561578038142e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (closed_form) = 3.4028256028571357757301542604696
y[1] (numeric) = 3.4028256028571357757301542604676
absolute error = 2.0e-30
relative error = 5.8774684142517544016705804843574e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (closed_form) = 3.4045465305197310438882200848828
y[1] (numeric) = 3.4045465305197310438882200848806
absolute error = 2.2e-30
relative error = 6.4619472234504973630087198823901e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (closed_form) = 3.4061270046997258795304996135461
y[1] (numeric) = 3.406127004699725879530499613544
absolute error = 2.1e-30
relative error = 6.1653602378961491844934583882559e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (closed_form) = 3.4075668673510193405998927656458
y[1] (numeric) = 3.4075668673510193405998927656437
absolute error = 2.1e-30
relative error = 6.1627550734829802469221392941379e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (closed_form) = 3.4088659744885461792934258191104
y[1] (numeric) = 3.4088659744885461792934258191084
absolute error = 2.0e-30
relative error = 5.8670537796666315318839854776390e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1402.5MB, alloc=44.3MB, time=15.63
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (closed_form) = 3.4100241962026752285998772926148
y[1] (numeric) = 3.4100241962026752285998772926128
absolute error = 2.0e-30
relative error = 5.8650610228137212362609871990264e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (closed_form) = 3.4110414166722002571588139546605
y[1] (numeric) = 3.4110414166722002571588139546586
absolute error = 1.9e-30
relative error = 5.5701463802618766475791538191947e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (closed_form) = 3.4119175341759219933663767324308
y[1] (numeric) = 3.411917534175921993366376732429
absolute error = 1.8e-30
relative error = 5.2756257499487094584080404273056e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (closed_form) = 3.4126524611028201605350575964098
y[1] (numeric) = 3.412652461102820160535057596408
absolute error = 1.8e-30
relative error = 5.2744896250534654516088759536424e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (closed_form) = 3.4132461239608145059124281107904
y[1] (numeric) = 3.4132461239608145059124281107885
absolute error = 1.9e-30
relative error = 5.5665484732029620118554559281096e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (closed_form) = 3.4136984633841139474632186099931
y[1] (numeric) = 3.413698463384113947463218609991
absolute error = 2.1e-30
relative error = 6.1516856937569098131026181432796e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (closed_form) = 3.4140094341391531035061940619509
y[1] (numeric) = 3.4140094341391531035061940619489
absolute error = 2.0e-30
relative error = 5.8582146258898742263411233467217e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (closed_form) = 3.4141790051291156115578100221132
y[1] (numeric) = 3.4141790051291156115578100221114
absolute error = 1.8e-30
relative error = 5.2721313009536491900676710489514e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (closed_form) = 3.4142071593970437840545337323786
y[1] (numeric) = 3.4142071593970437840545337323766
absolute error = 2.0e-30
relative error = 5.8578753620597651027677342592510e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (closed_form) = 3.4140938941275342899908495039764
y[1] (numeric) = 3.4140938941275342899908495039745
absolute error = 1.9e-30
relative error = 5.5651662166296151894529822398540e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1442.3MB, alloc=44.3MB, time=16.06
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (closed_form) = 3.413839220647019692906197647083
y[1] (numeric) = 3.4138392206470196929061976470813
absolute error = 1.7e-30
relative error = 4.9797307082253323477865730732441e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (closed_form) = 3.4134431644226358170672828674832
y[1] (numeric) = 3.4134431644226358170672828674815
absolute error = 1.7e-30
relative error = 4.9803084982302471548060985974292e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (closed_form) = 3.4129057650596750551081900410706
y[1] (numeric) = 3.4129057650596750551081900410691
absolute error = 1.5e-30
relative error = 4.3950817961531742590055241263407e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (closed_form) = 3.4122270762976258717954211180514
y[1] (numeric) = 3.4122270762976258717954211180499
absolute error = 1.5e-30
relative error = 4.3959559737962907398618243589594e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (closed_form) = 3.4114071660047988999641762506302
y[1] (numeric) = 3.4114071660047988999641762506287
absolute error = 1.5e-30
relative error = 4.3970125142132914124279761538514e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (closed_form) = 3.4104461161715401660118072776096
y[1] (numeric) = 3.4104461161715401660118072776081
absolute error = 1.5e-30
relative error = 4.3982515744416831580160878097915e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (closed_form) = 3.4093440229020321236202385939827
y[1] (numeric) = 3.4093440229020321236202385939811
absolute error = 1.6e-30
relative error = 4.6929848946076163590508409570709e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (closed_form) = 3.4081009964046833155971507143099
y[1] (numeric) = 3.4081009964046833155971507143082
absolute error = 1.7e-30
relative error = 4.9881150875322807035138887614737e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (closed_form) = 3.4067171609811076248617338230849
y[1] (numeric) = 3.4067171609811076248617338230834
absolute error = 1.5e-30
relative error = 4.4030658523116484726101279535948e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (closed_form) = 3.4051926550136942166407288098392
y[1] (numeric) = 3.4051926550136942166407288098376
absolute error = 1.6e-30
relative error = 4.6987062468968161505457755689197e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (closed_form) = 3.4035276309517694148701778379018
y[1] (numeric) = 3.4035276309517694148701778379001
absolute error = 1.7e-30
relative error = 4.9948176842760301890816106227627e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1482.2MB, alloc=44.3MB, time=16.50
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (closed_form) = 3.4017222552963518966037125405356
y[1] (numeric) = 3.4017222552963518966037125405341
absolute error = 1.5e-30
relative error = 4.4095310769847749084390050485452e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (closed_form) = 3.3997767085835027288952350533153
y[1] (numeric) = 3.3997767085835027288952350533136
absolute error = 1.7e-30
relative error = 5.0003283912968953543127635454261e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (closed_form) = 3.397691185366271913138428691628
y[1] (numeric) = 3.3976911853662719131384286916263
absolute error = 1.7e-30
relative error = 5.0033976228382262411204909425910e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (closed_form) = 3.395465894195243242193619825997
y[1] (numeric) = 3.3954658941952432421936198259952
absolute error = 1.8e-30
relative error = 5.3011871009430846142779356623883e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (closed_form) = 3.3931010575976794158000657040182
y[1] (numeric) = 3.3931010575976794158000657040165
absolute error = 1.7e-30
relative error = 5.0101661316377135045587580645114e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (closed_form) = 3.3905969120552694997447479775705
y[1] (numeric) = 3.3905969120552694997447479775689
absolute error = 1.6e-30
relative error = 4.7189331008684605703982508187368e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (closed_form) = 3.3879537079804809540232113337315
y[1] (numeric) = 3.3879537079804809540232113337299
absolute error = 1.6e-30
relative error = 4.7226147046552800577849054363749e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (closed_form) = 3.3851717096915185947699245680268
y[1] (numeric) = 3.3851717096915185947699245680254
absolute error = 1.4e-30
relative error = 4.1356838590842948904466841806446e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (closed_form) = 3.3822511953858929940411036017382
y[1] (numeric) = 3.3822511953858929940411036017366
absolute error = 1.6e-30
relative error = 4.7305770848207220295464470569254e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (closed_form) = 3.3791924571126009605879919008749
y[1] (numeric) = 3.3791924571126009605879919008734
absolute error = 1.5e-30
relative error = 4.4389303629119021134086641116885e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (closed_form) = 3.3759958007429208835493381133559
y[1] (numeric) = 3.3759958007429208835493381133544
absolute error = 1.5e-30
relative error = 4.4431334887025343286402963250595e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1522.2MB, alloc=44.3MB, time=16.95
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (closed_form) = 3.3726615459398258595043645441707
y[1] (numeric) = 3.3726615459398258595043645441693
absolute error = 1.4e-30
relative error = 4.1510242902534591648712405675614e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (closed_form) = 3.3691900261260176615480321958476
y[1] (numeric) = 3.3691900261260176615480321958461
absolute error = 1.5e-30
relative error = 4.4521086325449533077683632074112e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (closed_form) = 3.3655815884505847469650565774149
y[1] (numeric) = 3.3655815884505847469650565774136
absolute error = 1.3e-30
relative error = 3.8626310663842261780087610796717e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (closed_form) = 3.3618365937542876376741219792859
y[1] (numeric) = 3.3618365937542876376741219792848
absolute error = 1.1e-30
relative error = 3.2720210198306789013322652548255e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (closed_form) = 3.357955416533475144875321039439
y[1] (numeric) = 3.357955416533475144875321039438
absolute error = 1.0e-30
relative error = 2.9780026115782442614030262437416e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (closed_form) = 3.3539384449026350462482851443764
y[1] (numeric) = 3.3539384449026350462482851443754
absolute error = 1.0e-30
relative error = 2.9815693293948632261985542595246e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (closed_form) = 3.3497860805555829606020781868441
y[1] (numeric) = 3.3497860805555829606020781868431
absolute error = 1.0e-30
relative error = 2.9852652556074379206648025564892e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (closed_form) = 3.3454987387252933010570461942881
y[1] (numeric) = 3.3454987387252933010570461942871
absolute error = 1.0e-30
relative error = 2.9890909490553908433128443405151e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (closed_form) = 3.3410768481423763236298305489831
y[1] (numeric) = 3.3410768481423763236298305489821
absolute error = 1.0e-30
relative error = 2.9930469888951985498508256311647e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (closed_form) = 3.3365208509922054234820839543391
y[1] (numeric) = 3.3365208509922054234820839543381
absolute error = 1.0e-30
relative error = 2.9971339747588352146343903064896e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (closed_form) = 3.3318312028706989660675371417556
y[1] (numeric) = 3.3318312028706989660675371417547
absolute error = 9e-31
relative error = 2.7012172742261427781080989285275e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1562.2MB, alloc=44.3MB, time=17.39
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (closed_form) = 3.3270083727387610749574532601354
y[1] (numeric) = 3.3270083727387610749574532601344
absolute error = 1.0e-30
relative error = 3.0057032864537388693701447081702e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (closed_form) = 3.3220528428753859322277215190272
y[1] (numeric) = 3.3220528428753859322277215190262
absolute error = 1.0e-30
relative error = 3.0101869154328535273955530881237e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (closed_form) = 3.3169651088294302809384717566206
y[1] (numeric) = 3.3169651088294302809384717566198
absolute error = 8e-31
relative error = 2.4118432776711452077842169103991e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (closed_form) = 3.3117456793700589524157725238352
y[1] (numeric) = 3.3117456793700589524157725238344
absolute error = 8e-31
relative error = 2.4156444288082270804304204232296e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (closed_form) = 3.3063950764358683737413892584141
y[1] (numeric) = 3.3063950764358683737413892584132
absolute error = 9e-31
relative error = 2.7219977625001662874274593208125e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (closed_form) = 3.3009138350826931430574566374359
y[1] (numeric) = 3.3009138350826931430574566374348
absolute error = 1.1e-30
relative error = 3.3324105231375821416689630155309e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (closed_form) = 3.2953025034301008919850402654125
y[1] (numeric) = 3.2953025034301008919850402654114
absolute error = 1.1e-30
relative error = 3.3380850433458025523598033464223e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (closed_form) = 3.2895616426065807856257583757773
y[1] (numeric) = 3.2895616426065807856257583757762
absolute error = 1.1e-30
relative error = 3.3439105859964450818714848931204e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (closed_form) = 3.2836918266934311412507872858484
y[1] (numeric) = 3.2836918266934311412507872858473
absolute error = 1.1e-30
relative error = 3.3498880469171906111032971371309e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (closed_form) = 3.2776936426673517768686215428311
y[1] (numeric) = 3.2776936426673517768686215428299
absolute error = 1.2e-30
relative error = 3.6611109237880234810843685504126e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (closed_form) = 3.2715676903417468303888924347823
y[1] (numeric) = 3.2715676903417468303888924347809
absolute error = 1.4e-30
relative error = 4.2792940037066953787928635339564e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1602.2MB, alloc=44.3MB, time=17.83
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (closed_form) = 3.2653145823067439190514143303698
y[1] (numeric) = 3.2653145823067439190514143303685
absolute error = 1.3e-30
relative error = 3.9812396852790519085901917662444e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (closed_form) = 3.2589349438679356371545320755981
y[1] (numeric) = 3.2589349438679356371545320755967
absolute error = 1.4e-30
relative error = 4.2958820108829189689484517054381e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (closed_form) = 3.2524294129838495178819480310268
y[1] (numeric) = 3.2524294129838495178819480310254
absolute error = 1.4e-30
relative error = 4.3044746625741818492973738541621e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (closed_form) = 3.2457986402021527121797378753321
y[1] (numeric) = 3.2457986402021527121797378753307
absolute error = 1.4e-30
relative error = 4.3132681820114574755776644842845e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (closed_form) = 3.2390432885945977641625048832341
y[1] (numeric) = 3.2390432885945977641625048832326
absolute error = 1.5e-30
relative error = 4.6309970764572318035952822649604e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (closed_form) = 3.2321640336907159884169203892412
y[1] (numeric) = 3.2321640336907159884169203892397
absolute error = 1.5e-30
relative error = 4.6408535716771551111870251149571e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (closed_form) = 3.2251615634102650798096647484362
y[1] (numeric) = 3.2251615634102650798096647484346
absolute error = 1.6e-30
relative error = 4.9609917783720896688954754172623e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (closed_form) = 3.2180365779944377109824945293591
y[1] (numeric) = 3.2180365779944377109824945293576
absolute error = 1.5e-30
relative error = 4.6612273156162760973768362550544e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (closed_form) = 3.2107897899358379966173604546018
y[1] (numeric) = 3.2107897899358379966173604546003
absolute error = 1.5e-30
relative error = 4.6717477572082813603941466558306e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (closed_form) = 3.2034219239072328267667968253815
y[1] (numeric) = 3.2034219239072328267667968253802
absolute error = 1.3e-30
relative error = 4.0581604012199000199350860673162e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (closed_form) = 3.1959337166890851940568757001753
y[1] (numeric) = 3.1959337166890851940568757001739
absolute error = 1.4e-30
relative error = 4.3805664450712332987318598928027e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1642.1MB, alloc=44.3MB, time=18.28
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (closed_form) = 3.1883259170958767613696168392924
y[1] (numeric) = 3.188325917095876761369616839291
absolute error = 1.4e-30
relative error = 4.3910191003158361584618354908880e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (closed_form) = 3.1805992859012270376866875187885
y[1] (numeric) = 3.1805992859012270376866875187869
absolute error = 1.6e-30
relative error = 5.0304985198619192674746439498641e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (closed_form) = 3.172754595761816650114407364941
y[1] (numeric) = 3.1727545957618166501144073649394
absolute error = 1.6e-30
relative error = 5.0429365137073285046768184855531e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (closed_form) = 3.1647926311401223196994586468184
y[1] (numeric) = 3.1647926311401223196994586468168
absolute error = 1.6e-30
relative error = 5.0556235004364158946980789782899e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (closed_form) = 3.1567141882259712674733331503803
y[1] (numeric) = 3.1567141882259712674733331503787
absolute error = 1.6e-30
relative error = 5.0685614997003494108051868206537e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (closed_form) = 3.148520074856922895219540079033
y[1] (numeric) = 3.1485200748569228952195400790314
absolute error = 1.6e-30
relative error = 5.0817525756849692139058857438118e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (closed_form) = 3.140211110437485702729149881648
y[1] (numeric) = 3.1402111104374857027291498816463
absolute error = 1.7e-30
relative error = 5.4136487650448463210792095406045e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (closed_form) = 3.1317881258571775197856294424397
y[1] (numeric) = 3.1317881258571775197856294424379
absolute error = 1.8e-30
relative error = 5.7475152458065339706431969624632e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (closed_form) = 3.1232519634074372467874872367796
y[1] (numeric) = 3.1232519634074372467874872367778
absolute error = 1.8e-30
relative error = 5.7632237843411700334494820853108e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (closed_form) = 3.1146034766973964127654262030843
y[1] (numeric) = 3.1146034766973964127654262030826
