|\^/| Maple 2016 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> 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 7
# Begin Function number 8
> 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 8
# Begin Function number 9
> 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 9
# Begin Function number 10
> 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 10
# Begin Function number 11
> 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 11
# Begin Function number 12
> 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 12
# Begin Function number 13
> 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 13
# Begin Function number 14
> 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 14
# Begin Function number 15
> 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 15
# Begin Function number 16
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 16
# Begin Function number 17
> 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 17
# Begin Function number 18
> 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 18
# Begin Function number 19
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 19
# Begin Function number 20
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 20
# Begin Function number 21
> 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 21
# Begin Function number 22
> 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 22
# Begin Function number 23
> 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 23
# Begin Function number 24
> 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 24
# Begin Function number 25
> 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 25
# Begin Function number 26
> 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 26
# Begin Function number 27
> 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 27
# Begin Function number 28
> 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 28
# Begin Function number 29
> 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 29
# Begin Function number 30
> 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 30
# Begin Function number 31
> 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 31
# Begin Function number 32
> 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 32
# Begin Function number 33
> 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 33
# Begin Function number 34
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 34
# Begin Function number 35
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 35
# Begin Function number 36
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 36
# Begin Function number 37
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 37
# Begin Function number 38
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 38
# Begin Function number 39
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 39
# Begin Function number 40
> 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 40
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(1.0) + sin(c(x)));
> end;
exact_soln_y := proc(x) return c(1.0) + 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_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_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_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_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_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_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_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_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_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)*17*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_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)*17*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_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_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_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_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_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 cos 1 $eq_no = 1
> array_tmp1[1] := cos(array_x[1]);
> array_tmp1_g[1] := sin(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 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_tmp2[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 cos ID_LINEAR iii = 2 $eq_no = 1
> array_tmp1[2] := neg(array_tmp1_g[1]) * array_x[2] / c(1);
> array_tmp1_g[2] := 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 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_tmp2[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 cos ID_LINEAR iii = 3 $eq_no = 1
> array_tmp1[3] := neg(array_tmp1_g[2]) * array_x[2] / c(2);
> array_tmp1_g[3] := 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 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_tmp2[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 cos ID_LINEAR iii = 4 $eq_no = 1
> array_tmp1[4] := neg(array_tmp1_g[3]) * array_x[2] / c(3);
> array_tmp1_g[4] := 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 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_tmp2[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 cos ID_LINEAR iii = 5 $eq_no = 1
> array_tmp1[5] := neg(array_tmp1_g[4]) * array_x[2] / c(4);
> array_tmp1_g[5] := 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 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_tmp2[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 cos LINEAR $eq_no = 1
> array_tmp1[kkk] := neg(array_tmp1_g[kkk - 1]) * array_x[2] / c(kkk - 1);
> array_tmp1_g[kkk] := 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 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_tmp2[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_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] := cos(array_x[1]);