absolute error = 1.7e-30
relative error = 5.4581586796487283302924374467295e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (closed_form) = 3.105843530568518973568012481138
y[1] (numeric) = 3.1058435305685189735680124811365
absolute error = 1.5e-30
relative error = 4.8296058228195022609115663415012e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1682.0MB, alloc=44.3MB, time=18.72
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (closed_form) = 3.0969730010081178861649081855758
y[1] (numeric) = 3.0969730010081178861649081855743
absolute error = 1.5e-30
relative error = 4.8434390597261398318100717786461e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (closed_form) = 3.0879927750617571073381686100673
y[1] (numeric) = 3.0879927750617571073381686100656
absolute error = 1.7e-30
relative error = 5.5051942275545042780002781097469e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (closed_form) = 3.0789037507445477764887366413833
y[1] (numeric) = 3.0789037507445477764887366413817
absolute error = 1.6e-30
relative error = 5.1966548146010872254805862504048e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (closed_form) = 3.0697068369513474528659341326429
y[1] (numeric) = 3.0697068369513474528659341326414
absolute error = 1.5e-30
relative error = 4.8864601073427321329223155497054e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (closed_form) = 3.0604029533658713872213935670731
y[1] (numeric) = 3.0604029533658713872213935670715
absolute error = 1.6e-30
relative error = 5.2280697162453688432404115072133e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (closed_form) = 3.0509930303687249166845242646285
y[1] (numeric) = 3.0509930303687249166845242646268
absolute error = 1.7e-30
relative error = 5.5719563534845180743633542290717e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (closed_form) = 3.0414780089443661795433861693787
y[1] (numeric) = 3.0414780089443661795433861693768
absolute error = 1.9e-30
relative error = 6.2469628069395462156045525042841e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (closed_form) = 3.0318588405870084535819623177043
y[1] (numeric) = 3.0318588405870084535819623177025
absolute error = 1.8e-30
relative error = 5.9369518656465414683871883626387e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (closed_form) = 3.0221364872054715276615818033849
y[1] (numeric) = 3.0221364872054715276615818033832
absolute error = 1.7e-30
relative error = 5.6251595756747798626627440304046e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (closed_form) = 3.0123119210269916213300448379021
y[1] (numeric) = 3.0123119210269916213300448379003
absolute error = 1.8e-30
relative error = 5.9754768005111620022480848645665e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (closed_form) = 3.0023861244999994713863308603183
y[1] (numeric) = 3.0023861244999994713863308603165
absolute error = 1.8e-30
relative error = 5.9952315437101278707169643604475e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1721.8MB, alloc=44.3MB, time=19.16
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (closed_form) = 2.992360090195876307511215234787
y[1] (numeric) = 2.9923600901958763075112152347853
absolute error = 1.7e-30
relative error = 5.6811344515984372593159887318720e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (closed_form) = 2.9822348207096975412843617266149
y[1] (numeric) = 2.9822348207096975412843617266131
absolute error = 1.8e-30
relative error = 6.0357420130036737796336804472050e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (closed_form) = 2.9720113285599740941362757308538
y[1] (numeric) = 2.9720113285599740941362757308521
absolute error = 1.7e-30
relative error = 5.7200320323936969341961604266945e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (closed_form) = 2.9616906360874013900187744432238
y[1] (numeric) = 2.9616906360874013900187744432221
absolute error = 1.7e-30
relative error = 5.7399648001244918335928056050530e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (closed_form) = 2.9512737753526261378103313681589
y[1] (numeric) = 2.9512737753526261378103313681574
absolute error = 1.5e-30
relative error = 5.0825511768076343945078322130641e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (closed_form) = 2.9407617880330411266928605655122
y[1] (numeric) = 2.9407617880330411266928605655106
absolute error = 1.6e-30
relative error = 5.4407671050098094258755455109737e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (closed_form) = 2.9301557253186183549343989069881
y[1] (numeric) = 2.9301557253186183549343989069864
absolute error = 1.7e-30
relative error = 5.8017394273990196640091826088350e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (closed_form) = 2.9194566478067909086780026374151
y[1] (numeric) = 2.9194566478067909086780026374134
absolute error = 1.7e-30
relative error = 5.8230013495049017078278623700538e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (closed_form) = 2.9086656253963941024613812088541
y[1] (numeric) = 2.9086656253963941024613812088525
absolute error = 1.6e-30
relative error = 5.5008041695475098374005748475306e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (closed_form) = 2.8977837371806764872648343358656
y[1] (numeric) = 2.8977837371806764872648343358639
absolute error = 1.7e-30
relative error = 5.8665523523641929834667944963686e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=1761.7MB, alloc=44.3MB, time=19.61
x[1] = 4.82
y[1] (closed_form) = 2.8868120713393914248975302821285
y[1] (numeric) = 2.8868120713393914248975302821267
absolute error = 1.8e-30
relative error = 6.2352517431619846605156600466560e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (closed_form) = 2.8757517250299800194747633623156
y[1] (numeric) = 2.8757517250299800194747633623139
absolute error = 1.7e-30
relative error = 5.9114978014392995559405702866904e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (closed_form) = 2.8646038042778562876023623453078
y[1] (numeric) = 2.864603804277856287602362345306
absolute error = 1.8e-30
relative error = 6.2835914597054220082283820210976e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (closed_form) = 2.8533694238658055386598025978259
y[1] (numeric) = 2.8533694238658055386598025978241
absolute error = 1.8e-30
relative error = 6.3083314237009021574764667249874e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (closed_form) = 2.8420497072225070252518259480575
y[1] (numeric) = 2.8420497072225070252518259480557
absolute error = 1.8e-30
relative error = 6.3334571363254348925559728791856e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (closed_form) = 2.8306457863101920114706256256645
y[1] (numeric) = 2.8306457863101920114706256256627
absolute error = 1.8e-30
relative error = 6.3589729548829877466828829623448e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (closed_form) = 2.8191588015114484930681520952868
y[1] (numeric) = 2.819158801511448493068152095285
absolute error = 1.8e-30
relative error = 6.3848833170907498123082679399703e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (closed_form) = 2.8075899015151838889721934675351
y[1] (numeric) = 2.8075899015151838889721934675333
absolute error = 1.8e-30
relative error = 6.4111927423181939954065289185260e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (closed_form) = 2.7959402432017571077820481057964
y[1] (numeric) = 2.7959402432017571077820481057945
absolute error = 1.9e-30
relative error = 6.7955672680050715956124040036524e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (closed_form) = 2.7842109915272914759414169027503
y[1] (numeric) = 2.7842109915272914759414169027483
absolute error = 2.0e-30
relative error = 7.1833636390570062168602809148301e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (closed_form) = 2.7724033194071800961992923655293
y[1] (numeric) = 2.7724033194071800961992923655274
absolute error = 1.9e-30
relative error = 6.8532597212669435010930277861785e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1801.6MB, alloc=44.3MB, time=20.05
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (closed_form) = 2.7605184075987952857259198762633
y[1] (numeric) = 2.7605184075987952857259198762615
absolute error = 1.8e-30
relative error = 6.5205143897798130939584148667314e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (closed_form) = 2.7485574445834138228422777227835
y[1] (numeric) = 2.7485574445834138228422777227814
absolute error = 2.1e-30
relative error = 7.6403715124763831015535864242384e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (closed_form) = 2.7365216264473698097400076517426
y[1] (numeric) = 2.7365216264473698097400076517406
absolute error = 2.0e-30
relative error = 7.3085481242713834179540379049993e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (closed_form) = 2.7244121567624470358064850001614
y[1] (numeric) = 2.7244121567624470358064850001593
absolute error = 2.1e-30
relative error = 7.7080848240507533450300577912988e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (closed_form) = 2.7122302464655228022190232000654
y[1] (numeric) = 2.7122302464655228022190232000633
absolute error = 2.1e-30
relative error = 7.7427054828278004709182080661998e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (closed_form) = 2.6999771137374752433254567572481
y[1] (numeric) = 2.6999771137374752433254567572461
absolute error = 2.0e-30
relative error = 7.4074701960398336586749632960589e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (closed_form) = 2.6876539838813662539780544167141
y[1] (numeric) = 2.6876539838813662539780544167121
absolute error = 2.0e-30
relative error = 7.4414340982677646658153089267321e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5
y[1] (closed_form) = 2.6752620891999122044265152346424
y[1] (numeric) = 2.6752620891999122044265152346403
absolute error = 2.1e-30
relative error = 7.8496981977120782685350327959017e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.01
y[1] (closed_form) = 2.662802668872254695596450860034
y[1] (numeric) = 2.6628026688722546955964508600318
absolute error = 2.2e-30
relative error = 8.2619715900004710697314105277826e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.02
y[1] (closed_form) = 2.6502769688300436775751354828495
y[1] (numeric) = 2.6502769688300436775751354828473
absolute error = 2.2e-30
relative error = 8.3010191986507092856908384606571e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.03
y[1] (closed_form) = 2.6376862416328453228894111499265
y[1] (numeric) = 2.6376862416328453228894111499244
absolute error = 2.1e-30
relative error = 7.9615231214915327487914732625188e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1841.5MB, alloc=44.3MB, time=20.48
TOP MAIN SOLVE Loop
x[1] = 5.04
y[1] (closed_form) = 2.6250317463428871136845942319657
y[1] (numeric) = 2.6250317463428871136845942319634
absolute error = 2.3e-30
relative error = 8.7617987980689708959599697259437e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.05
y[1] (closed_form) = 2.6123147483991526681912864048498
y[1] (numeric) = 2.6123147483991526681912864048475
absolute error = 2.3e-30
relative error = 8.8044520722836264688062350052931e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.06
y[1] (closed_form) = 2.5995365194908388968925228359918
y[1] (numeric) = 2.5995365194908388968925228359896
absolute error = 2.2e-30
relative error = 8.4630470989917288781052259133180e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.07
y[1] (closed_form) = 2.5866983374301881425701888425363
y[1] (numeric) = 2.586698337430188142570188842534
absolute error = 2.3e-30
relative error = 8.8916437093510685271215527014594e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.08
y[1] (closed_form) = 2.573801486024708020910727516367
y[1] (numeric) = 2.5738014860247080209107275163647
absolute error = 2.3e-30
relative error = 8.9361981197407717364240581131462e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.09
y[1] (closed_form) = 2.5608472549487917395795946339389
y[1] (numeric) = 2.5608472549487917395795946339368
absolute error = 2.1e-30
relative error = 8.2004110004678622591515381891506e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.1
y[1] (closed_form) = 2.5478369396147517336255706946159
y[1] (numeric) = 2.5478369396147517336255706946137
absolute error = 2.2e-30
relative error = 8.6347755062090167725958981268813e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.11
y[1] (closed_form) = 2.5347718410432795137439180440519
y[1] (numeric) = 2.5347718410432795137439180440497
absolute error = 2.2e-30
relative error = 8.6792821522528365853044170602497e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.12
y[1] (closed_form) = 2.5216532657333446813056070002912
y[1] (numeric) = 2.5216532657333446813056070002888
absolute error = 2.4e-30
relative error = 9.5175654504666183746409329672483e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.13
y[1] (closed_form) = 2.5084825255315461201426909338882
y[1] (numeric) = 2.5084825255315461201426909338857
absolute error = 2.5e-30
relative error = 9.9661846337568220553184264340339e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.14
y[1] (closed_form) = 2.4952609375009284298617781206076
y[1] (numeric) = 2.4952609375009284298617781206051
absolute error = 2.5e-30
relative error = 1.0018992252184326140603540965261e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1881.5MB, alloc=44.3MB, time=20.94
TOP MAIN SOLVE Loop
x[1] = 5.15
y[1] (closed_form) = 2.4819898237892767189329497450112
y[1] (numeric) = 2.4819898237892767189329497450087
absolute error = 2.5e-30
relative error = 1.0072563457102442826307372263289e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.16
y[1] (closed_form) = 2.468670511496902927965061189887
y[1] (numeric) = 2.4686705114969029279650611898843
absolute error = 2.7e-30
relative error = 1.0937061010879204511371753215649e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.17
y[1] (closed_form) = 2.4553043325439369044249213847113
y[1] (numeric) = 2.4553043325439369044249213847086
absolute error = 2.7e-30
relative error = 1.0996600153442218320224926096733e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.18
y[1] (closed_form) = 2.441892623537135499582287892781
y[1] (numeric) = 2.4418926235371354995822878927784
absolute error = 2.6e-30
relative error = 1.0647478824166487988317044933128e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.19
y[1] (closed_form) = 2.4284367256362230066599911882643
y[1] (numeric) = 2.4284367256362230066599911882616
absolute error = 2.7e-30
relative error = 1.1118263743489674334536441490119e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.2
y[1] (closed_form) = 2.4149379844197763060339905138132
y[1] (numeric) = 2.4149379844197763060339905138105
absolute error = 2.7e-30
relative error = 1.1180411329066547256040785533881e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.21
y[1] (closed_form) = 2.4013977497506681288570793066914
y[1] (numeric) = 2.4013977497506681288570793066888
absolute error = 2.6e-30
relative error = 1.0827027718627421500666286067222e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.22
y[1] (closed_form) = 2.3878173756410818946677475829961
y[1] (numeric) = 2.3878173756410818946677475829934
absolute error = 2.7e-30
relative error = 1.1307397406282393035614504935016e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.23
y[1] (closed_form) = 2.3741982201171116213879531333671
y[1] (numeric) = 2.3741982201171116213879531333646
absolute error = 2.5e-30
relative error = 1.0529870584591218244125045516134e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.24
y[1] (closed_form) = 2.3605416450829604476059687208406
y[1] (numeric) = 2.3605416450829604476059687208382
absolute error = 2.4e-30
relative error = 1.0167158054589851566423262891200e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.25
y[1] (closed_form) = 2.3468490161847513471789094752536
y[1] (numeric) = 2.3468490161847513471789094752512
absolute error = 2.4e-30
relative error = 1.0226478071016497125814303629410e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1921.5MB, alloc=44.3MB, time=21.38
TOP MAIN SOLVE Loop
x[1] = 5.26
y[1] (closed_form) = 2.3331217026739636549699895386006
y[1] (numeric) = 2.3331217026739636549699895385982
absolute error = 2.4e-30
relative error = 1.0286647272833594175968963531285e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.27
y[1] (closed_form) = 2.3193610772705090599541317197985
y[1] (numeric) = 2.3193610772705090599541317197961
absolute error = 2.4e-30
relative error = 1.0347677313031350632320365421201e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.28
y[1] (closed_form) = 2.3055685160254607579785166391619
y[1] (numeric) = 2.3055685160254607579785166391595
absolute error = 2.4e-30
relative error = 1.0409580037713771505197710443823e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.29
y[1] (closed_form) = 2.2917453981834494911484033162804
y[1] (numeric) = 2.291745398183449491148403316278
absolute error = 2.4e-30
relative error = 1.0472367488562902532816192501093e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.3
y[1] (closed_form) = 2.2778931060447402341196130342938
y[1] (numeric) = 2.2778931060447402341196130342913
absolute error = 2.5e-30
relative error = 1.0975054068015153609899722218718e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.31
y[1] (closed_form) = 2.2640130248270033195141115205415
y[1] (numeric) = 2.2640130248270033195141115205391
absolute error = 2.4e-30
relative error = 1.0600645728102150172907501852769e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.32
y[1] (closed_form) = 2.2501065425267938252309575405181
y[1] (numeric) = 2.2501065425267938252309575405158
absolute error = 2.3e-30
relative error = 1.0221738200081750365876466972004e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.33
y[1] (closed_form) = 2.2361750497807530755984533511439
y[1] (numeric) = 2.2361750497807530755984533511416
absolute error = 2.3e-30
relative error = 1.0285420187589986187488624136654e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.34
y[1] (closed_form) = 2.2222199397265461361017167681517
y[1] (numeric) = 2.2222199397265461361017167681495
absolute error = 2.2e-30
relative error = 9.9000101685286812939030967635142e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.35
y[1] (closed_form) = 2.2082426078635492078203170556062
y[1] (numeric) = 2.2082426078635492078203170556039
absolute error = 2.3e-30
relative error = 1.0415522242935186703459176408738e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.36
y[1] (closed_form) = 2.1942444519133008527204374229757
y[1] (numeric) = 2.1942444519133008527204374229736
absolute error = 2.1e-30
relative error = 9.5704924680059090955019940719380e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1961.4MB, alloc=44.3MB, time=21.83
TOP MAIN SOLVE Loop
x[1] = 5.37
y[1] (closed_form) = 2.1802268716797310045627446555546
y[1] (numeric) = 2.1802268716797310045627446555525
absolute error = 2.1e-30
relative error = 9.6320251221473977914976152055425e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.38
y[1] (closed_form) = 2.166191268909181742408399655278
y[1] (numeric) = 2.166191268909181742408399655276
absolute error = 2.0e-30
relative error = 9.2327950384876684488639321036967e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.39
y[1] (closed_form) = 2.1521390471502338245292093242972
y[1] (numeric) = 2.1521390471502338245292093242951
absolute error = 2.1e-30
relative error = 9.7577338359281477815640608278760e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.4
y[1] (closed_form) = 2.1380716116133529999517179437535
y[1] (numeric) = 2.1380716116133529999517179437514
absolute error = 2.1e-30
relative error = 9.8219348154357430526784464660379e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.41
y[1] (closed_form) = 2.1239903690303701328871226214372
y[1] (numeric) = 2.1239903690303701328871226214351
absolute error = 2.1e-30
relative error = 9.8870504811124823716311890030229e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.42
y[1] (closed_form) = 2.1098967275138091919174703108124
y[1] (numeric) = 2.1098967275138091919174703108102
absolute error = 2.2e-30
relative error = 1.0427050629119481800195981171522e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.43
y[1] (closed_form) = 2.0957920964160771710219914967793
y[1] (numeric) = 2.0957920964160771710219914967773
absolute error = 2.0e-30
relative error = 9.5429313022990826951196730409465e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.44
y[1] (closed_form) = 2.08167788618853002333412657347
y[1] (numeric) = 2.081677886188530023334126573468
absolute error = 2.0e-30
relative error = 9.6076343668228180758207553544149e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.45
y[1] (closed_form) = 2.0675555082404287009184245477154
y[1] (numeric) = 2.0675555082404287009184245477134
absolute error = 2.0e-30
relative error = 9.6732590347819918828607102887221e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.46
y[1] (closed_form) = 2.0534263747977994048458001365863
y[1] (numeric) = 2.0534263747977994048458001365844
absolute error = 1.9e-30
relative error = 9.2528274854124863495091433676268e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.47
y[1] (closed_form) = 2.0392918987622121594245256670798
y[1] (numeric) = 2.0392918987622121594245256670779
absolute error = 1.9e-30
relative error = 9.3169594855608552960768163254516e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2001.4MB, alloc=44.3MB, time=22.26
TOP MAIN SOLVE Loop
x[1] = 5.48
y[1] (closed_form) = 2.0251534935694918326118505495682
y[1] (numeric) = 2.0251534935694918326118505495664
absolute error = 1.8e-30
relative error = 8.8882151684579663883612721156817e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.49
y[1] (closed_form) = 2.011012573048375731386466739209
y[1] (numeric) = 2.0110125730483757313864667392072
absolute error = 1.8e-30
relative error = 8.9507147997164722973276226740127e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.5
y[1] (closed_form) = 1.9968705512791319062044979941963
y[1] (numeric) = 1.9968705512791319062044979941945
absolute error = 1.8e-30
relative error = 9.0141045890379680416926129360407e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.51
y[1] (closed_form) = 1.9827288424521523025907496450351
y[1] (numeric) = 1.9827288424521523025907496450335
absolute error = 1.6e-30
relative error = 8.0696864126977140665982414607978e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.52
y[1] (closed_form) = 1.9685888607265349004322211023162
y[1] (numeric) = 1.9685888607265349004322211023145
absolute error = 1.7e-30
relative error = 8.6356274482452955015296330806490e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.53
y[1] (closed_form) = 1.954452020088668982642103927312
y[1] (numeric) = 1.9544520200886689826421039273102
absolute error = 1.8e-30
relative error = 9.2097425851279692681230633340516e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.54
y[1] (closed_form) = 1.9403197342108376745495538489584
y[1] (numeric) = 1.9403197342108376745495538489567
absolute error = 1.7e-30
relative error = 8.7614426118869529644284829895163e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.55
y[1] (closed_form) = 1.9261934163098518936434669256154
y[1] (numeric) = 1.9261934163098518936434669256139
absolute error = 1.5e-30
relative error = 7.7873799551950423520509217152435e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.56
y[1] (closed_form) = 1.912074479005729846157480824793
y[1] (numeric) = 1.9120744790057298461574808247916
absolute error = 1.4e-30
relative error = 7.3218905192855966641153919941397e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.57
y[1] (closed_form) = 1.8979643341804362024287760270908
y[1] (numeric) = 1.8979643341804362024287760270893
absolute error = 1.5e-30
relative error = 7.9032043594629401599492647532797e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.58
y[1] (closed_form) = 1.8838643928366950769954241127546
y[1] (numeric) = 1.883864392836695076995424112753
absolute error = 1.6e-30
relative error = 8.4931803270125176994981070585392e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2041.4MB, alloc=44.3MB, time=22.70
TOP MAIN SOLVE Loop
x[1] = 5.59
y[1] (closed_form) = 1.8697760649568909320166179382882
y[1] (numeric) = 1.8697760649568909320166179382865
absolute error = 1.7e-30
relative error = 9.0919978700187006374388480941062e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.6
y[1] (closed_form) = 1.8557007593620715138078594915594
y[1] (numeric) = 1.8557007593620715138078594915575
absolute error = 1.9e-30
relative error = 1.0238719741932730029984322471728e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.61
y[1] (closed_form) = 1.8416398835710669220799547453862
y[1] (numeric) = 1.8416398835710669220799547453842
absolute error = 2.0e-30
relative error = 1.0859886440566555690870548794579e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.62
y[1] (closed_form) = 1.8275948436597388998574912258192
y[1] (numeric) = 1.8275948436597388998574912258172
absolute error = 2.0e-30
relative error = 1.0943344510619332017781627209100e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.63
y[1] (closed_form) = 1.8135670441203744190305145799346
y[1] (numeric) = 1.8135670441203744190305145799327
absolute error = 1.9e-30
relative error = 1.0476590904978358471093201625722e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.64
y[1] (closed_form) = 1.7995578877212376220636773540144
y[1] (numeric) = 1.7995578877212376220636773540124
absolute error = 2.0e-30
relative error = 1.1113840869729288035468645379577e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.65
y[1] (closed_form) = 1.7855687753662941645516494087916
y[1] (numeric) = 1.7855687753662941645516494087897
absolute error = 1.9e-30
relative error = 1.0640867079512136116406354910605e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.66
y[1] (closed_form) = 1.7716011059551219860696384391713
y[1] (numeric) = 1.7716011059551219860696384391692
absolute error = 2.1e-30
relative error = 1.1853684178345714920592234845013e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.67
y[1] (closed_form) = 1.7576562762430225181251949112187
y[1] (numeric) = 1.7576562762430225181251949112166
absolute error = 2.1e-30
relative error = 1.1947728508606555865626059023800e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.68
y[1] (closed_form) = 1.7437356807013463179739326311258
y[1] (numeric) = 1.7437356807013463179739326311237
absolute error = 2.1e-30
relative error = 1.2043109648105387963011081276820e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.69
y[1] (closed_form) = 1.7298407113780470956193884569321
y[1] (numeric) = 1.7298407113780470956193884569301
absolute error = 2.0e-30
relative error = 1.1561758182964345148121925122045e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2081.3MB, alloc=44.3MB, time=23.14
TOP MAIN SOLVE Loop
x[1] = 5.7
y[1] (closed_form) = 1.7159727577584780784781165768751
y[1] (numeric) = 1.7159727577584780784781165768731
absolute error = 2.0e-30
relative error = 1.1655196686295520723755908532165e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.71
y[1] (closed_form) = 1.702133206626444633957548202174
y[1] (numeric) = 1.702133206626444633957548202172
absolute error = 2.0e-30
relative error = 1.1749961708131613489440545913817e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.72
y[1] (closed_form) = 1.6883234419255270445685697930567
y[1] (numeric) = 1.6883234419255270445685697930547
absolute error = 2.0e-30
relative error = 1.1846071376696676788590294705296e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.73
y[1] (closed_form) = 1.674544844620687303179744591348
y[1] (numeric) = 1.6745448446206873031797445913461
absolute error = 1.9e-30
relative error = 1.1346366782015814561955300550717e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.74
y[1] (closed_form) = 1.6607987925601737676183247512693
y[1] (numeric) = 1.6607987925601737676183247512676
absolute error = 1.7e-30
relative error = 1.0236038270351800615117301709055e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.75
y[1] (closed_form) = 1.6470866603377374840375148963345
y[1] (numeric) = 1.6470866603377374840375148963328
absolute error = 1.7e-30
relative error = 1.0321254132744979913257817103342e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.76
y[1] (closed_form) = 1.6334098191551739573028310281927
y[1] (numeric) = 1.6334098191551739573028310281912
absolute error = 1.5e-30
relative error = 9.1832434359665128076261607414103e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.77
y[1] (closed_form) = 1.619769636685204114105968008674
y[1] (numeric) = 1.6197696366852041141059680086724
absolute error = 1.6e-30
relative error = 9.8779478498827653627754065963315e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.78
y[1] (closed_form) = 1.6061674769347081705955987451057
y[1] (numeric) = 1.6061674769347081705955987451041
absolute error = 1.6e-30
relative error = 9.9616012836564310358073327180236e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.79
y[1] (closed_form) = 1.592604700108326081024370601911
y[1] (numeric) = 1.5926047001083260810243706019094
absolute error = 1.6e-30
relative error = 1.0046435250951921114510894757574e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.8
y[1] (closed_form) = 1.5790826624724382072535684249411
y[1] (numeric) = 1.5790826624724382072535684249394
absolute error = 1.7e-30
relative error = 1.0765744190606439015438556509944e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2121.3MB, alloc=44.3MB, time=23.59
TOP MAIN SOLVE Loop
x[1] = 5.81
y[1] (closed_form) = 1.5656027162195398109351446479906
y[1] (numeric) = 1.5656027162195398109351446479888
absolute error = 1.8e-30
relative error = 1.1497169629000511744998748786024e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.82
y[1] (closed_form) = 1.5521662093330229308088773987068
y[1] (numeric) = 1.5521662093330229308088773987049
absolute error = 1.9e-30
relative error = 1.2240957112553324878155312567400e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.83
y[1] (closed_form) = 1.5387744854523791668142454947682
y[1] (numeric) = 1.5387744854523791668142454947664
absolute error = 1.8e-30
relative error = 1.1697620522157436327960168655633e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.84
y[1] (closed_form) = 1.5254288837388368506262785040301
y[1] (numeric) = 1.5254288837388368506262785040282
absolute error = 1.9e-30
relative error = 1.2455513464141879408232108009517e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.85
y[1] (closed_form) = 1.5121307387414460387863596323048
y[1] (numeric) = 1.5121307387414460387863596323027
absolute error = 2.1e-30
relative error = 1.3887688056310795464266081556810e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.86
y[1] (closed_form) = 1.4988813802636247198170728914176
y[1] (numeric) = 1.4988813802636247198170728914155
absolute error = 2.1e-30
relative error = 1.4010448242613100916317687520789e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.87
y[1] (closed_form) = 1.4856821332301795805891719394539
y[1] (numeric) = 1.4856821332301795805891719394517
absolute error = 2.2e-30
relative error = 1.4808012769304467250668885329705e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.88
y[1] (closed_form) = 1.4725343175548146297532182376728
y[1] (numeric) = 1.4725343175548146297532182376707
absolute error = 2.1e-30
relative error = 1.4261127737159362714291552337645e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.89
y[1] (closed_form) = 1.4594392480081409272631362478279
y[1] (numeric) = 1.4594392480081409272631362478255
absolute error = 2.4e-30
relative error = 1.6444672179918053786585001394973e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.9
y[1] (closed_form) = 1.4463982340862006189087417889509
y[1] (numeric) = 1.4463982340862006189087417889486
absolute error = 2.3e-30
relative error = 1.5901568086835257425580695029645e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.91
y[1] (closed_form) = 1.4334125798795184233442273614185
y[1] (numeric) = 1.4334125798795184233442273614161
absolute error = 2.4e-30
relative error = 1.6743260340311269211938107908218e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2161.3MB, alloc=44.3MB, time=24.03
TOP MAIN SOLVE Loop
x[1] = 5.92
y[1] (closed_form) = 1.4204835839426936663547781927022
y[1] (numeric) = 1.4204835839426936663547781926998
absolute error = 2.4e-30
relative error = 1.6895654600516825134736399706326e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.93
y[1] (closed_form) = 1.4076125391645459030492194006656
y[1] (numeric) = 1.4076125391645459030492194006634
absolute error = 2.2e-30
relative error = 1.5629300953128453596873971227230e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.94
y[1] (closed_form) = 1.394800732638827113308263388891
y[1] (numeric) = 1.3948007326388271133082633888887
absolute error = 2.3e-30
relative error = 1.6489810667425045380840142975314e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.95
y[1] (closed_form) = 1.3820494455355133991610731713017
y[1] (numeric) = 1.3820494455355133991610731712995
absolute error = 2.2e-30
relative error = 1.5918388499823528141059357125483e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.96
y[1] (closed_form) = 1.3693599529726890548131474084177
y[1] (numeric) = 1.3693599529726890548131474084154
absolute error = 2.3e-30
relative error = 1.6796168129548563793244843961232e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.97
y[1] (closed_form) = 1.3567335238890358208117614476402
y[1] (numeric) = 1.3567335238890358208117614476377
absolute error = 2.5e-30
relative error = 1.8426610354801473670405186134335e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.98
y[1] (closed_form) = 1.3441714209169400733172892227959
y[1] (numeric) = 1.3441714209169400733172892227935
absolute error = 2.4e-30
relative error = 1.7854865552511269932528378263290e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 5.99
y[1] (closed_form) = 1.3316749002562306376557352242898
y[1] (numeric) = 1.3316749002562306376557352242873
absolute error = 2.5e-30
relative error = 1.8773350759400580700277528770807e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6
y[1] (closed_form) = 1.319245211548559852265903148689
y[1] (numeric) = 1.3192452115485598522659031486864
absolute error = 2.6e-30
relative error = 1.9708239053966784720914842677427e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.01
y[1] (closed_form) = 1.3068835977524404448301244131061
y[1] (numeric) = 1.3068835977524404448301244131035
absolute error = 2.6e-30
relative error = 1.9894656298934675484099106163659e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.02
y[1] (closed_form) = 1.2945912950189507167967978720894
y[1] (numeric) = 1.2945912950189507167967978720868
absolute error = 2.6e-30
relative error = 2.0083558494512665613666563579930e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2201.2MB, alloc=44.3MB, time=24.47
TOP MAIN SOLVE Loop
x[1] = 6.03
y[1] (closed_form) = 1.2823695325681204656727098154137
y[1] (numeric) = 1.2823695325681204656727098154113
absolute error = 2.4e-30
relative error = 1.8715354186508717102248627389495e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.04
y[1] (closed_form) = 1.2702195325660100063898936267222
y[1] (numeric) = 1.2702195325660100063898936267198
absolute error = 2.4e-30
relative error = 1.8894371708736719810103584407570e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.05
y[1] (closed_form) = 1.2581425100024945837424586096369
y[1] (numeric) = 1.2581425100024945837424586096345
absolute error = 2.4e-30
relative error = 1.9075740473908964389048762849476e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.06
y[1] (closed_form) = 1.2461396725697663973502983149748
y[1] (numeric) = 1.2461396725697663973502983149723
absolute error = 2.5e-30
relative error = 2.0061956577022749081783206148186e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.07
y[1] (closed_form) = 1.2342122205415663888459340231986
y[1] (numeric) = 1.2342122205415663888459340231962
absolute error = 2.4e-30
relative error = 1.9445602304495830855588206808970e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.08
y[1] (closed_form) = 1.222361346653157868005134855879
y[1] (numeric) = 1.2223613466531578680051348558765
absolute error = 2.5e-30
relative error = 2.0452217397458078070393068466207e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.09
y[1] (closed_form) = 1.2105882359820539803586798093356
y[1] (numeric) = 1.210588235982053980358679809333
absolute error = 2.6e-30
relative error = 2.1477162281284079466422095021635e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.1
y[1] (closed_form) = 1.1988940658295109434391070885767
y[1] (numeric) = 1.1988940658295109434391070885742
absolute error = 2.5e-30
relative error = 2.0852551290845351299339781359080e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.11
y[1] (closed_form) = 1.1872800056027989022400707593291
y[1] (numeric) = 1.1872800056027989022400707593267
absolute error = 2.4e-30
relative error = 2.0214271180128953256511017657598e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.12
y[1] (closed_form) = 1.175747216698262176704651489065
y[1] (numeric) = 1.1757472166982621767046514890626
absolute error = 2.4e-30
relative error = 2.0412550979620340194686572116360e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.13
y[1] (closed_form) = 1.1642968523851805951204230770255
y[1] (numeric) = 1.1642968523851805951204230770231
absolute error = 2.4e-30
relative error = 2.0613299736088401740570719556579e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2241.1MB, alloc=44.3MB, time=24.92
TOP MAIN SOLVE Loop
x[1] = 6.14
y[1] (closed_form) = 1.1529300576904435271911533670237
y[1] (numeric) = 1.1529300576904435271911533670213
absolute error = 2.4e-30
relative error = 2.0816527281869071333991118210803e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.15
y[1] (closed_form) = 1.141647969284048149285727720845
y[1] (numeric) = 1.1416479692840481492857277208426