array_tmp1_g[1] := sin(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[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] := neg(array_tmp1_g[1])*array_x[2]/c(1);
array_tmp1_g[2] := array_tmp1[1]*array_x[2]/c(1);
array_tmp2[2] := array_tmp1[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[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] := neg(array_tmp1_g[2])*array_x[2]/c(2);
array_tmp1_g[3] := array_tmp1[2]*array_x[2]/c(2);
array_tmp2[3] := array_tmp1[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[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] := neg(array_tmp1_g[3])*array_x[2]/c(3);
array_tmp1_g[4] := array_tmp1[3]*array_x[2]/c(3);
array_tmp2[4] := array_tmp1[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[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] := neg(array_tmp1_g[4])*array_x[2]/c(4);
array_tmp1_g[5] := array_tmp1[4]*array_x[2]/c(4);
array_tmp2[5] := array_tmp1[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[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] := neg(array_tmp1_g[kkk - 1])*array_x[2]/c(kkk - 1)
;
array_tmp1_g[kkk] := array_tmp1[kkk - 1]*array_x[2]/c(kkk - 1);
array_tmp2[kkk] := array_tmp1[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_tmp2[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_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_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_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_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/cospostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = 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(5.0) ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := false;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 3;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=100000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=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(1.0) + sin(c(x)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := c(0.0);
> x_end := c(5.0) ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := false;
> 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 ) = 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,"2016-08-26T16:26:35-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"cos")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = 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,"cos diffeq.mxt")
> ;
> logitem_str(html_log_file,"cos 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_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_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_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_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/cospostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = 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(5.0) ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := false;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 3;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=100000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=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(1.0) + sin(c(x)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := c(0.);
x_end := c(5.0);
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := false;
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 ) = 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, "2016-08-26T16:26:35-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "cos");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = 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,
"cos diffeq.mxt");
logitem_str(html_log_file,
"cos 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/cospostode.ode#################
diff ( y , x , 1 ) = 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(5.0) ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := false;
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(1.0) + 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=4.4MB, alloc=8.3MB, time=0.08
TOP MAIN SOLVE Loop
x[1] = 0.01
y[1] (closed_form) = 1.0099998333341666646825424382691
y[1] (numeric) = 1.0099998333341666646825424382693
absolute error = 2e-31
relative error = 1.9801983465657500986123806865695e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
memory used=7.7MB, alloc=40.3MB, time=0.13
TOP MAIN SOLVE Loop
x[1] = 0.02
y[1] (closed_form) = 1.019998666693333079366490294693
y[1] (numeric) = 1.0199986666933330793664902946931
absolute error = 1e-31
relative error = 9.8039343839716433351236613050985e-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) = 1.0299955002024956607685263419263
y[1] (numeric) = 1.0299955002024956607685263419263
absolute error = 0
relative error = 0 %
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) = 1.0399893341866341594525468117159
y[1] (numeric) = 1.039989334186634159452546811716
absolute error = 1e-31
relative error = 9.6154832278360869901409491156178e-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) = 1.0499791692706783287948650008455
y[1] (numeric) = 1.0499791692706783287948650008456
absolute error = 1e-31
relative error = 9.5239984684134814593878718895478e-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) = 1.059964006479444599199091137857
y[1] (numeric) = 1.0599640064794445991990911378572
absolute error = 2e-31
relative error = 1.8868565232160881795834037030603e-29 %
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) = 1.0699428473375327639765473068079
y[1] (numeric) = 1.0699428473375327639765473068081
absolute error = 2e-31
relative error = 1.8692587225353579440261174032035e-29 %
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) = 1.0799146939691726873068763473145
y[1] (numeric) = 1.0799146939691726873068763473147
absolute error = 2e-31
relative error = 1.8519981357500559443613321565121e-29 %