absolute error = 2.4e-30
relative error = 2.1022242097142180470580987059102e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.16
y[1] (closed_form) = 1.1304517153654333919423523656643
y[1] (numeric) = 1.1304517153654333919423523656618
absolute error = 2.5e-30
relative error = 2.2115053354506539927427662965005e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.17
y[1] (closed_form) = 1.1193424155506609361385658004711
y[1] (numeric) = 1.1193424155506609361385658004687
absolute error = 2.4e-30
relative error = 2.1441160154905048136859059059188e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.18
y[1] (closed_form) = 1.1083211807604545401334157373048
y[1] (numeric) = 1.1083211807604545401334157373025
absolute error = 2.3e-30
relative error = 2.0752107240447183217834391835473e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.19
y[1] (closed_form) = 1.0973891131091088928558171096453
y[1] (numeric) = 1.097389113109108892855817109643
absolute error = 2.3e-30
relative error = 2.0958837412589862693823937703924e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.2
y[1] (closed_form) = 1.0865473057942791028611766652291
y[1] (numeric) = 1.0865473057942791028611766652268
absolute error = 2.3e-30
relative error = 2.1167969288908893243090326852515e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.21
y[1] (closed_form) = 1.0757968429876618438155466944416
y[1] (numeric) = 1.0757968429876618438155466944395
absolute error = 2.1e-30
relative error = 1.9520414227726866381524525939680e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.22
y[1] (closed_form) = 1.0651387997265790883016607371408
y[1] (numeric) = 1.0651387997265790883016607371386
absolute error = 2.2e-30
relative error = 2.0654585116650896102316089721158e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.23
y[1] (closed_form) = 1.0545742418064752714831240770046
y[1] (numeric) = 1.0545742418064752714831240770025
absolute error = 2.1e-30
relative error = 1.9913249506291000614628874465906e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2281.0MB, alloc=44.3MB, time=25.36
TOP MAIN SOLVE Loop
x[1] = 6.24
y[1] (closed_form) = 1.0441042256743386348208072060246
y[1] (numeric) = 1.0441042256743386348208072060224
absolute error = 2.2e-30
relative error = 2.1070693383882454252864354817768e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.25
y[1] (closed_form) = 1.0337297983230574076182553689473
y[1] (numeric) = 1.0337297983230574076182553689451
absolute error = 2.2e-30
relative error = 2.1282157132056128934762101632098e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.26
y[1] (closed_form) = 1.0234519971867213906899234247838
y[1] (numeric) = 1.0234519971867213906899234247817
absolute error = 2.1e-30
relative error = 2.0518793316858125566388576018238e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.27
y[1] (closed_form) = 1.0132718500368794119066208124552
y[1] (numeric) = 1.013271850036879411906620812453
absolute error = 2.2e-30
relative error = 2.1711843666829666662661981886730e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.28
y[1] (closed_form) = 1.0031903748797630277861602438701
y[1] (numeric) = 1.0031903748797630277861602438678
absolute error = 2.3e-30
relative error = 2.2926854738570090045124478255600e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.29
y[1] (closed_form) = 0.99320857985448674867340442971298
y[1] (numeric) = 0.99320857985448674867340442971069
absolute error = 2.29e-30
relative error = 2.3056586969229604253304996469553e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.3
y[1] (closed_form) = 0.9833274631322349674023599703662
y[1] (numeric) = 0.98332746313223496740235997036393
absolute error = 2.27e-30
relative error = 2.3084883572449731502424065395497e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.31
y[1] (closed_form) = 0.97354801281644567266344158982794
y[1] (numeric) = 0.97354801281644567266344158982562
absolute error = 2.32e-30
relative error = 2.3830360387550979235704821245074e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.32
y[1] (closed_form) = 0.96387120684400092862139002461076
y[1] (numeric) = 0.96387120684400092862139002460849
absolute error = 2.27e-30
relative error = 2.3550864305124857787937979673340e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.33
y[1] (closed_form) = 0.95429801288743400165354078331755
y[1] (numeric) = 0.95429801288743400165354078331532
absolute error = 2.23e-30
relative error = 2.3367962312450542645134302586804e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.34
y[1] (closed_form) = 0.94482938825816291341427616061244
y[1] (numeric) = 0.94482938825816291341427616061016
absolute error = 2.28e-30
relative error = 2.4131340836077150836004085020519e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2320.9MB, alloc=44.3MB, time=25.80
TOP MAIN SOLVE Loop
x[1] = 6.35
y[1] (closed_form) = 0.93546627981076009678971562340151
y[1] (numeric) = 0.93546627981076009678971562339925
absolute error = 2.26e-30
relative error = 2.4159074985120640598434218807532e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.36
y[1] (closed_form) = 0.92620962384826772769727407939828
y[1] (numeric) = 0.92620962384826772769727407939604
absolute error = 2.24e-30
relative error = 2.4184589992631714215800218814302e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.37
y[1] (closed_form) = 0.91706034602856820111800444509109
y[1] (numeric) = 0.91706034602856820111800444508887
absolute error = 2.22e-30
relative error = 2.4207785339470372345377291990580e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.38
y[1] (closed_form) = 0.90801936127181911423609693563169
y[1] (numeric) = 0.90801936127181911423609693562948
absolute error = 2.21e-30
relative error = 2.4338688074938833122305495757719e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.39
y[1] (closed_form) = 0.89908757366896201311008386978999
y[1] (numeric) = 0.89908757366896201311008386978776
absolute error = 2.23e-30
relative error = 2.4802923155748907892774863534243e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.4
y[1] (closed_form) = 0.89026587639131405192484041252885
y[1] (numeric) = 0.89026587639131405192484041252666
absolute error = 2.19e-30
relative error = 2.4599392811472773920014650730509e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.41
y[1] (closed_form) = 0.88155515160125160558311602230258
y[1] (numeric) = 0.88155515160125160558311602230035
absolute error = 2.23e-30
relative error = 2.5296205188631035535944182330865e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.42
y[1] (closed_form) = 0.87295627036399476720090737519323
y[1] (numeric) = 0.87295627036399476720090737519097
absolute error = 2.26e-30
relative error = 2.5889040227154247748815714903222e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.43
y[1] (closed_form) = 0.86447009256050155198341055488262
y[1] (numeric) = 0.86447009256050155198341055488038
absolute error = 2.24e-30
relative error = 2.5911827595623031013925147512841e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.44
y[1] (closed_form) = 0.85609746680148051798857699176355
y[1] (numeric) = 0.85609746680148051798857699176135
absolute error = 2.20e-30
relative error = 2.5698008524888621520808706954211e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.45
y[1] (closed_form) = 0.84783923034253040244454088508621
y[1] (numeric) = 0.84783923034253040244454088508397
absolute error = 2.24e-30
relative error = 2.6420103244043462583338438557132e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2360.7MB, alloc=44.3MB, time=26.25
TOP MAIN SOLVE Loop
x[1] = 6.46
y[1] (closed_form) = 0.8396962090004152595865696313847
y[1] (numeric) = 0.83969620900041525958656963138246
absolute error = 2.24e-30
relative error = 2.6676314314512907851828295952486e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.47
y[1] (closed_form) = 0.83166921707048347242998307824102
y[1] (numeric) = 0.83166921707048347242998307823876
absolute error = 2.26e-30
relative error = 2.7174265364308492154266806683550e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.48
y[1] (closed_form) = 0.823759057245238896509047050662
y[1] (numeric) = 0.82375905724523889650904705065979
absolute error = 2.21e-30
relative error = 2.6828233092702340656702703045876e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.49
y[1] (closed_form) = 0.81596652053407227839961010669111
y[1] (numeric) = 0.81596652053407227839961010668884
absolute error = 2.27e-30
relative error = 2.7819768861524162363396065872486e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.5
y[1] (closed_form) = 0.80829238618416097581674099698117
y[1] (numeric) = 0.80829238618416097581674099697897
absolute error = 2.20e-30
relative error = 2.7217873601233613300348598546685e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.51
y[1] (closed_form) = 0.80073742160254488924944038438876
y[1] (numeric) = 0.80073742160254488924944038438651
absolute error = 2.25e-30
relative error = 2.8099098896826793320556486564698e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.52
y[1] (closed_form) = 0.79330238227938639747432684523248
y[1] (numeric) = 0.79330238227938639747432684523022
absolute error = 2.26e-30
relative error = 2.8488506406678984137493335444113e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.53
y[1] (closed_form) = 0.78598801171242197089079594304616
y[1] (numeric) = 0.78598801171242197089079594304395
absolute error = 2.21e-30
relative error = 2.8117477201530102569985514312092e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.54
y[1] (closed_form) = 0.7787950413326130174533620798865
y[1] (numeric) = 0.77879504133261301745336207988423
absolute error = 2.27e-30
relative error = 2.9147591850556135632979072518520e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.55
y[1] (closed_form) = 0.77172419043100339605463246914531
y[1] (numeric) = 0.77172419043100339605463246914303
absolute error = 2.28e-30
relative error = 2.9544233915054982076924208829505e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.56
y[1] (closed_form) = 0.76477616608679091154662306346296
y[1] (numeric) = 0.76477616608679091154662306346076
absolute error = 2.20e-30
relative error = 2.8766586846671319651836925867724e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2400.6MB, alloc=44.3MB, time=26.69
TOP MAIN SOLVE Loop
x[1] = 6.57
y[1] (closed_form) = 0.75795166309661998419097408513452
y[1] (numeric) = 0.75795166309661998419097408513226
absolute error = 2.26e-30
relative error = 2.9817204843469104096952128781606e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.58
y[1] (closed_form) = 0.75125136390510256421219755840566
y[1] (numeric) = 0.75125136390510256421219755840337
absolute error = 2.29e-30
relative error = 3.0482473776770019412416540643131e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.59
y[1] (closed_form) = 0.74467593853657423930460247403209
y[1] (numeric) = 0.74467593853657423930460247402985
absolute error = 2.24e-30
relative error = 3.0080198433724254975582295621785e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.6
y[1] (closed_form) = 0.73822604452809235942527717273921
y[1] (numeric) = 0.73822604452809235942527717273698
absolute error = 2.23e-30
relative error = 3.0207549794934657922115260505336e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.61
y[1] (closed_form) = 0.73190232686368287900481493945434
y[1] (numeric) = 0.73190232686368287900481493945217
absolute error = 2.17e-30
relative error = 2.9648764874116371362080276806226e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.62
y[1] (closed_form) = 0.72570541790984249183676762024235
y[1] (numeric) = 0.72570541790984249183676762024016
absolute error = 2.19e-30
relative error = 3.0177534106160871018221366352647e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.63
y[1] (closed_form) = 0.7196359373523025083785902748168
y[1] (numeric) = 0.71963593735230250837859027481458
absolute error = 2.22e-30
relative error = 3.0848931866408227918534528048947e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.64
y[1] (closed_form) = 0.71369449213406079902365017690234
y[1] (numeric) = 0.71369449213406079902365017690011
absolute error = 2.23e-30
relative error = 3.1245862544517374110684404133941e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.65
y[1] (closed_form) = 0.70788167639468800009833308640711
y[1] (numeric) = 0.70788167639468800009833308640488
absolute error = 2.23e-30
relative error = 3.1502439946709914524210999787136e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.66
y[1] (closed_form) = 0.70219807141091405191306908970309
y[1] (numeric) = 0.70219807141091405191306908970082
absolute error = 2.27e-30
relative error = 3.2327061158668942445513711453796e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.67
y[1] (closed_form) = 0.69664424553850101016396185217604
y[1] (numeric) = 0.6966442455385010101639618521738
absolute error = 2.24e-30
relative error = 3.2154144878760837968063466965543e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2440.5MB, alloc=44.3MB, time=27.13
TOP MAIN SOLVE Loop
x[1] = 6.68
y[1] (closed_form) = 0.69122075415540794335544195775286
y[1] (numeric) = 0.6912207541554079433554419577507
absolute error = 2.16e-30
relative error = 3.1249061707345158198583535734157e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.69
y[1] (closed_form) = 0.68592813960625359970683964246542
y[1] (numeric) = 0.68592813960625359970683964246327
absolute error = 2.15e-30
relative error = 3.1344391283235210669668950321415e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.7
y[1] (closed_form) = 0.68076693114808239722990530813655
y[1] (numeric) = 0.6807669311480823972299053081343
absolute error = 2.25e-30
relative error = 3.3050959102926423941252067796716e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.71
y[1] (closed_form) = 0.67573764489743916033307520651799
y[1] (numeric) = 0.67573764489743916033307520651579
absolute error = 2.20e-30
relative error = 3.2557014051420910105077241264478e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.72
y[1] (closed_form) = 0.6708407837787578954347176281642
y[1] (numeric) = 0.670840783778757895434717628162
absolute error = 2.20e-30
relative error = 3.2794666829999353629021926557095e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.73
y[1] (closed_form) = 0.66607683747406976666478906112911
y[1] (numeric) = 0.66607683747406976666478906112689
absolute error = 2.22e-30
relative error = 3.3329488057545975545614575642658e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.74
y[1] (closed_form) = 0.66144628237403530081542027332393
y[1] (numeric) = 0.66144628237403530081542027332171
absolute error = 2.22e-30
relative error = 3.3562816197742754788460098461008e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.75
y[1] (closed_form) = 0.65694958153030571827913090007311
y[1] (numeric) = 0.65694958153030571827913090007092
absolute error = 2.19e-30
relative error = 3.3335891544349407371185432371309e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.76
y[1] (closed_form) = 0.65258718460921815380187995685478
y[1] (numeric) = 0.65258718460921815380187995685263
absolute error = 2.15e-30
relative error = 3.2945789477730269000856999119608e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.77
y[1] (closed_form) = 0.64835952784682939749028978475927
y[1] (numeric) = 0.64835952784682939749028978475713
absolute error = 2.14e-30
relative error = 3.3006378530548265323229184494590e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.78
y[1] (closed_form) = 0.64426703400529265266147094868322
y[1] (numeric) = 0.64426703400529265266147094868106
absolute error = 2.16e-30
relative error = 3.3526470950588100452604628290321e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2480.5MB, alloc=44.3MB, time=27.58
TOP MAIN SOLVE Loop
x[1] = 6.79
y[1] (closed_form) = 0.64031011233058167282331052515318
y[1] (numeric) = 0.64031011233058167282331052515105
absolute error = 2.13e-30
relative error = 3.3265131363415290288582856136328e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.8
y[1] (closed_form) = 0.63648915851156650533629598253336
y[1] (numeric) = 0.63648915851156650533629598253121
absolute error = 2.15e-30
relative error = 3.3779051398578212266192635920290e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.81
y[1] (closed_form) = 0.63280455464044493414840503795799
y[1] (numeric) = 0.63280455464044493414840503795586
absolute error = 2.13e-30
relative error = 3.3659681877767945482163274257404e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.82
y[1] (closed_form) = 0.62925666917453357842581431419592
y[1] (numeric) = 0.62925666917453357842581431419374
absolute error = 2.18e-30
relative error = 3.4644050779147880348248959008192e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.83
y[1] (closed_form) = 0.62584585689942246793772308057454
y[1] (numeric) = 0.62584585689942246793772308057239
absolute error = 2.15e-30
relative error = 3.4353506958591548122334849443680e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.84
y[1] (closed_form) = 0.62257245889349677970704917742639
y[1] (numeric) = 0.6225724588934967797070491774242
absolute error = 2.19e-30
relative error = 3.5176628338046068621628791040918e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.85
y[1] (closed_form) = 0.61943680249382928372376693355664
y[1] (numeric) = 0.61943680249382928372376693355448
absolute error = 2.16e-30
relative error = 3.4870385345267203839424053805702e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.86
y[1] (closed_form) = 0.61643920126344690844789287577948
y[1] (numeric) = 0.61643920126344690844789287577736
absolute error = 2.12e-30
relative error = 3.4391063963078137402058773350933e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.87
y[1] (closed_form) = 0.61357995495997469941829116079586
y[1] (numeric) = 0.61357995495997469941829116079365
absolute error = 2.21e-30
relative error = 3.6018125790047421466264241311551e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.88
y[1] (closed_form) = 0.61085934950566030654530790147714
y[1] (numeric) = 0.61085934950566030654530790147493
absolute error = 2.21e-30
relative error = 3.6178540965092027895327481685328e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.89
y[1] (closed_form) = 0.60827765695878199761352561346565
y[1] (numeric) = 0.60827765695878199761352561346345
absolute error = 2.20e-30
relative error = 3.6167693730514188665156919509032e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2520.4MB, alloc=44.3MB, time=28.01
TOP MAIN SOLVE Loop
x[1] = 6.9
y[1] (closed_form) = 0.60583513548644305716946093065304
y[1] (numeric) = 0.60583513548644305716946093065089
absolute error = 2.15e-30
relative error = 3.5488202549918155965267272392744e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.91
y[1] (closed_form) = 0.60353202933875529133164556107738
y[1] (numeric) = 0.60353202933875529133164556107522
absolute error = 2.16e-30
relative error = 3.5789318461963812359420626060626e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.92
y[1] (closed_form) = 0.60136856882441422015109580086292
y[1] (numeric) = 0.60136856882441422015109580086069
absolute error = 2.23e-30
relative error = 3.7082084359003283227125966196125e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.93
y[1] (closed_form) = 0.59934497028766839998258062073236
y[1] (numeric) = 0.59934497028766839998258062073017
absolute error = 2.19e-30
relative error = 3.6539891190692111699270634669543e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.94
y[1] (closed_form) = 0.59746143608668517891525903089959
y[1] (numeric) = 0.5974614360866851789152590308974
absolute error = 2.19e-30
relative error = 3.6655085461988792459189602480366e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.95
y[1] (closed_form) = 0.59571815457331504866911518355922
y[1] (numeric) = 0.59571815457331504866911518355699
absolute error = 2.23e-30
relative error = 3.7433809644381986723642381963868e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.96
y[1] (closed_form) = 0.59411530007425661650513858558769
y[1] (numeric) = 0.59411530007425661650513858558549
absolute error = 2.20e-30
relative error = 3.7029849251904956302014441836041e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.97
y[1] (closed_form) = 0.59265303287362408063636259901217
y[1] (numeric) = 0.59265303287362408063636259901001
absolute error = 2.16e-30
relative error = 3.6446282735223819377721762834637e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.98
y[1] (closed_form) = 0.59133149919691895237769306999634
y[1] (numeric) = 0.59133149919691895237769306999414
absolute error = 2.20e-30
relative error = 3.7204174020626276544386972588262e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 6.99
y[1] (closed_form) = 0.59015083119640762784895524979462
y[1] (numeric) = 0.59015083119640762784895524979242
absolute error = 2.20e-30
relative error = 3.7278605463284008374867957230694e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7
y[1] (closed_form) = 0.58911114693790627146180338668716
y[1] (numeric) = 0.589111146937906271461803386685
absolute error = 2.16e-30
relative error = 3.6665407049710250741677425241890e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2560.4MB, alloc=44.3MB, time=28.48
TOP MAIN SOLVE Loop
x[1] = 7.01
y[1] (closed_form) = 0.58821255038897433269113173754996
y[1] (numeric) = 0.58821255038897433269113173754774
absolute error = 2.22e-30
relative error = 3.7741459248565065594060958651566e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.02
y[1] (closed_form) = 0.58745513140851787676947115473058
y[1] (numeric) = 0.58745513140851787676947115472842
absolute error = 2.16e-30
relative error = 3.6768765553567531891422228739768e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.03
y[1] (closed_form) = 0.58683896573780376896263794636405
y[1] (numeric) = 0.58683896573780376896263794636191
absolute error = 2.14e-30
relative error = 3.6466562804149912782266343175815e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.04
y[1] (closed_form) = 0.58636411499288561100071929043072
y[1] (numeric) = 0.58636411499288561100071929042857
absolute error = 2.15e-30
relative error = 3.6666636736903418308676081946703e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.05
y[1] (closed_form) = 0.58603062665844218706444040541493
y[1] (numeric) = 0.58603062665844218706444040541278
absolute error = 2.15e-30
relative error = 3.6687502362450594359442583884040e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.06
y[1] (closed_form) = 0.58583853408302903547718022961729
y[1] (numeric) = 0.58583853408302903547718022961507
absolute error = 2.22e-30
relative error = 3.7894400433641779668267234190379e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.07
y[1] (closed_form) = 0.58578785647574362094150939715216
y[1] (numeric) = 0.58578785647574362094150939714996
absolute error = 2.20e-30
relative error = 3.7556258220096747320341933895436e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.08
y[1] (closed_form) = 0.58587859890430444080024784296141
y[1] (numeric) = 0.58587859890430444080024784295925
absolute error = 2.16e-30
relative error = 3.6867706109074101463330571206457e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.09
y[1] (closed_form) = 0.58611075229454425740981519163572
y[1] (numeric) = 0.58611075229454425740981519163358
absolute error = 2.14e-30
relative error = 3.6511870693758639936814650991318e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.1
y[1] (closed_form) = 0.58648429343131750730221429005751
y[1] (numeric) = 0.58648429343131750730221429005534
absolute error = 2.17e-30
relative error = 3.7000138355011653406512153858766e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.11
y[1] (closed_form) = 0.58699918496082179639548785729313
y[1] (numeric) = 0.58699918496082179639548785729099
absolute error = 2.14e-30
relative error = 3.6456609392785280384197997668709e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2600.2MB, alloc=44.3MB, time=28.92
TOP MAIN SOLVE Loop
x[1] = 7.12
y[1] (closed_form) = 0.58765537539433324910506177896328
y[1] (numeric) = 0.58765537539433324910506177896114
absolute error = 2.14e-30
relative error = 3.6415901046833783186469814500696e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.13
y[1] (closed_form) = 0.58845279911335533782417669231118
y[1] (numeric) = 0.58845279911335533782417669230904
absolute error = 2.14e-30
relative error = 3.6366553158119411173470337027953e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.14
y[1] (closed_form) = 0.58939137637618067789475049574267
y[1] (numeric) = 0.58939137637618067789475049574052
absolute error = 2.15e-30
relative error = 3.6478307728543292208305518520690e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.15
y[1] (closed_form) = 0.59047101332586513189464284083519
y[1] (numeric) = 0.59047101332586513189464284083302
absolute error = 2.17e-30
relative error = 3.6750322217806060876563308568914e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.16
y[1] (closed_form) = 0.59169160199961342583753794512227
y[1] (numeric) = 0.59169160199961342583753794512008
absolute error = 2.19e-30
relative error = 3.7012524642887035746223807690028e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.17
y[1] (closed_form) = 0.59305302033957533873164705813445
y[1] (numeric) = 0.59305302033957533873164705813233
absolute error = 2.12e-30
relative error = 3.5747225413102396513602125768313e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.18
y[1] (closed_form) = 0.59455513220505138588727150509341
y[1] (numeric) = 0.59455513220505138588727150509125
absolute error = 2.16e-30
relative error = 3.6329683876230586421601111303598e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.19
y[1] (closed_form) = 0.59619778738610677541506692080511
y[1] (numeric) = 0.59619778738610677541506692080291
absolute error = 2.20e-30
relative error = 3.6900505948628193477327806924827e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.2
y[1] (closed_form) = 0.59798082161859227653070377326272
y[1] (numeric) = 0.59798082161859227653070377326051
absolute error = 2.21e-30
relative error = 3.6957707005018222630272350629392e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.21
y[1] (closed_form) = 0.59990405660057049759161105943477
y[1] (numeric) = 0.59990405660057049759161105943255
absolute error = 2.22e-30
relative error = 3.7005917455866205611545902431687e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.22
y[1] (closed_form) = 0.60196730001014593125168801827152
y[1] (numeric) = 0.60196730001014593125168801826934
absolute error = 2.18e-30
relative error = 3.6214591722229046730741543772551e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2640.2MB, alloc=44.3MB, time=29.37
TOP MAIN SOLVE Loop
x[1] = 7.23
y[1] (closed_form) = 0.60417034552469698374432671119311
y[1] (numeric) = 0.60417034552469698374432671119092
absolute error = 2.19e-30
relative error = 3.6248055142429664931947502072772e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.24
y[1] (closed_form) = 0.60651297284150806510684380544745
y[1] (numeric) = 0.60651297284150806510684380544524
absolute error = 2.21e-30
relative error = 3.6437802635056081220681463726103e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.25
y[1] (closed_form) = 0.60899494769979967715449246836974
y[1] (numeric) = 0.60899494769979967715449246836759
absolute error = 2.15e-30
relative error = 3.5304069567746714841381280763192e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.26
y[1] (closed_form) = 0.61161602190415429621361531680418
y[1] (numeric) = 0.61161602190415429621361531680202
absolute error = 2.16e-30
relative error = 3.5316275614808719467154961383381e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.27
y[1] (closed_form) = 0.61437593334933570804518661026465
y[1] (numeric) = 0.61437593334933570804518661026249
absolute error = 2.16e-30
relative error = 3.5157627158741886172341683847303e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.28
y[1] (closed_form) = 0.61727440604649931304593404377702
y[1] (numeric) = 0.61727440604649931304593404377485
absolute error = 2.17e-30
relative error = 3.5154543566747748607776991975730e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.29
y[1] (closed_form) = 0.62031115015079078071836187641728
y[1] (numeric) = 0.62031115015079078071836187641512
absolute error = 2.16e-30
relative error = 3.4821234463944874873851007050388e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.3
y[1] (closed_form) = 0.62348586199033029356722719529539
y[1] (numeric) = 0.62348586199033029356722719529326
absolute error = 2.13e-30
relative error = 3.4162763421779632740446772132087e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.31
y[1] (closed_form) = 0.62679822409657948202223312342711
y[1] (numeric) = 0.62679822409657948202223312342496
absolute error = 2.15e-30
relative error = 3.4301309693384193885540987868884e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.32
y[1] (closed_form) = 0.63024790523608801371875239692257
y[1] (numeric) = 0.63024790523608801371875239692041
absolute error = 2.16e-30
relative error = 3.4272228151093556955326035125558e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=2680.1MB, alloc=44.3MB, time=29.81
x[1] = 7.33
y[1] (closed_form) = 0.63383456044361666250410864201688
y[1] (numeric) = 0.63383456044361666250410864201469
absolute error = 2.19e-30
relative error = 3.4551602842029209109474130536765e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.34
y[1] (closed_form) = 0.63755783105663354489011718931125
y[1] (numeric) = 0.63755783105663354489011718930907
absolute error = 2.18e-30
relative error = 3.4192976602405704784858849588340e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.35
y[1] (closed_form) = 0.64141734475118007435698693903173
y[1] (numeric) = 0.64141734475118007435698693902952
absolute error = 2.21e-30
relative error = 3.4454946036068103382406182194295e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.36
y[1] (closed_form) = 0.64541271557910304694304108274388
y[1] (numeric) = 0.6454127155791030469430410827417
absolute error = 2.18e-30
relative error = 3.3776836857699233365131891776317e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.37
y[1] (closed_form) = 0.64954354400664913494272434402149
y[1] (numeric) = 0.64954354400664913494272434401921
absolute error = 2.28e-30
relative error = 3.5101572805050626299069728437159e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.38
y[1] (closed_form) = 0.65380941695441792929568890821861
y[1] (numeric) = 0.65380941695441792929568890821636
absolute error = 2.25e-30
relative error = 3.4413698268235019361398272470154e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.39
y[1] (closed_form) = 0.65820990783866953539601422376479
y[1] (numeric) = 0.65820990783866953539601422376254
absolute error = 2.25e-30
relative error = 3.4183623996001682705029879752799e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.4
y[1] (closed_form) = 0.66274457661398259159640263476514
y[1] (numeric) = 0.66274457661398259159640263476286
absolute error = 2.28e-30
relative error = 3.4402393930535206699918191999302e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.41
y[1] (closed_form) = 0.66741296981725844464104865560316
y[1] (numeric) = 0.66741296981725844464104865560089
absolute error = 2.27e-30
relative error = 3.4011925189609953354519944363409e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.42
y[1] (closed_form) = 0.6722146206130670816463086245788
y[1] (numeric) = 0.67221462061306708164630862457652
absolute error = 2.28e-30
relative error = 3.3917738919760701997854325182055e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.43
y[1] (closed_form) = 0.67714904884033028407376082030574
y[1] (numeric) = 0.67714904884033028407376082030348
absolute error = 2.26e-30
relative error = 3.3375222247899830182434862595201e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2720.1MB, alloc=44.3MB, time=30.25
TOP MAIN SOLVE Loop
x[1] = 7.44
y[1] (closed_form) = 0.68221576106033733541916123349283
y[1] (numeric) = 0.68221576106033733541916123349059
absolute error = 2.24e-30
relative error = 3.2834187186154546544598912251871e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.45
y[1] (closed_form) = 0.68741425060608848108653905489578
y[1] (numeric) = 0.68741425060608848108653905489353
absolute error = 2.25e-30
relative error = 3.2731355191082964381859294928971e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.46
y[1] (closed_form) = 0.69274399763296120614256388272073
y[1] (numeric) = 0.69274399763296120614256388271848
absolute error = 2.25e-30
relative error = 3.2479530788978770489242446520266e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.47
y[1] (closed_form) = 0.69820446917069426436563097014857
y[1] (numeric) = 0.69820446917069426436563097014628
absolute error = 2.29e-30
relative error = 3.2798415093503932675709840953254e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.48
y[1] (closed_form) = 0.70379511917668426023007948426229
y[1] (numeric) = 0.70379511917668426023007948426004
absolute error = 2.25e-30
relative error = 3.1969531170265883920230917447647e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.49
y[1] (closed_form) = 0.7095153885905894542117590248268
y[1] (numeric) = 0.70951538859058945421175902482453
absolute error = 2.27e-30
relative error = 3.1993668305196612448103633364305e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.5
y[1] (closed_form) = 0.71536470539023533107991686567905
y[1] (numeric) = 0.71536470539023533107991686567675
absolute error = 2.30e-30
relative error = 3.2151432446549589156103444549356e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.51
y[1] (closed_form) = 0.72134248464881634066516454828915
y[1] (numeric) = 0.72134248464881634066516454828685
absolute error = 2.30e-30
relative error = 3.1884992897926272128223513353707e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.52
y[1] (closed_form) = 0.72744812859338809097711498924585
y[1] (numeric) = 0.72744812859338809097711498924358
absolute error = 2.27e-30
relative error = 3.1204974083709979661226081454243e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.53
y[1] (closed_form) = 0.73368102666464414450112166974221
y[1] (numeric) = 0.7336810266646441445011216697399
absolute error = 2.31e-30
relative error = 3.1485072068735264267716375741645e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.54
y[1] (closed_form) = 0.74004055557797144004430406400985
y[1] (numeric) = 0.74004055557797144004430406400751
absolute error = 2.34e-30
relative error = 3.1619888698835710962750289054818e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2760.0MB, alloc=44.3MB, time=30.70
TOP MAIN SOLVE Loop
x[1] = 7.55
y[1] (closed_form) = 0.74652607938577823463955405276666
y[1] (numeric) = 0.74652607938577823463955405276438
absolute error = 2.28e-30
relative error = 3.0541464832359550581308371027107e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.56
y[1] (closed_form) = 0.75313694954108833276527269949021
y[1] (numeric) = 0.75313694954108833276527269948783
absolute error = 2.38e-30
relative error = 3.1601158347764161968047208258163e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.57
y[1] (closed_form) = 0.7598725049623952435109104302038
y[1] (numeric) = 0.75987250496239524351091043020147
absolute error = 2.33e-30
relative error = 3.0663038664825852729342160318859e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.58
y[1] (closed_form) = 0.76673207209976978032663901358165
y[1] (numeric) = 0.76673207209976978032663901357932
absolute error = 2.33e-30
relative error = 3.0388711843226671356707955276612e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.59
y[1] (closed_form) = 0.77371496500221449265226985699767
y[1] (numeric) = 0.77371496500221449265226985699528
absolute error = 2.39e-30
relative error = 3.0889928566822530672079776499421e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.6
y[1] (closed_form) = 0.78082048538625819403838423261938
y[1] (numeric) = 0.78082048538625819403838423261701
absolute error = 2.37e-30
relative error = 3.0352687261113578282094376936623e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.61
y[1] (closed_form) = 0.78804792270578372736402523675188
y[1] (numeric) = 0.78804792270578372736402523674946
absolute error = 2.42e-30
relative error = 3.0708792324340694207780750455469e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.62
y[1] (closed_form) = 0.79539655422308198443261932361648
y[1] (numeric) = 0.79539655422308198443261932361412
absolute error = 2.36e-30
relative error = 2.9670734521916213460584726797006e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.63
y[1] (closed_form) = 0.80286564508112507460337930703817
y[1] (numeric) = 0.80286564508112507460337930703571
absolute error = 2.46e-30
relative error = 3.0640244916089675060534457885700e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.64
y[1] (closed_form) = 0.81045444837705141520155312950598
y[1] (numeric) = 0.81045444837705141520155312950357
absolute error = 2.41e-30
relative error = 2.9736402888849154922221949915838e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.65
y[1] (closed_form) = 0.81816220523685539525971474495037
y[1] (numeric) = 0.81816220523685539525971474494796
absolute error = 2.41e-30
relative error = 2.9456261662714089195802282441707e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2800.0MB, alloc=44.3MB, time=31.14
TOP MAIN SOLVE Loop
x[1] = 7.66
y[1] (closed_form) = 0.82598814489127414368596416512567
y[1] (numeric) = 0.82598814489127414368596416512322
absolute error = 2.45e-30
relative error = 2.9661442662987573209108224337495e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.67
y[1] (closed_form) = 0.83393148475286381324545861227259
y[1] (numeric) = 0.83393148475286381324545861227021
absolute error = 2.38e-30
relative error = 2.8539514858409677233774118509721e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.68
y[1] (closed_form) = 0.84199143049425767279110664749629
y[1] (numeric) = 0.8419914304942576727911066474939
absolute error = 2.39e-30
relative error = 2.8385086990695918320695400359135e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.69