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) = 1.0898785491980110496912539826071
y[1] (numeric) = 1.0898785491980110496912539826074
absolute error = 3e-31
relative error = 2.7526002802858676403953661284301e-29 %
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) = 1.0998334166468281523068141984106
y[1] (numeric) = 1.0998334166468281523068141984109
absolute error = 3e-31
relative error = 2.7276858064073005304723741039317e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
memory used=37.9MB, alloc=40.3MB, time=0.50
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (closed_form) = 1.1097783008371748086649494900834
y[1] (numeric) = 1.1097783008371748086649494900837
absolute error = 3e-31
relative error = 2.7032426185814890938254107462050e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (closed_form) = 1.119712207288919359967350614271
y[1] (numeric) = 1.1197122072889193599673506142712
absolute error = 2e-31
relative error = 1.7861732568250369765302667137980e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (closed_form) = 1.1296341426196948595412058107083
y[1] (numeric) = 1.1296341426196948595412058107084
absolute error = 1e-31
relative error = 8.8524236500229634256218959208415e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (closed_form) = 1.1395431146442364817179883517054
y[1] (numeric) = 1.1395431146442364817179883517053
absolute error = 1e-31
relative error = 8.7754468185453288747766003261553e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (closed_form) = 1.1494381324735992214977254386876
y[1] (numeric) = 1.1494381324735992214977254386877
absolute error = 1e-31
relative error = 8.6999027763938257948745204743370e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (closed_form) = 1.159318206614245963311463159686
y[1] (numeric) = 1.159318206614245963311463159686
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (closed_form) = 1.1691823490669960101576243766708
y[1] (numeric) = 1.1691823490669960101576243766709
absolute error = 1e-31
relative error = 8.5529857750418229057076547011110e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (closed_form) = 1.1790295734258241783418027396992
y[1] (numeric) = 1.1790295734258241783418027396992
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (closed_form) = 1.1888588949765005779928511529813
y[1] (numeric) = 1.1888588949765005779928511529813
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (closed_form) = 1.1986693307950612154594126271184
y[1] (numeric) = 1.1986693307950612154594126271184
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (closed_form) = 1.2084598998460995706087124262276
y[1] (numeric) = 1.2084598998460995706087124262277
absolute error = 1e-31
relative error = 8.2749953070627542800285284189377e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (closed_form) = 1.218229623080869319951791005457
y[1] (numeric) = 1.218229623080869319951791005457
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] = 0.23
y[1] (closed_form) = 1.2279775235351883954046172123601
y[1] (numeric) = 1.2279775235351883954046172123601
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=78.7MB, alloc=44.3MB, time=1.01
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (closed_form) = 1.2377026264271345883607920844898
y[1] (numeric) = 1.2377026264271345883607920844899
absolute error = 1e-31
relative error = 8.0794851578096049324790437368211e-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) = 1.2474039592545229295968487048494
y[1] (numeric) = 1.2474039592545229295968487048495
absolute error = 1e-31
relative error = 8.0166492384521756598648137763579e-30 %
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) = 1.2570805518921550973533884643652
y[1] (numeric) = 1.2570805518921550973533884643652
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] = 0.27
y[1] (closed_form) = 1.2667314366888311287322865210205
y[1] (numeric) = 1.2667314366888311287322865210205
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] = 0.28
y[1] (closed_form) = 1.2763556485641137333196695584578
y[1] (numeric) = 1.2763556485641137333196695584579
absolute error = 1e-31
relative error = 7.8348068669182383313778144673928e-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) = 1.2859522251048355326839402055044
y[1] (numeric) = 1.2859522251048355326839402055045
absolute error = 1e-31
relative error = 7.7763386576703993762228663985883e-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) = 1.295520206661339575105320745685
y[1] (numeric) = 1.2955202066613395751053207456851
absolute error = 1e-31
relative error = 7.7189070062988900384443781475276e-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) = 1.305058636443443501565643323959
y[1] (numeric) = 1.305058636443443501565643323959
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] = 0.32
y[1] (closed_form) = 1.3145665606161177666617575434172
y[1] (numeric) = 1.3145665606161177666617575434171
absolute error = 1e-31
relative error = 7.6070701169464929556001576561235e-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) = 1.3240430283948683467001956961702
y[1] (numeric) = 1.3240430283948683467001956961702
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] = 0.34
y[1] (closed_form) = 1.3334870921408143967817714870308
y[1] (numeric) = 1.3334870921408143967817714870309
absolute error = 1e-31
relative error = 7.4991352064351394557937651507292e-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) = 1.3428978074554513491896349069176
y[1] (numeric) = 1.3428978074554513491896349069177
absolute error = 1e-31
relative error = 7.4465830121118395126555205393477e-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) = 1.3522742332750899768499134359207
y[1] (numeric) = 1.3522742332750899768499134359208
absolute error = 1e-31
relative error = 7.3949497475677505164259935311850e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=119.6MB, alloc=44.3MB, time=1.50