y[1] (closed_form) = 0.85016717612759818199941706492118
y[1] (numeric) = 0.8501671761275981819994170649188
absolute error = 2.38e-30
relative error = 2.7994494104566504042804770856820e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.7
y[1] (closed_form) = 0.85845790408513510547022214170434
y[1] (numeric) = 0.85845790408513510547022214170187
absolute error = 2.47e-30
relative error = 2.8772523244832804520263047140981e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.71
y[1] (closed_form) = 0.86686278530098160644603014278012
y[1] (numeric) = 0.86686278530098160644603014277776
absolute error = 2.36e-30
relative error = 2.7224608554173765323770873459787e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.72
y[1] (closed_form) = 0.87538097929402014460976499608769
y[1] (numeric) = 0.87538097929402014460976499608525
absolute error = 2.44e-30
relative error = 2.7873577993067869215932120356782e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.73
y[1] (closed_form) = 0.88401163425194988744020138218134
y[1] (numeric) = 0.88401163425194988744020138217899
absolute error = 2.35e-30
relative error = 2.6583360545798343308572132460570e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.74
y[1] (closed_form) = 0.89275388711646723045399897071758
y[1] (numeric) = 0.89275388711646723045399897071515
absolute error = 2.43e-30
relative error = 2.7219147797258329092814418328449e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.75
y[1] (closed_form) = 0.90160686366957090835329513064641
y[1] (numeric) = 0.90160686366957090835329513064397
absolute error = 2.44e-30
relative error = 2.7062793089985098137126091412053e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.76
y[1] (closed_form) = 0.91056967862098306663966204106089
y[1] (numeric) = 0.91056967862098306663966204105849
absolute error = 2.40e-30
relative error = 2.6357126273243496802484616012647e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2839.9MB, alloc=44.3MB, time=31.59
TOP MAIN SOLVE Loop
x[1] = 7.77
y[1] (closed_form) = 0.9196414356966775516601174571664
y[1] (numeric) = 0.91964143569667755166011745716397
absolute error = 2.43e-30
relative error = 2.6423341812117731428288034388110e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.78
y[1] (closed_form) = 0.92882122772850656632995785942085
y[1] (numeric) = 0.92882122772850656632995785941839
absolute error = 2.46e-30
relative error = 2.6485182794713810328972773210696e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.79
y[1] (closed_form) = 0.93810813674491672894153033333811
y[1] (numeric) = 0.93810813674491672894153033333571
absolute error = 2.40e-30
relative error = 2.5583404577723962887338280625233e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.8
y[1] (closed_form) = 0.94750123406274546352865876645141
y[1] (numeric) = 0.94750123406274546352865876644903
absolute error = 2.38e-30
relative error = 2.5118700793611753201650333393347e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.81
y[1] (closed_form) = 0.95699958038008854222418465679748
y[1] (numeric) = 0.95699958038008854222418465679512
absolute error = 2.36e-30
relative error = 2.4660407887145427499060249160454e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.82
y[1] (closed_form) = 0.96660222587022949293377613950805
y[1] (numeric) = 0.96660222587022949293377613950563
absolute error = 2.42e-30
relative error = 2.5036151740921972702353747388505e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.83
y[1] (closed_form) = 0.97630821027662147946351209608496
y[1] (numeric) = 0.97630821027662147946351209608258
absolute error = 2.38e-30
relative error = 2.4377547734907039939649413002851e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.84
y[1] (closed_form) = 0.98611656300891215599237989088459
y[1] (numeric) = 0.98611656300891215599237989088222
absolute error = 2.37e-30
relative error = 2.4033669942308643876215649318762e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.85
y[1] (closed_form) = 0.99602630324000189348425993036111
y[1] (numeric) = 0.99602630324000189348425993035874
absolute error = 2.37e-30
relative error = 2.3794552335521266233934563779412e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.86
y[1] (closed_form) = 1.0060364400041256722976374323518
y[1] (numeric) = 1.0060364400041256722976374323495
absolute error = 2.3e-30
relative error = 2.2861994939175045091617872550651e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.87
y[1] (closed_form) = 1.016145972295948832885515072286
y[1] (numeric) = 1.0161459722959488328855150722838
absolute error = 2.2e-30
relative error = 2.1650432713217092501604706476804e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2879.8MB, alloc=44.3MB, time=32.03
TOP MAIN SOLVE Loop
x[1] = 7.88
y[1] (closed_form) = 1.0263538891706667750930360320368
y[1] (numeric) = 1.0263538891706667750930360320345
absolute error = 2.3e-30
relative error = 2.2409424510082852901016601083818e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.89
y[1] (closed_form) = 1.0366591698450985961663038271389
y[1] (numeric) = 1.0366591698450985961663038271367
absolute error = 2.2e-30
relative error = 2.1222018422204590584757045050399e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.9
y[1] (closed_form) = 1.0470607837997645581928424479146
y[1] (numeric) = 1.0470607837997645581928424479123
absolute error = 2.3e-30
relative error = 2.1966251010312331567464005655212e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.91
y[1] (closed_form) = 1.0575576908819371773120170411462
y[1] (numeric) = 1.0575576908819371773120170411441
absolute error = 2.1e-30
relative error = 1.9857072745116447797275829377825e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.92
y[1] (closed_form) = 1.0681488414096556296723697116501
y[1] (numeric) = 1.0681488414096556296723697116482
absolute error = 1.9e-30
relative error = 1.7787783184715485244803807314339e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.93
y[1] (closed_form) = 1.0788331762766930727819530928743
y[1] (numeric) = 1.0788331762766930727819530928724
absolute error = 1.9e-30
relative error = 1.7611620051928201669582068531489e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.94
y[1] (closed_form) = 1.0896096270584663856069991293797
y[1] (numeric) = 1.0896096270584663856069991293779
absolute error = 1.8e-30
relative error = 1.6519677830484287879607281432034e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.95
y[1] (closed_form) = 1.1004771161188777365331710268819
y[1] (numeric) = 1.1004771161188777365331710268802
absolute error = 1.7e-30
relative error = 1.5447845076465538373807208266900e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.96
y[1] (closed_form) = 1.1114345567180772951216365878451
y[1] (numeric) = 1.1114345567180772951216365878433
absolute error = 1.8e-30
relative error = 1.6195285535436000218254461980170e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.97
y[1] (closed_form) = 1.1224808531211363114785892857504
y[1] (numeric) = 1.1224808531211363114785892857485
absolute error = 1.9e-30
relative error = 1.6926792067026510646266999117984e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 7.98
y[1] (closed_form) = 1.1336149007076196960208407235378
y[1] (numeric) = 1.1336149007076196960208407235359
absolute error = 1.9e-30
relative error = 1.6760541863149390910135049020855e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2919.7MB, alloc=44.3MB, time=32.47
TOP MAIN SOLVE Loop
x[1] = 7.99
y[1] (closed_form) = 1.144835586082047142470818095744
y[1] (numeric) = 1.1448355860820471424708180957422
absolute error = 1.8e-30
relative error = 1.5722781697938930673658875335544e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8
y[1] (closed_form) = 1.1561417871852317480607177835859
y[1] (numeric) = 1.1561417871852317480607177835841
absolute error = 1.8e-30
relative error = 1.5569024664200743352121106765067e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.01
y[1] (closed_form) = 1.1675323734064849971765765418579
y[1] (numeric) = 1.1675323734064849971765765418561
absolute error = 1.8e-30
relative error = 1.5417131387527844927234265538912e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.02
y[1] (closed_form) = 1.1790062056966768880373997118827
y[1] (numeric) = 1.1790062056966768880373997118809
absolute error = 1.8e-30
relative error = 1.5267095213772660015049016233933e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.03
y[1] (closed_form) = 1.1905621366821398964908950058704
y[1] (numeric) = 1.1905621366821398964908950058686
absolute error = 1.8e-30
relative error = 1.5118908493228604849040593132480e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.04
y[1] (closed_form) = 1.2021990107794053866243519427395
y[1] (numeric) = 1.2021990107794053866243519427376
absolute error = 1.9e-30
relative error = 1.5804371680261147095929734549146e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.05
y[1] (closed_form) = 1.213915664310760994645219204251
y[1] (numeric) = 1.2139156643107609946452192042492
absolute error = 1.8e-30
relative error = 1.4828048215540631649589889130024e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.06
y[1] (closed_form) = 1.2257109256206174303892893526318
y[1] (numeric) = 1.2257109256206174303892893526298
absolute error = 2.0e-30
relative error = 1.6317061047549484395078450544811e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.07
y[1] (closed_form) = 1.2375836151926730598733121025612
y[1] (numeric) = 1.2375836151926730598733121025593
absolute error = 1.9e-30
relative error = 1.5352498018521348337399029668720e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.08
y[1] (closed_form) = 1.2495325457678645525314177128683
y[1] (numeric) = 1.2495325457678645525314177128664
absolute error = 1.9e-30
relative error = 1.5205686369956928524498692225679e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.09
y[1] (closed_form) = 1.2615565224630917981689187339872
y[1] (numeric) = 1.2615565224630917981689187339853
absolute error = 1.9e-30
relative error = 1.5060759991081466244395172110908e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2959.6MB, alloc=44.3MB, time=32.91
TOP MAIN SOLVE Loop
x[1] = 8.1
y[1] (closed_form) = 1.2736543428907052212407318320024
y[1] (numeric) = 1.2736543428907052212407318320003
absolute error = 2.1e-30
relative error = 1.6487989945794933165246306684895e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.11
y[1] (closed_form) = 1.2858247972787435438225642770893
y[1] (numeric) = 1.2858247972787435438225642770873
absolute error = 2.0e-30
relative error = 1.5554218616974114850044947993836e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.12
y[1] (closed_form) = 1.2980666685919099735987657795216
y[1] (numeric) = 1.2980666685919099735987657795195
absolute error = 2.1e-30
relative error = 1.6177905579210309355024822333072e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.13
y[1] (closed_form) = 1.3103787326532747193488600420006
y[1] (numeric) = 1.3103787326532747193488600419985
absolute error = 2.1e-30
relative error = 1.6025901120570601525259384804259e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.14
y[1] (closed_form) = 1.3227597582666916637826258000013
y[1] (numeric) = 1.3227597582666916637826257999992
absolute error = 2.1e-30
relative error = 1.5875898755430712269120652443877e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.15
y[1] (closed_form) = 1.335208507339916952158457396012
y[1] (numeric) = 1.3352085073399169521584573960097
absolute error = 2.3e-30
relative error = 1.7225774007253735540260404460605e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.16
y[1] (closed_form) = 1.3477237350084171849287415334612
y[1] (numeric) = 1.3477237350084171849287415334589
absolute error = 2.3e-30
relative error = 1.7065812081922230080593860753663e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.17
y[1] (closed_form) = 1.360304189759854833696158822621
y[1] (numeric) = 1.3603041897598548336961588226186
absolute error = 2.4e-30
relative error = 1.7643112607215381885412802255525e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.18
y[1] (closed_form) = 1.3729486135592384320430519891663
y[1] (numeric) = 1.3729486135592384320430519891638
absolute error = 2.5e-30
relative error = 1.8208984482813149590716189660642e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.19
y[1] (closed_form) = 1.3856557419747250263190692866238
y[1] (numeric) = 1.3856557419747250263190692866212
absolute error = 2.6e-30
relative error = 1.8763679326978353834979310188898e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=2999.5MB, alloc=44.3MB, time=33.36
TOP MAIN SOLVE Loop
x[1] = 8.2
y[1] (closed_form) = 1.398424304304062306246839374574
y[1] (numeric) = 1.3984243043040623062468393745716
absolute error = 2.4e-30
relative error = 1.7162173115936942456172234723917e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.21
y[1] (closed_form) = 1.4112530237016577712379851860634
y[1] (numeric) = 1.4112530237016577712379851860609
absolute error = 2.5e-30
relative error = 1.7714753896098690775476891950955e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.22
y[1] (closed_form) = 1.4241406173062622256087358017996
y[1] (numeric) = 1.4241406173062622256087358017972
absolute error = 2.4e-30
relative error = 1.6852268454638694401148775557837e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.23
y[1] (closed_form) = 1.4370857963692548344520173279467
y[1] (numeric) = 1.4370857963692548344520173279442
absolute error = 2.5e-30
relative error = 1.7396316951403732240378076967724e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.24
y[1] (closed_form) = 1.4500872663835169117673394253125
y[1] (numeric) = 1.4500872663835169117673394253101
absolute error = 2.4e-30
relative error = 1.6550728053667713463912516116587e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.25
y[1] (closed_form) = 1.4631437272128815535770589667361
y[1] (numeric) = 1.4631437272128815535770589667335
absolute error = 2.6e-30
relative error = 1.7769956236306991397447736931646e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.26
y[1] (closed_form) = 1.4762538732221461711735835309881
y[1] (numeric) = 1.4762538732221461711735835309854
absolute error = 2.7e-30
relative error = 1.8289537111302162428390839087469e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.27
y[1] (closed_form) = 1.4894163934076349233525334293992
y[1] (numeric) = 1.4894163934076349233525334293966
absolute error = 2.6e-30
relative error = 1.7456501831911903908892475612223e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.28
y[1] (closed_form) = 1.5026299715282979914974406131996
y[1] (numeric) = 1.502629971528297991497440613197
absolute error = 2.6e-30
relative error = 1.7302995742561867283769092017136e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.29
y[1] (closed_form) = 1.515893286237334587697725023419
y[1] (numeric) = 1.5158932862373345876977250234164
absolute error = 2.6e-30
relative error = 1.7151603108247641745903891398419e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.3
y[1] (closed_form) = 1.5292050112143265337088220601935
y[1] (numeric) = 1.5292050112143265337088220601908
absolute error = 2.7e-30
relative error = 1.7656233011268755762885405682085e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=3039.5MB, alloc=44.3MB, time=33.81
TOP MAIN SOLVE Loop
x[1] = 8.31
y[1] (closed_form) = 1.542563815297869197506676107493
y[1] (numeric) = 1.5425638152978691975066761074903
absolute error = 2.7e-30
relative error = 1.7503327727667654265611878870502e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.32
y[1] (closed_form) = 1.555968362618686524453470075961
y[1] (numeric) = 1.5559683626186865244534700759583
absolute error = 2.7e-30
relative error = 1.7352537910577527944400266487642e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.33
y[1] (closed_form) = 1.5694173127332168516824032137891
y[1] (numeric) = 1.5694173127332168516824032137866
absolute error = 2.5e-30
relative error = 1.5929478920084856064894850334274e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.34
y[1] (closed_form) = 1.582909320757656147231399848758
y[1] (numeric) = 1.5829093207576561472313998487554
absolute error = 2.6e-30
relative error = 1.6425451325003984329664942222180e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.35
y[1] (closed_form) = 1.5964430375024452697135380175099
y[1] (numeric) = 1.5964430375024452697135380175073
absolute error = 2.6e-30
relative error = 1.6286205889735778207488586713848e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.36
y[1] (closed_form) = 1.6100171096071877999103032820059
y[1] (numeric) = 1.6100171096071877999103032820031
absolute error = 2.8e-30
relative error = 1.7391119530916937848543967782874e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.37
y[1] (closed_form) = 1.6236301796759849526169395593417
y[1] (numeric) = 1.6236301796759849526169395593389
absolute error = 2.8e-30
relative error = 1.7245306443852712065588934819307e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.38
y[1] (closed_form) = 1.6372808864131740353614911471161
y[1] (numeric) = 1.6372808864131740353614911471133
absolute error = 2.8e-30
relative error = 1.7101524993271126422772378813232e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.39
y[1] (closed_form) = 1.6509678647594568802647790453627
y[1] (numeric) = 1.6509678647594568802647790453598
absolute error = 2.9e-30
relative error = 1.7565453949174988389310599334472e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.4
y[1] (closed_form) = 1.6646897460284046363115655591631
y[1] (numeric) = 1.6646897460284046363115655591602
absolute error = 2.9e-30
relative error = 1.7420663561596283411735939897581e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.41
y[1] (closed_form) = 1.6784451580433252716674336798615
y[1] (numeric) = 1.6784451580433252716674336798588
absolute error = 2.7e-30
relative error = 1.6086316476062696573697803986824e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=3079.3MB, alloc=44.3MB, time=34.27
TOP MAIN SOLVE Loop
x[1] = 8.42
y[1] (closed_form) = 1.6922327252744800994052054286866
y[1] (numeric) = 1.692232725274480099405205428684
absolute error = 2.6e-30
relative error = 1.5364316982927274821040371765519e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.43
y[1] (closed_form) = 1.7060510689766356051026732445605
y[1] (numeric) = 1.7060510689766356051026732445578
absolute error = 2.7e-30
relative error = 1.5826020973801086961298498108048e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.44
y[1] (closed_form) = 1.7198988073269368212435107838682
y[1] (numeric) = 1.7198988073269368212435107838654
absolute error = 2.8e-30
relative error = 1.6280027569480987224544988676200e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.45
y[1] (closed_form) = 1.7337745555630884611988171367941
y[1] (numeric) = 1.7337745555630884611988171367915
absolute error = 2.6e-30
relative error = 1.4996182702402056280176580984733e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.46