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (closed_form) = 1.3616154319649619780372924691272
y[1] (numeric) = 1.3616154319649619780372924691273
absolute error = 1e-31
relative error = 7.3442175854080117807128590095045e-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) = 1.3709204694129826718454854663492
y[1] (numeric) = 1.3709204694129826718454854663495
absolute error = 3e-31
relative error = 2.1883107495539667077660402456053e-29 %
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) = 1.3801884151231614282311820978472
y[1] (numeric) = 1.3801884151231614282311820978475
absolute error = 3e-31
relative error = 2.1736162737841081757625165280629e-29 %
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) = 1.3894183423086504916663117567957
y[1] (numeric) = 1.3894183423086504916663117567961
absolute error = 4e-31
relative error = 2.8789025437461983026083732979462e-29 %
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) = 1.3986093279844228935937976400511
y[1] (numeric) = 1.3986093279844228935937976400516
absolute error = 5e-31
relative error = 3.5749797316207287870165505201510e-29 %
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) = 1.4077604530595701859727871580863
y[1] (numeric) = 1.4077604530595701859727871580867
absolute error = 4e-31
relative error = 2.8413925048871490923052581195161e-29 %
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) = 1.4168708024292107662169186726246
y[1] (numeric) = 1.4168708024292107662169186726249
absolute error = 3e-31
relative error = 2.1173419586715529166330801579148e-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) = 1.4259394650659996027697207507799
y[1] (numeric) = 1.4259394650659996027697207507803
absolute error = 4e-31
relative error = 2.8051681701753447261985717099476e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (closed_form) = 1.4349655341112302104208442462319
y[1] (numeric) = 1.4349655341112302104208442462324
absolute error = 5e-31
relative error = 3.4844042460551731847519063385221e-29 %
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) = 1.4439481069655197652415136439289
y[1] (numeric) = 1.4439481069655197652415136439294
absolute error = 5e-31
relative error = 3.4627283181994543002758864568262e-29 %
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) = 1.4528862853790682907032748003964
y[1] (numeric) = 1.4528862853790682907032748003969
absolute error = 5e-31
relative error = 3.4414255611859290797412211906585e-29 %
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) = 1.4617791755414828891366429425886
y[1] (numeric) = 1.4617791755414828891366429425892
absolute error = 6e-31
relative error = 4.1045871362734636705558110945309e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=160.4MB, alloc=44.3MB, time=1.98
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (closed_form) = 1.470625888171158036181358337188
y[1] (numeric) = 1.4706258881711580361813583371884
absolute error = 4e-31
relative error = 2.7199303590217106671794064553187e-29 %
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) = 1.4794255386042030002732879352156
y[1] (numeric) = 1.479425538604203000273287935216
absolute error = 4e-31
relative error = 2.7037521630009774990915545126646e-29 %
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) = 1.4881772468829074945001302376746
y[1] (numeric) = 1.488177246882907494500130237675
absolute error = 4e-31
relative error = 2.6878518727377958024857408638253e-29 %
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) = 1.4968801378437367143344589425478
y[1] (numeric) = 1.4968801378437367143344589425482
absolute error = 4e-31
relative error = 2.6722246483689869118903246514981e-29 %
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) = 1.5055333412048469618136610224661
y[1] (numeric) = 1.5055333412048469618136610224665
absolute error = 4e-31
relative error = 2.6568657701056845070873377362415e-29 %
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) = 1.5141359916531131046772806829582
y[1] (numeric) = 1.5141359916531131046772806829587
absolute error = 5e-31
relative error = 3.3022132936296348981582067488772e-29 %
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) = 1.5226872289306591677883781077573
y[1] (numeric) = 1.5226872289306591677883781077579
absolute error = 6e-31
relative error = 3.9404021298672301158003874876426e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (closed_form) = 1.531186197920883403851869441112
y[1] (numeric) = 1.5311861979208834038518694411126
absolute error = 6e-31
relative error = 3.9185306190371112556752834385463e-29 %
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) = 1.5396320487339692409944634930788
y[1] (numeric) = 1.5396320487339692409944634930795
absolute error = 7e-31
relative error = 4.5465408477019301853749732172866e-29 %
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) = 1.5480239367918735561826960595765
y[1] (numeric) = 1.5480239367918735561826960595772
absolute error = 7e-31
relative error = 4.5218939020457315429431439300054e-29 %
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) = 1.5563610229127837757225433788758
y[1] (numeric) = 1.5563610229127837757225433788764
absolute error = 6e-31
relative error = 3.8551466604906304799974669785872e-29 %
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) = 1.5646424733950353572009454456587
y[1] (numeric) = 1.5646424733950353572009454456594
absolute error = 7e-31
relative error = 4.4738655117875385321219124982355e-29 %
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) = 1.5728674601004812611909760321627
y[1] (numeric) = 1.5728674601004812611909760321634
absolute error = 7e-31
relative error = 4.4504703527611990434728090305917e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=201.3MB, alloc=44.3MB, time=2.47
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (closed_form) = 1.5810351605373050758429632275822
y[1] (numeric) = 1.5810351605373050758429632275829
absolute error = 7e-31
relative error = 4.4274790180005187553451391410259e-29 %
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) = 1.5891447579422695131181120907946
y[1] (numeric) = 1.5891447579422695131181120907954
absolute error = 8e-31
relative error = 5.0341543525329516782827297901670e-29 %
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) = 1.5971954413623920518835462392079
y[1] (numeric) = 1.5971954413623920518835462392088
absolute error = 9e-31
relative error = 5.6348770895082747293050351741781e-29 %
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) = 1.6051864057360395603725216786059
y[1] (numeric) = 1.6051864057360395603725216786068
absolute error = 9e-31
relative error = 5.6068254551864053800525020244413e-29 %
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) = 1.6131168519734337886151454793963
y[1] (numeric) = 1.6131168519734337886151454793972
absolute error = 9e-31
relative error = 5.5792610367870732702968302895188e-29 %
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) = 1.6209859870365596803574439141266
y[1] (numeric) = 1.6209859870365596803574439141274
absolute error = 8e-31
relative error = 4.9352678332681775277662166636701e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (closed_form) = 1.6287930240184685137041781874202
y[1] (numeric) = 1.6287930240184685137041781874209
absolute error = 7e-31
relative error = 4.2976608425851341267979340722509e-29 %
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) = 1.6365371822219679402374292070087
y[1] (numeric) = 1.6365371822219679402374292070094
absolute error = 7e-31
relative error = 4.2773241427340641810785892224047e-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) = 1.6442176872376910536726143513987
y[1] (numeric) = 1.6442176872376910536726143513994
absolute error = 7e-31
relative error = 4.2573438142245622631782192164894e-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) = 1.6518337710215366812101279728528
y[1] (numeric) = 1.6518337710215366812101279728535
absolute error = 7e-31
relative error = 4.2377145465860158229872241611631e-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) = 1.6593846719714731536180038326482
y[1] (numeric) = 1.6593846719714731536180038326489
absolute error = 7e-31
relative error = 4.2184311559799309376528132729256e-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) = 1.6668696350036978737325941307615
y[1] (numeric) = 1.6668696350036978737325941307622
absolute error = 7e-31
relative error = 4.1994885820716692229395781169713e-29 %
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) = 1.6742879116281450674838811576082
y[1] (numeric) = 1.674287911628145067483881157609
absolute error = 8e-31
relative error = 4.7781507257138812309971330533846e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=242.2MB, alloc=44.3MB, time=2.96
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (closed_form) = 1.6816387600233341667332419527799
y[1] (numeric) = 1.6816387600233341667332419527806
absolute error = 7e-31
relative error = 4.1626062424386965556705541681775e-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) = 1.6889214451105513391477556387697
y[1] (numeric) = 1.6889214451105513391477556387704
absolute error = 7e-31
relative error = 4.1446569467544434100238736338463e-29 %
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) = 1.6961352386273567470198837344522
y[1] (numeric) = 1.6961352386273567470198837344528
absolute error = 6e-31
relative error = 3.5374537733533925365070462532402e-29 %
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) = 1.7032794192004101843678973251179
y[1] (numeric) = 1.7032794192004101843678973251185
absolute error = 6e-31
relative error = 3.5226163906898189319837465571838e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (closed_form) = 1.7103532724176078098140288749692
y[1] (numeric) = 1.7103532724176078098140288749698
absolute error = 6e-31
relative error = 3.5080471951381820106893663116140e-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) = 1.7173560908995227616271746105814
y[1] (numeric) = 1.7173560908995227616271746105822
absolute error = 8e-31
relative error = 4.6583233625180972831297527110775e-29 %
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) = 1.7242871743701425109281768525145
y[1] (numeric) = 1.7242871743701425109281768525153
absolute error = 8e-31
relative error = 4.6395983910987946615790129715406e-29 %
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) = 1.7311458297268958793813133646877
y[1] (numeric) = 1.7311458297268958793813133646885
absolute error = 8e-31
relative error = 4.6212166893311774433978156587850e-29 %
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) = 1.7379313711099627187285802261381
y[1] (numeric) = 1.7379313711099627187285802261388
absolute error = 7e-31
relative error = 4.0277769976206354415989172671390e-29 %
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) = 1.7446431199708593212565726706296
y[1] (numeric) = 1.7446431199708593212565726706304
absolute error = 8e-31
relative error = 4.5854650205674290356033266224534e-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) = 1.7512804051402927027120715242355
y[1] (numeric) = 1.7512804051402927027120715242362
absolute error = 7e-31
relative error = 3.9970754994196600259695207516921e-29 %
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) = 1.7578425628952769722945887295286
y[1] (numeric) = 1.7578425628952769722945887295293
absolute error = 7e-31
relative error = 3.9821541176421174391537662615219e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=283.1MB, alloc=44.3MB, time=3.45
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (closed_form) = 1.7643289370255050781448028237228