y[1] (closed_form) = 1.747676926121829994791046866951
y[1] (numeric) = 1.7476769261218299947910468669485
absolute error = 2.5e-30
relative error = 1.4304703361550965549553050092501e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.47
y[1] (closed_form) = 1.7616045287776908180481649929499
y[1] (numeric) = 1.7616045287776908180481649929475
absolute error = 2.4e-30
relative error = 1.3623943176765485973943598702931e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.48
y[1] (closed_form) = 1.7755559707820116417466804191106
y[1] (numeric) = 1.7755559707820116417466804191083
absolute error = 2.3e-30
relative error = 1.2953689085830431091008462402425e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.49
y[1] (closed_form) = 1.7895298570022181967205542829194
y[1] (numeric) = 1.789529857002218196720554282917
absolute error = 2.4e-30
relative error = 1.3411343714714144052056346769954e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.5
y[1] (closed_form) = 1.8035247900613333286815133626179
y[1] (numeric) = 1.8035247900613333286815133626156
absolute error = 2.3e-30
relative error = 1.2752805022002402316839943413563e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.51
y[1] (closed_form) = 1.8175393704777135314575462050684
y[1] (numeric) = 1.8175393704777135314575462050661
absolute error = 2.3e-30
relative error = 1.2654471409857156367440109016931e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.52
y[1] (closed_form) = 1.8315721968049959451127048471569
y[1] (numeric) = 1.8315721968049959451127048471546
absolute error = 2.3e-30
relative error = 1.2557517547013063138884231138090e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=3119.3MB, alloc=44.3MB, time=34.70
TOP MAIN SOLVE Loop
x[1] = 8.53
y[1] (closed_form) = 1.8456218657722418243650222602545
y[1] (numeric) = 1.845621865772241824365022260252
absolute error = 2.5e-30
relative error = 1.3545569904450359545845169147854e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.54
y[1] (closed_form) = 1.859686972424262463072489560388
y[1] (numeric) = 1.8596869724242624630724895603854
absolute error = 2.6e-30
relative error = 1.3980847521939004686699093488695e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.55
y[1] (closed_form) = 1.8737661102621135423115822670094
y[1] (numeric) = 1.8737661102621135423115822670069
absolute error = 2.5e-30
relative error = 1.3342113438321739838041218646888e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.56
y[1] (closed_form) = 1.8878578713837438527306059908769
y[1] (numeric) = 1.8878578713837438527306059908745
absolute error = 2.4e-30
relative error = 1.2712821427816868172600558848298e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.57
y[1] (closed_form) = 1.901960846624784326422833094414
y[1] (numeric) = 1.9019608466247843264228330944117
absolute error = 2.3e-30
relative error = 1.2092783108977112271574239051361e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.58
y[1] (closed_form) = 1.9160736256994632995335668130314
y[1] (numeric) = 1.916073625699463299533566813029
absolute error = 2.4e-30
relative error = 1.2525614714433946766088300157548e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.59
y[1] (closed_form) = 1.9301947973416339141923011250723
y[1] (numeric) = 1.9301947973416339141923011250699
absolute error = 2.4e-30
relative error = 1.2433978183473536409184641298824e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.6
y[1] (closed_form) = 1.944322949445899557147305597597
y[1] (numeric) = 1.9443229494458995571473055975947
absolute error = 2.3e-30
relative error = 1.1829310561064264668854401961939e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.61
y[1] (closed_form) = 1.9584566692088232226763758897024
y[1] (numeric) = 1.9584566692088232226763758897001
absolute error = 2.3e-30
relative error = 1.1743941217393149456533644350051e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.62
y[1] (closed_form) = 1.9725945432702066789551329151711
y[1] (numeric) = 1.9725945432702066789551329151688
absolute error = 2.3e-30
relative error = 1.1659770670292000341299704460989e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.63
y[1] (closed_form) = 1.9867351578544253100839660807336
y[1] (numeric) = 1.9867351578544253100839660807312
absolute error = 2.4e-30
relative error = 1.2080120445403906114389110331937e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=3159.2MB, alloc=44.3MB, time=35.16
TOP MAIN SOLVE Loop
x[1] = 8.64
y[1] (closed_form) = 2.0008770989118045004071965480436
y[1] (numeric) = 2.0008770989118045004071965480413
absolute error = 2.3e-30
relative error = 1.1494958892032280510539006081667e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.65
y[1] (closed_form) = 2.0150189522600234236038418639322
y[1] (numeric) = 2.0150189522600234236038418639299
absolute error = 2.3e-30
relative error = 1.1414284701492980604943133568616e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.66
y[1] (closed_form) = 2.0291593037255320962889089805942
y[1] (numeric) = 2.0291593037255320962889089805919
absolute error = 2.3e-30
relative error = 1.1334743387457086147366622511097e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.67
y[1] (closed_form) = 2.0432967392849675545377026882523
y[1] (numeric) = 2.04329673928496755453770268825
absolute error = 2.3e-30
relative error = 1.1256319044510702509758967989482e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.68
y[1] (closed_form) = 2.057429845206555011833343450402
y[1] (numeric) = 2.0574298452065550118333434503998
absolute error = 2.2e-30
relative error = 1.0692952691075265815618401694305e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.69
y[1] (closed_form) = 2.0715572081914798584395337953625
y[1] (numeric) = 2.0715572081914798584395337953602
absolute error = 2.3e-30
relative error = 1.1102758788920709023841340592785e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.7
y[1] (closed_form) = 2.0856774155152163651164455942737
y[1] (numeric) = 2.0856774155152163651164455942715
absolute error = 2.2e-30
relative error = 1.0548131670000094402044857139008e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.71
y[1] (closed_form) = 2.0997890551687989584271301639961
y[1] (numeric) = 2.0997890551687989584271301639939
absolute error = 2.2e-30
relative error = 1.0477242914399062009046146138923e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.72
y[1] (closed_form) = 2.113890716000021940624646224237
y[1] (numeric) = 2.1138907160000219406246462242348
absolute error = 2.2e-30
relative error = 1.0407349743050658090995526065431e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.73
y[1] (closed_form) = 2.1279809878545535342655830371279
y[1] (numeric) = 2.1279809878545535342655830371258
absolute error = 2.1e-30
relative error = 9.8685092206450388588764621480315e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.74
y[1] (closed_form) = 2.1420584617169501402631120221331
y[1] (numeric) = 2.1420584617169501402631120221309
absolute error = 2.2e-30
relative error = 1.0270494663514492852313306139164e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=3199.2MB, alloc=44.3MB, time=35.61
TOP MAIN SOLVE Loop
x[1] = 8.75
y[1] (closed_form) = 2.1561217298515567080712730311345
y[1] (numeric) = 2.1561217298515567080712730311324
absolute error = 2.1e-30
relative error = 9.7397098267943315932908490036514e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.76
y[1] (closed_form) = 2.1701693859432791280808934388279
y[1] (numeric) = 2.1701693859432791280808934388259
absolute error = 2.0e-30
relative error = 9.2158704889788414928955424972439e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.77
y[1] (closed_form) = 2.1842000252382145691052103924856
y[1] (numeric) = 2.1842000252382145691052103924837
absolute error = 1.9e-30
relative error = 8.6988370023152116261774247553836e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.78
y[1] (closed_form) = 2.1982122446841256980386392161264
y[1] (numeric) = 2.1982122446841256980386392161244
absolute error = 2.0e-30
relative error = 9.0983025175869311731434119689740e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.79
y[1] (closed_form) = 2.212204643070744734383783551761
y[1] (numeric) = 2.212204643070744734383783551759
absolute error = 2.0e-30
relative error = 9.0407549150779059254076106394469e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.8
y[1] (closed_form) = 2.2261758211698933093581541924069
y[1] (numeric) = 2.2261758211698933093581541924051
absolute error = 1.8e-30
relative error = 8.0856147249594569000494126579935e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.81
y[1] (closed_form) = 2.2401243818754041177114520950235
y[1] (numeric) = 2.2401243818754041177114520950218
absolute error = 1.7e-30
relative error = 7.5888643226889984566283423791881e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.82
y[1] (closed_form) = 2.2540489303428303702048348329082
y[1] (numeric) = 2.2540489303428303702048348329063
absolute error = 1.9e-30
relative error = 8.4292757553892977257690889060435e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.83
y[1] (closed_form) = 2.2679480741289290759233427165629
y[1] (numeric) = 2.2679480741289290759233427165609
absolute error = 2.0e-30
relative error = 8.8185440522846085515578939843684e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.84
y[1] (closed_form) = 2.2818204233309042062094890215573
y[1] (numeric) = 2.2818204233309042062094890215554
absolute error = 1.9e-30
relative error = 8.3266850474870453440607485796544e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.85
y[1] (closed_form) = 2.2956645907253958160176565475257
y[1] (numeric) = 2.2956645907253958160176565475238
absolute error = 1.9e-30
relative error = 8.2764703854217148555752418324819e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=3239.1MB, alloc=44.3MB, time=36.05
TOP MAIN SOLVE Loop
x[1] = 8.86
y[1] (closed_form) = 2.3094791919072012238929889503568
y[1] (numeric) = 2.3094791919072012238929889503549
absolute error = 1.9e-30
relative error = 8.2269630601475677218655298525021e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.87
y[1] (closed_form) = 2.3232628454277143785723795564228
y[1] (numeric) = 2.3232628454277143785723795564208
absolute error = 2.0e-30
relative error = 8.6085825542128813506832497507166e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.88
y[1] (closed_form) = 2.3370141729330695683862633142472
y[1] (numeric) = 2.3370141729330695683862633142452
absolute error = 2.0e-30
relative error = 8.5579284163685668168290609057742e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.89
y[1] (closed_form) = 2.35073179930197565920539107852
y[1] (numeric) = 2.3507317993019756592053910785179
absolute error = 2.1e-30
relative error = 8.9333883202821021493507566558442e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.9
y[1] (closed_form) = 2.3644143527832270776236530311141
y[1] (numeric) = 2.3644143527832270776236530311121
absolute error = 2.0e-30
relative error = 8.4587542688773505692417624535354e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.91
y[1] (closed_form) = 2.3780604651328777883932250607736
y[1] (numeric) = 2.3780604651328777883932250607716
absolute error = 2.0e-30
relative error = 8.4102150863024709590051534798140e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.92
y[1] (closed_form) = 2.391668771751064548828605853659
y[1] (numeric) = 2.3916687717510645488286058536569
absolute error = 2.1e-30
relative error = 8.7804800765219728216405522825234e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.93
y[1] (closed_form) = 2.4052379118184657579681232896477
y[1] (numeric) = 2.4052379118184657579681232896457
absolute error = 2.0e-30
relative error = 8.3151857459618701294391760038081e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.94
y[1] (closed_form) = 2.418766528432382254721709322332
y[1] (numeric) = 2.4187665284323822547217093223301
absolute error = 1.9e-30
relative error = 7.8552434791273629337684080989347e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.95
y[1] (closed_form) = 2.4322532687424264570385288523496
y[1] (numeric) = 2.4322532687424264570385288523478
absolute error = 1.8e-30
relative error = 7.4005450959088358903134355931116e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.96
y[1] (closed_form) = 2.4456967840858062732936197368834
y[1] (numeric) = 2.4456967840858062732936197368816
absolute error = 1.8e-30
relative error = 7.3598657516035223064322253824126e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=3279.1MB, alloc=44.3MB, time=36.48
TOP MAIN SOLVE Loop
x[1] = 8.97
y[1] (closed_form) = 2.4590957301221902576151414883655
y[1] (numeric) = 2.4590957301221902576151414883637
absolute error = 1.8e-30
relative error = 7.3197638381916901506430416774866e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.98
y[1] (closed_form) = 2.4724487669681405227490871923298
y[1] (numeric) = 2.472448766968140522749087192328
absolute error = 1.8e-30
relative error = 7.2802317445277701795331703863797e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 8.99
y[1] (closed_form) = 2.4857545593310999672821992271839
y[1] (numeric) = 2.4857545593310999672821992271821
absolute error = 1.8e-30
relative error = 7.2412619872026626716348166337547e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9
y[1] (closed_form) = 2.4990117766429204186120221448288
y[1] (numeric) = 2.4990117766429204186120221448269
absolute error = 1.9e-30
relative error = 7.6030053870029752888521753392286e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.01
y[1] (closed_form) = 2.5122190931929183389610687884018
y[1] (numeric) = 2.5122190931929183389610687884
absolute error = 1.8e-30
relative error = 7.1649801758025823290704443286731e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.02
y[1] (closed_form) = 2.5253751882604447889753776159455
y[1] (numeric) = 2.5253751882604447889753776159437
absolute error = 1.8e-30
relative error = 7.1276537774171081766607774736141e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.03
y[1] (closed_form) = 2.5384787462469563920215759756844
y[1] (numeric) = 2.5384787462469563920215759756826
absolute error = 1.8e-30
relative error = 7.0908610232062453302819834349515e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.04
y[1] (closed_form) = 2.5515284568075740921960783966351
y[1] (numeric) = 2.5515284568075740921960783966333
absolute error = 1.8e-30
relative error = 7.0545950416407551965926462892023e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.05
y[1] (closed_form) = 2.5645230149821165502802509076205
y[1] (numeric) = 2.5645230149821165502802509076186
absolute error = 1.9e-30
relative error = 7.4087851382111673645883126307826e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.06
y[1] (closed_form) = 2.5774611213255950744111400009037
y[1] (numeric) = 2.5774611213255950744111400009018
absolute error = 1.9e-30
relative error = 7.3715951883022971566040983826523e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.07
y[1] (closed_form) = 2.590341482038157036083444580621
y[1] (numeric) = 2.5903414820381570360834445806191
absolute error = 1.9e-30
relative error = 7.3349402508314231676189152512484e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=3318.9MB, alloc=44.3MB, time=36.94
TOP MAIN SOLVE Loop
x[1] = 9.08
y[1] (closed_form) = 2.6031628090944647772494165178653
y[1] (numeric) = 2.6031628090944647772494165178634
absolute error = 1.9e-30
relative error = 7.2988135561944866442769873594890e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.09
y[1] (closed_form) = 2.615923820372497070733795218897
y[1] (numeric) = 2.6159238203724970707337952188952
absolute error = 1.8e-30
relative error = 6.8809343222528827773926416019081e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.1
y[1] (closed_form) = 2.62862323978176025392506890559
y[1] (numeric) = 2.6286232397817602539250689055882
absolute error = 1.8e-30
relative error = 6.8476911135786954275832152463391e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.11
y[1] (closed_form) = 2.6412597973908962147365357372524
y[1] (numeric) = 2.6412597973908962147365357372506
absolute error = 1.8e-30
relative error = 6.8149297610863039811361653533758e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.12
y[1] (closed_form) = 2.6538322295546744691449083015452
y[1] (numeric) = 2.6538322295546744691449083015433
absolute error = 1.9e-30
relative error = 7.1594578543453326624271915815904e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.13
y[1] (closed_form) = 2.6663392790403556312045339925759
y[1] (numeric) = 2.6663392790403556312045339925739
absolute error = 2.0e-30
relative error = 7.5009208907570894329679273687160e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.14
y[1] (closed_form) = 2.6787796951534136392955323947999
y[1] (numeric) = 2.6787796951534136392955323947979
absolute error = 2.0e-30
relative error = 7.4660861571352923635401375033119e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.15
y[1] (closed_form) = 2.6911522338626041664879930316364
y[1] (numeric) = 2.6911522338626041664879930316344
absolute error = 2.0e-30
relative error = 7.4317609194831944932604480876388e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.16
y[1] (closed_form) = 2.7034556579243667082854203869158
y[1] (numeric) = 2.7034556579243667082854203869136
absolute error = 2.2e-30
relative error = 8.1377328810678364471584501491699e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.17
y[1] (closed_form) = 2.7156887370065479076423199155477
y[1] (numeric) = 2.7156887370065479076423199155456
absolute error = 2.1e-30
relative error = 7.7328449736650971886768417834457e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.18
y[1] (closed_form) = 2.7278502478114337450265257119842
y[1] (numeric) = 2.7278502478114337450265257119821
absolute error = 2.1e-30
relative error = 7.6983698122169251737057209920690e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=3358.8MB, alloc=44.3MB, time=37.38
TOP MAIN SOLVE Loop
x[1] = 9.19
y[1] (closed_form) = 2.7399389741980782904097900870034
y[1] (numeric) = 2.7399389741980782904097900870013
absolute error = 2.1e-30
relative error = 7.6644042797143875012687401331654e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.2
y[1] (closed_form) = 2.7519537073039167844133762807175
y[1] (numeric) = 2.7519537073039167844133762807154
absolute error = 2.1e-30
relative error = 7.6309423171851446223899479135899e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.21
y[1] (closed_form) = 2.7638932456656508874018836490052
y[1] (numeric) = 2.7638932456656508874018836490031
absolute error = 2.1e-30
relative error = 7.5979779728946800258498012901377e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.22
y[1] (closed_form) = 2.775756395339394008101133312638
y[1] (numeric) = 2.7757563953393940081011333126358
absolute error = 2.2e-30
relative error = 7.9257675626502670741876019803285e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.23
y[1] (closed_form) = 2.7875419700200646973073732539797
y[1] (numeric) = 2.7875419700200646973073732539777
absolute error = 2.0e-30