y[1] (numeric) = 1.7643289370255050781448028237235
absolute error = 7e-31
relative error = 3.9675141370187753384304018799463e-29 %
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) = 1.770738878898969291209645130756
y[1] (numeric) = 1.7707388788989692912096451307566
absolute error = 6e-31
relative error = 3.3884160287544768327536475014808e-29 %
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) = 1.7770717475268238654903337129732
y[1] (numeric) = 1.7770717475268238654903337129739
absolute error = 7e-31
relative error = 3.9390643679648837966999098752550e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (closed_form) = 1.7833269096274833884613823157136
y[1] (numeric) = 1.7833269096274833884613823157143
absolute error = 7e-31
relative error = 3.9252477839086833517872115367222e-29 %
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) = 1.7895037396899504118789575178716
y[1] (numeric) = 1.7895037396899504118789575178724
absolute error = 8e-31
relative error = 4.4705131498557699358608134208664e-29 %
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) = 1.7956016200363660302682761024816
y[1] (numeric) = 1.7956016200363660302682761024824
absolute error = 8e-31
relative error = 4.4553312442645141348869358057048e-29 %
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) = 1.8016199408837771520843192159106
y[1] (numeric) = 1.8016199408837771520843192159115
absolute error = 9e-31
relative error = 4.9955042102748305038287288061183e-29 %
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) = 1.8075581004051142868702197986342
y[1] (numeric) = 1.8075581004051142868702197986351
absolute error = 9e-31
relative error = 4.9790930637211043253493024400224e-29 %
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) = 1.8134155047893737506854221021026
y[1] (numeric) = 1.8134155047893737506854221021035
absolute error = 9e-31
relative error = 4.9630103946008448100944406404851e-29 %
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) = 1.8191915683009982716332221464304
y[1] (numeric) = 1.8191915683009982716332221464313
absolute error = 9e-31
relative error = 4.9472524811696387292373206787783e-29 %
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) = 1.8248857133384500574766200378563
y[1] (numeric) = 1.8248857133384500574766200378572
absolute error = 9e-31
relative error = 4.9318156935621900477061711002299e-29 %
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) = 1.8304973704919704680845332877192
y[1] (numeric) = 1.83049737049197046808453328772
absolute error = 8e-31
relative error = 4.3703968817228586350733847675265e-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) = 1.8360259786005205167892594115471
y[1] (numeric) = 1.836025978600520516789259411548
absolute error = 9e-31
relative error = 4.9018914246845768913208584277820e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=324.1MB, alloc=44.3MB, time=3.94
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (closed_form) = 1.8414709848078965066525023216303
y[1] (numeric) = 1.8414709848078965066525023216311
absolute error = 8e-31
relative error = 4.3443530014862359549586890180649e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (closed_form) = 1.846831844618015190123098784782
y[1] (numeric) = 1.8468318446180151901230987847827
absolute error = 7e-31
relative error = 3.7902746914393970488367383007240e-29 %
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) = 1.8521080219493629236165499854554
y[1] (numeric) = 1.8521080219493629236165499854562
absolute error = 8e-31
relative error = 4.3194024890513226845517955118111e-29 %
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) = 1.8572989891886033721462743852944
y[1] (numeric) = 1.8572989891886033721462743852955
absolute error = 1.1e-30
relative error = 5.9225790053358940517847462123588e-29 %
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) = 1.8624042272433384032807916921162
y[1] (numeric) = 1.8624042272433384032807916921172
absolute error = 1.0e-30
relative error = 5.3694036201805817188446247790652e-29 %
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) = 1.8674232255940168943814094850003
y[1] (numeric) = 1.8674232255940168943814094850013
absolute error = 1.0e-30
relative error = 5.3549724898698611141401121522493e-29 %
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) = 1.8723554823449862622829459219974
y[1] (numeric) = 1.8723554823449862622829459219984
absolute error = 1.0e-30
relative error = 5.3408661412285568070262524031186e-29 %
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) = 1.8772005042746816103070632577768
y[1] (numeric) = 1.8772005042746816103070632577779
absolute error = 1.1e-30
relative error = 5.8597896042278196380934455626260e-29 %
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) = 1.8819578068849474737353349876248
y[1] (numeric) = 1.8819578068849474737353349876258
absolute error = 1.0e-30
relative error = 5.3136154080692122957341156507597e-29 %
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) = 1.886626914449487231608600628636
y[1] (numeric) = 1.8866269144494872316086006286371
absolute error = 1.1e-30
relative error = 5.8305115419228348335536951665219e-29 %
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) = 1.8912073600614353399518025778717
y[1] (numeric) = 1.8912073600614353399518025778728
absolute error = 1.1e-30
relative error = 5.8163902236731291534928778388767e-29 %
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) = 1.8956986856800476292406259593394
y[1] (numeric) = 1.8956986856800476292406259593404
absolute error = 1.0e-30
relative error = 5.2750999278203755255959132055767e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=365.1MB, alloc=44.3MB, time=4.44
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (closed_form) = 1.9001004421765049971191032473392
y[1] (numeric) = 1.9001004421765049971191032473402
absolute error = 1.0e-30
relative error = 5.2628796762687535009278191791115e-29 %
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) = 1.9044121893788259160370815224114
y[1] (numeric) = 1.9044121893788259160370815224123
absolute error = 9e-31
relative error = 4.7258676720272340422802519244920e-29 %
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) = 1.9086334961158832645942155781022
y[1] (numeric) = 1.908633496115883264594215578103
absolute error = 8e-31
relative error = 4.1914804577621630303147857094057e-29 %
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) = 1.9127639402605210809440330497537
y[1] (numeric) = 1.9127639402605210809440330497543
absolute error = 6e-31
relative error = 3.1368219954955820335072147995742e-29 %
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) = 1.9168031087717669266186616668743
y[1] (numeric) = 1.9168031087717669266186616668748
absolute error = 5e-31
relative error = 2.6085099596921345796118316130116e-29 %
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) = 1.920750597736135639573013008962
y[1] (numeric) = 1.9207505977361356395730130089624
absolute error = 4e-31
relative error = 2.0825192009387064613750607235507e-29 %
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) = 1.9246060124080203461075380258748
y[1] (numeric) = 1.9246060124080203461075380258753
absolute error = 5e-31
relative error = 2.5979343137061706020260311860534e-29 %
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) = 1.9283689672491666926020211116027
y[1] (numeric) = 1.9283689672491666926020211116031
absolute error = 4e-31
relative error = 2.0742918331163724667277379735309e-29 %
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) = 1.9320390859672263496701344354948
y[1] (numeric) = 1.9320390859672263496701344354952
absolute error = 4e-31
relative error = 2.0703514898082413720831378318989e-29 %
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) = 1.9356160015533859334164648885436
y[1] (numeric) = 1.9356160015533859334164648885441
absolute error = 5e-31
relative error = 2.5831569877431062108566013131424e-29 %
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) = 1.9390993563190675809352452718884
y[1] (numeric) = 1.9390993563190675809352452718887
absolute error = 3e-31
relative error = 1.5471099973416562548265133844310e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (closed_form) = 1.9424888019316975100238235653892
y[1] (numeric) = 1.9424888019316975100238235653896
absolute error = 4e-31
relative error = 2.0592139300994793785274148373407e-29 %
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) = 1.9457839994495389862847059630818
y[1] (numeric) = 1.9457839994495389862847059630823
absolute error = 5e-31
relative error = 2.5696582978452370414875475162960e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=406.1MB, alloc=44.3MB, time=4.93
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (closed_form) = 1.948984619355586214348490847036
y[1] (numeric) = 1.9489846193555862143484908470365
absolute error = 5e-31
relative error = 2.5654384084637896612308481610887e-29 %
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) = 1.9520903415905157638568162214254
y[1] (numeric) = 1.9520903415905157638568162214259
absolute error = 5e-31
relative error = 2.5613568662637414246640984027622e-29 %
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) = 1.9551008555846922350901817421829
y[1] (numeric) = 1.9551008555846922350901817421835
absolute error = 6e-31
relative error = 3.0688953886246654502982622085829e-29 %
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) = 1.9580158602892249637007538591603
y[1] (numeric) = 1.9580158602892249637007538591609
absolute error = 6e-31
relative error = 3.0643265571473564380330401348300e-29 %
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) = 1.9608350642060726589055612912854
y[1] (numeric) = 1.960835064206072658905561291286
absolute error = 6e-31
relative error = 3.0599208008498944225981200454844e-29 %
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) = 1.9635581854171929647013486300396
y[1] (numeric) = 1.9635581854171929647013486300402
absolute error = 6e-31
relative error = 3.0556772111773163294871175131656e-29 %
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) = 1.9661849516127340291692578059375
y[1] (numeric) = 1.9661849516127340291692578059382
absolute error = 7e-31
relative error = 3.5601940673273660634899321296923e-29 %
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) = 1.9687151001182652627358998459728
y[1] (numeric) = 1.9687151001182652627358998459735
absolute error = 7e-31
relative error = 3.5556185857361960772126246903190e-29 %
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) = 1.9711483779210445623376830377638
y[1] (numeric) = 1.9711483779210445623376830377646
absolute error = 8e-31
relative error = 4.0585478442965009614917397508622e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (closed_form) = 1.9734845416953193747878703480896
y[1] (numeric) = 1.9734845416953193747878703480906
absolute error = 1.0e-30
relative error = 5.0671792906011378093288912483107e-29 %
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) = 1.9757233578266590692611135392652
y[1] (numeric) = 1.9757233578266590692611135392662
absolute error = 1.0e-30
relative error = 5.0614373517354317078567354657180e-29 %
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) = 1.9778646024353161856784924394266
y[1] (numeric) = 1.9778646024353161856784924394277
absolute error = 1.1e-30
relative error = 5.5615536000067236657075199581456e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=447.2MB, alloc=44.3MB, time=5.42
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (closed_form) = 1.9799080613986142228876885048919
y[1] (numeric) = 1.9799080613986142228876885048929
absolute error = 1.0e-30