relative error = 7.1747798652359089731506375199684e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.24
y[1] (closed_form) = 2.7992487911600161674479261038611
y[1] (numeric) = 2.7992487911600161674479261038591
absolute error = 2.0e-30
relative error = 7.1447740062118403702275337806406e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.25
y[1] (closed_form) = 2.8108756880868900751401811572893
y[1] (numeric) = 2.8108756880868900751401811572873
absolute error = 2.0e-30
relative error = 7.1152203865736228054677561013694e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.26
y[1] (closed_form) = 2.8224214981206827814688858768887
y[1] (numeric) = 2.8224214981206827814688858768865
absolute error = 2.2e-30
relative error = 7.7947252083534515655358944795343e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.27
y[1] (closed_form) = 2.8338850666900123834532640466342
y[1] (numeric) = 2.833885066690012383453264046632
absolute error = 2.2e-30
relative error = 7.7631941600567720040375012634376e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.28
y[1] (closed_form) = 2.8452652474475748900977027339896
y[1] (numeric) = 2.8452652474475748900977027339874
absolute error = 2.2e-30
relative error = 7.7321437850955083890518705674373e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.29
y[1] (closed_form) = 2.8565609023847779975046161510853
y[1] (numeric) = 2.8565609023847779975046161510831
absolute error = 2.2e-30
relative error = 7.7015686875898456943680889418444e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=3398.6MB, alloc=44.3MB, time=37.81
TOP MAIN SOLVE Loop
x[1] = 9.3
y[1] (closed_form) = 2.8677709019455409997675029560489
y[1] (numeric) = 2.8677709019455409997675029560467
absolute error = 2.2e-30
relative error = 7.6714635695183506804114969928641e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.31
y[1] (closed_form) = 2.8788941251392494557479406317273
y[1] (numeric) = 2.878894125139249455747940631725
absolute error = 2.3e-30
relative error = 7.9891788305648479504159869440255e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.32
y[1] (closed_form) = 2.8899294596528533163639678175814
y[1] (numeric) = 2.8899294596528533163639678175791
absolute error = 2.3e-30
relative error = 7.9586717672904121715699544639980e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.33
y[1] (closed_form) = 2.900875801962097302670540551208
y[1] (numeric) = 2.9008758019620973026705405512059
absolute error = 2.1e-30
relative error = 7.2391930691400158550493967786170e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.34
y[1] (closed_form) = 2.9117320574418724117869460466285
y[1] (numeric) = 2.9117320574418724117869460466262
absolute error = 2.3e-30
relative error = 7.8990784681633276898659137437818e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.35
y[1] (closed_form) = 2.9224971404756775156125405497065
y[1] (numeric) = 2.9224971404756775156125405497041
absolute error = 2.4e-30
relative error = 8.2121551694978433515759006131530e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.36
y[1] (closed_form) = 2.93316997456418010626215739178
y[1] (numeric) = 2.9331699745641801062621573917777
absolute error = 2.3e-30
relative error = 7.8413457792937535044464936913945e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.37
y[1] (closed_form) = 2.9437494924328653322371086870076
y[1] (numeric) = 2.9437494924328653322371086870054
absolute error = 2.2e-30
relative error = 7.4734620104573074127198821407954e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.38
y[1] (closed_form) = 2.9542346361387625605178708043778
y[1] (numeric) = 2.9542346361387625605178708043756
absolute error = 2.2e-30
relative error = 7.4469372645208685845084431236970e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.39
y[1] (closed_form) = 2.9646243571762387920111828511153
y[1] (numeric) = 2.9646243571762387920111828511131
absolute error = 2.2e-30
relative error = 7.4208389831063377119477145605208e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3438.5MB, alloc=44.3MB, time=38.27
TOP MAIN SOLVE Loop
x[1] = 9.4
y[1] (closed_form) = 2.9749176165818483510981743433053
y[1] (numeric) = 2.9749176165818483510981743433032
absolute error = 2.1e-30
relative error = 7.0590190070973452564844867322993e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.41
y[1] (closed_form) = 2.9851133850382283644019417010112
y[1] (numeric) = 2.9851133850382283644019417010091
absolute error = 2.1e-30
relative error = 7.0349086588317538726442060241571e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.42
y[1] (closed_form) = 2.9952106429770296393132760872758
y[1] (numeric) = 2.9952106429770296393132760872736
absolute error = 2.2e-30
relative error = 7.3450593705601755445575747254930e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.43
y[1] (closed_form) = 3.0052083806808726492724654644099
y[1] (numeric) = 3.0052083806808726492724654644076
absolute error = 2.3e-30
relative error = 7.6533794288131937368072200949650e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.44
y[1] (closed_form) = 3.0151055983843184302936057252201
y[1] (numeric) = 3.0151055983843184302936057252179
absolute error = 2.2e-30
relative error = 7.2965935295231356697057176223882e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.45
y[1] (closed_form) = 3.0249013063738442917259106013581
y[1] (numeric) = 3.0249013063738442917259106013559
absolute error = 2.2e-30
relative error = 7.2729645604116922270141802020092e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.46
y[1] (closed_form) = 3.034594525086814343764257032392
y[1] (numeric) = 3.0345945250868143437642570323898
absolute error = 2.2e-30
relative error = 7.2497329768861357809065237556976e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.47
y[1] (closed_form) = 3.0441842852094349447386901057381
y[1] (numeric) = 3.0441842852094349447386901057357
absolute error = 2.4e-30
relative error = 7.8838853865080112585071465792474e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.48
y[1] (closed_form) = 3.0536696277736852727197878842677
y[1] (numeric) = 3.0536696277736852727197878842653
absolute error = 2.4e-30
relative error = 7.8593963740267115585219237748595e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.49
y[1] (closed_form) = 3.0630496042532133284635007921944
y[1] (numeric) = 3.0630496042532133284635007921919
absolute error = 2.5e-30
relative error = 8.1618005680633186741906238926040e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.5
y[1] (closed_form) = 3.072323276658187780175084144712
y[1] (numeric) = 3.0723232766581877801750841447094
absolute error = 2.6e-30
relative error = 8.4626511140717557903346458464790e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3478.3MB, alloc=44.3MB, time=38.70
TOP MAIN SOLVE Loop
x[1] = 9.51
y[1] (closed_form) = 3.0814897176290961649866903686239
y[1] (numeric) = 3.0814897176290961649866903686212
absolute error = 2.7e-30
relative error = 8.7619958118094417892750791853285e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.52
y[1] (closed_form) = 3.0905480105294800674066380620896
y[1] (numeric) = 3.0905480105294800674066380620869
absolute error = 2.7e-30
relative error = 8.7363146950026819050788268913960e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.53
y[1] (closed_form) = 3.0994972495375980012997920243597
y[1] (numeric) = 3.099497249537598001299792024357
absolute error = 2.7e-30
relative error = 8.7110901627765682005769178120832e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.54
y[1] (closed_form) = 3.1083365397370068291872416978607
y[1] (numeric) = 3.108336539737006829187241697858
absolute error = 2.7e-30
relative error = 8.6863181173697627813413611709266e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.55
y[1] (closed_form) = 3.1170649972060526607988323192548
y[1] (numeric) = 3.1170649972060526607988323192522
absolute error = 2.6e-30
relative error = 8.3411799315397072167322603065815e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.56
y[1] (closed_form) = 3.1256817491062622818632690265674
y[1] (numeric) = 3.1256817491062622818632690265648
absolute error = 2.6e-30
relative error = 8.3181853070723773958693489536636e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.57
y[1] (closed_form) = 3.1341859337696262740665741904323
y[1] (numeric) = 3.1341859337696262740665741904298
absolute error = 2.5e-30
relative error = 7.9765529321776313667455038989756e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.58
y[1] (closed_form) = 3.1425767007847650979396378145668
y[1] (numeric) = 3.1425767007847650979396378145644
absolute error = 2.4e-30
relative error = 7.6370451018766585880485694340694e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.59
y[1] (closed_form) = 3.1508532110819695221383770801613
y[1] (numeric) = 3.1508532110819695221383770801587
absolute error = 2.6e-30
relative error = 8.2517331840640955120929869713409e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.6
y[1] (closed_form) = 3.1590146370171068951444438064041
y[1] (numeric) = 3.1590146370171068951444438064016
absolute error = 2.5e-30
relative error = 7.9138601344393259373468210005483e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.61
y[1] (closed_form) = 3.1670601624543848688292314164094
y[1] (numeric) = 3.1670601624543848688292314164067
absolute error = 2.7e-30
relative error = 8.5252564255286327198449379915437e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3518.3MB, alloc=44.3MB, time=39.14
TOP MAIN SOLVE Loop
x[1] = 9.62
y[1] (closed_form) = 3.1749889828479642975777945475861
y[1] (numeric) = 3.1749889828479642975777945475833
absolute error = 2.8e-30
relative error = 8.8189282392041585076134507478583e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.63
y[1] (closed_form) = 3.1828003053224131517507794370578
y[1] (numeric) = 3.1828003053224131517507794370552
absolute error = 2.6e-30
relative error = 8.1689070962201748679134758848741e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.64
y[1] (closed_form) = 3.1904933487519934001600635934959
y[1] (numeric) = 3.1904933487519934001600635934933
absolute error = 2.6e-30
relative error = 8.1492099051609895206714338278612e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.65
y[1] (closed_form) = 3.1980673438387729329359293732203
y[1] (numeric) = 3.1980673438387729329359293732177
absolute error = 2.6e-30
relative error = 8.1299101002642180636206653436978e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.66
y[1] (closed_form) = 3.2055215331895547136585777952904
y[1] (numeric) = 3.2055215331895547136585777952879
absolute error = 2.5e-30
relative error = 7.7990429142818847049599080811382e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.67
y[1] (closed_form) = 3.2128551713916154679028768572878
y[1] (numeric) = 3.2128551713916154679028768572855
absolute error = 2.3e-30
relative error = 7.1587416092701696372512487778197e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.68
y[1] (closed_form) = 3.2200675250872463343906052403635
y[1] (numeric) = 3.2200675250872463343906052403611
absolute error = 2.4e-30
relative error = 7.4532598503038318734636844385952e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.69
y[1] (closed_form) = 3.2271578730470880247471931814128
y[1] (numeric) = 3.2271578730470880247471931814104
absolute error = 2.4e-30
relative error = 7.4368843868611728757372343469920e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.7
y[1] (closed_form) = 3.2341255062422531584080972677162
y[1] (numeric) = 3.2341255062422531584080972677137
absolute error = 2.5e-30
relative error = 7.7300648820668765251127465790299e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.71
y[1] (closed_form) = 3.2409697279152285605014202619804
y[1] (numeric) = 3.2409697279152285605014202619779
absolute error = 2.5e-30
relative error = 7.7137406698585198573328499343038e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.72
y[1] (closed_form) = 3.2476898536495504325360727470818
y[1] (numeric) = 3.2476898536495504325360727470795
absolute error = 2.3e-30
relative error = 7.0819570329827032735518426607438e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3558.2MB, alloc=44.3MB, time=39.59
TOP MAIN SOLVE Loop
x[1] = 9.73
y[1] (closed_form) = 3.2542852114382454284364702230493
y[1] (numeric) = 3.2542852114382454284364702230469
absolute error = 2.4e-30
relative error = 7.3748913941667381289927635213407e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.74
y[1] (closed_form) = 3.2607551417510307918731962264869
y[1] (numeric) = 3.2607551417510307918731962264845
absolute error = 2.4e-30
relative error = 7.3602582704544816365128377418711e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.75
y[1] (closed_form) = 3.2670989976002668349318983339047
y[1] (numeric) = 3.2670989976002668349318983339023
absolute error = 2.4e-30
relative error = 7.3459665647194528218577589535556e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.76
y[1] (closed_form) = 3.2733161446056551629275103750451
y[1] (numeric) = 3.2733161446056551629275103750427
absolute error = 2.4e-30
relative error = 7.3320140615050007308406174244959e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.77
y[1] (closed_form) = 3.2794059610576761755952344416098
y[1] (numeric) = 3.2794059610576761755952344416075
absolute error = 2.3e-30
relative error = 7.0134653266843562166370852625306e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.78
y[1] (closed_form) = 3.2853678379797595009610280013021
y[1] (numeric) = 3.2853678379797595009610280012997
absolute error = 2.4e-30
relative error = 7.3051180822291410145358998607401e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.79
y[1] (closed_form) = 3.2912011791891811449000175906641
y[1] (numeric) = 3.2912011791891811449000175906617
absolute error = 2.4e-30
relative error = 7.2921704548953246605946297872697e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.8
y[1] (closed_form) = 3.2969054013566812667186307008181
y[1] (numeric) = 3.2969054013566812667186307008157
absolute error = 2.4e-30
relative error = 7.2795537263895912298046043314096e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.81
y[1] (closed_form) = 3.3024799340647966190325689569673
y[1] (numeric) = 3.3024799340647966190325689569649
absolute error = 2.4e-30
relative error = 7.2672659574527806158493299998068e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.82
y[1] (closed_form) = 3.3079242198649018187452449988707
y[1] (numeric) = 3.3079242198649018187452449988684
absolute error = 2.3e-30
relative error = 6.9530008764648598185460004334807e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.83
y[1] (closed_form) = 3.3132377143329537450471194526374
y[1] (numeric) = 3.313237714332953745047119452635
absolute error = 2.4e-30
relative error = 7.2436698085914016036534654466986e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3598.2MB, alloc=44.3MB, time=40.03
TOP MAIN SOLVE Loop
x[1] = 9.84
y[1] (closed_form) = 3.3184198861239334900425915702971
y[1] (numeric) = 3.3184198861239334900425915702947
absolute error = 2.4e-30
relative error = 7.2323578159462815654766607786463e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.85
y[1] (closed_form) = 3.3234702170249804178547489890459
y[1] (numeric) = 3.3234702170249804178547489890436
absolute error = 2.3e-30
relative error = 6.9204772415829124870268028582250e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.86
y[1] (closed_form) = 3.3283882020072130188463443701828
y[1] (numeric) = 3.3283882020072130188463443701805
absolute error = 2.3e-30
relative error = 6.9102516305428714606277505229320e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.87
y[1] (closed_form) = 3.3331733492762313769147607213119
y[1] (numeric) = 3.3331733492762313769147607213095
absolute error = 2.4e-30
relative error = 7.2003455821496305338365686066586e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.88
y[1] (closed_form) = 3.3378251803212961996563211544049
y[1] (numeric) = 3.3378251803212961996563211544026
absolute error = 2.3e-30
relative error = 6.8907143895972525600352969920260e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.89
y[1] (closed_form) = 3.3423432299631794935379090372785
y[1] (numeric) = 3.3423432299631794935379090372761
absolute error = 2.4e-30
relative error = 7.1805910849749542330653913899662e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.9
y[1] (closed_form) = 3.3467270464006820990482568061945
y[1] (numeric) = 3.3467270464006820990482568061921
absolute error = 2.4e-30
relative error = 7.1711853602794933152068843351053e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.91
y[1] (closed_form) = 3.3509761912558134341141527941132
y[1] (numeric) = 3.3509761912558134341141527941108
absolute error = 2.4e-30
relative error = 7.1620920681640977474200165865768e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.92
y[1] (closed_form) = 3.3550902396176289278448741145988
y[1] (numeric) = 3.3550902396176289278448741145966
absolute error = 2.2e-30
relative error = 6.5572006797967031295915860906723e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.93
y[1] (closed_form) = 3.3590687800847207608980022311041
y[1] (numeric) = 3.3590687800847207608980022311018
absolute error = 2.3e-30
relative error = 6.8471357705929157686206828211482e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.94
y[1] (closed_form) = 3.3629114148063576634279934623528
y[1] (numeric) = 3.3629114148063576634279934623504
absolute error = 2.4e-30
relative error = 7.1366732689811164969852420288251e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3638.1MB, alloc=44.3MB, time=40.47
TOP MAIN SOLVE Loop
x[1] = 9.95
y[1] (closed_form) = 3.36661775952226965667199261745
y[1] (numeric) = 3.3666177595222696566719926174477
absolute error = 2.3e-30
relative error = 6.8317824127630544423883561535811e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.96
y[1] (closed_form) = 3.3701874436010737597318850201653
y[1] (numeric) = 3.3701874436010737597318850201627
absolute error = 2.6e-30
relative error = 7.7147044296796679991760963257431e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.97
y[1] (closed_form) = 3.3736201100773368190139300327654
y[1] (numeric) = 3.3736201100773368190139300327627
absolute error = 2.7e-30
relative error = 8.0032721880416619840679696976519e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.98
y[1] (closed_form) = 3.3769154156872717540739177042946
y[1] (numeric) = 3.376915415687271754073917704292
absolute error = 2.6e-30
relative error = 7.6993340962046172988020580388641e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 9.99
y[1] (closed_form) = 3.3800730309030636502730108000159
y[1] (numeric) = 3.3800730309030636502730108000132
absolute error = 2.7e-30
relative error = 7.9879930856956465836112772463519e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
Finished!
diff ( y , x , 1 ) = sin ( x ) - cos ( x ) ;
Iterations = 10000
Total Elapsed Time = 40 Seconds
Elapsed Time(since restart) = 40 Seconds
Time to Timeout = 2 Minutes 19 Seconds
Percent Done = 100 %
> quit
memory used=3658.7MB, alloc=44.3MB, time=40.69