relative error = 5.0507395747133651219664071195626e-29 %
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) = 1.981853530372359727878131085206
y[1] (numeric) = 1.9818535303723597278781310852071
absolute error = 1.1e-30
relative error = 5.5503597170136329732435186414709e-29 %
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) = 1.9837008148112765448400382244429
y[1] (numeric) = 1.983700814811276544840038224444
absolute error = 1.1e-30
relative error = 5.5451910478982727110899791208657e-29 %
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) = 1.9854497299884601806594745788061
y[1] (numeric) = 1.9854497299884601806594745788073
absolute error = 1.2e-30
relative error = 6.0439707028340356570045886922494e-29 %
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) = 1.9871001010138503414290888619422
y[1] (numeric) = 1.9871001010138503414290888619435
absolute error = 1.3e-30
relative error = 6.5421968391865067597220966184484e-29 %
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) = 1.9886517628517197927362734733357
y[1] (numeric) = 1.9886517628517197927362734733369
absolute error = 1.2e-30
relative error = 6.0342389875198869636122954247078e-29 %
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) = 1.9901045603371777948572914954818
y[1] (numeric) = 1.9901045603371777948572914954829
absolute error = 1.1e-30
relative error = 5.5273477681676690736892003731658e-29 %
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) = 1.991458348191686462527604463958
y[1] (numeric) = 1.9914583481916864625276044639592
absolute error = 1.2e-30
relative error = 6.0257348645511054392812963653261e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (closed_form) = 1.992712991037588497665354134323
y[1] (numeric) = 1.9927129910375884976653541343244
absolute error = 1.4e-30
relative error = 7.0255977970567254326730166466215e-29 %
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) = 1.99386836341164484228683230125
y[1] (numeric) = 1.9938683634116448422868323012513
absolute error = 1.3e-30
relative error = 6.5199891018663402677453310778834e-29 %
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) = 1.9949243497775808978599284627356
y[1] (numeric) = 1.9949243497775808978599284627369
absolute error = 1.3e-30
relative error = 6.5165378333516268393615406838906e-29 %
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) = 1.9958808445376400564840751325627
y[1] (numeric) = 1.9958808445376400564840751325639
absolute error = 1.2e-30
relative error = 6.0123829700764952481122072872922e-29 %
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) = 1.9967377520431433885532007170437
y[1] (numeric) = 1.996737752043143388553200717045
absolute error = 1.3e-30
relative error = 6.5106196277893131194106809452181e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=488.2MB, alloc=44.3MB, time=5.91
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (closed_form) = 1.9974949866040544309417233711415
y[1] (numeric) = 1.9974949866040544309417233711426
absolute error = 1.1e-30
relative error = 5.5068974259110026167229077966595e-29 %
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) = 1.9981524724975481192427378648367
y[1] (numeric) = 1.9981524724975481192427378648378
absolute error = 1.1e-30
relative error = 5.5050853983383882197484659921568e-29 %
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) = 1.9987101439755830071723123941168
y[1] (numeric) = 1.9987101439755830071723123941179
absolute error = 1.1e-30
relative error = 5.5035493931702285521896375316990e-29 %
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) = 1.999167945271476015924265068709
y[1] (numeric) = 1.9991679452714760159242650687099
absolute error = 9e-31
relative error = 4.5018729023177937560825372378242e-29 %
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) = 1.99952583060547905600596353844
y[1] (numeric) = 1.9995258306054790560059635384409
absolute error = 9e-31
relative error = 4.5010671341388463686923932564950e-29 %
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) = 1.9997837641893569638976113476345
y[1] (numeric) = 1.9997837641893569638976113476353
absolute error = 8e-31
relative error = 4.0004325183842677922859062475748e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (closed_form) = 1.9999417202299662957451700234135
y[1] (numeric) = 1.9999417202299662957451700234142
absolute error = 7e-31
relative error = 3.5001019925696107334760124941429e-29 %
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) = 1.9999996829318346202105299238233
y[1] (numeric) = 1.999999682931834620210529923824
absolute error = 7e-31
relative error = 3.5000005548693773803393283384316e-29 %
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) = 1.9999576464987400525517942322517
y[1] (numeric) = 1.9999576464987400525517942322524
absolute error = 7e-31
relative error = 3.5000741201968298329443013249212e-29 %
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) = 1.9998156151342908719815843437455
y[1] (numeric) = 1.9998156151342908719815843437464
absolute error = 9e-31
relative error = 4.5004149041988730337202687422574e-29 %
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) = 1.9995736030415051643421138255462
y[1] (numeric) = 1.9995736030415051643421138255471
absolute error = 9e-31
relative error = 4.5009595977413925343755045393346e-29 %
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) = 1.9992316344213905321324131478443
y[1] (numeric) = 1.9992316344213905321324131478452
absolute error = 9e-31
relative error = 4.5017294869910075742432375232002e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=529.2MB, alloc=44.3MB, time=6.40
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (closed_form) = 1.9987897434705240139155188912468
y[1] (numeric) = 1.9987897434705240139155188912479
absolute error = 1.1e-30
relative error = 5.5033302206667122038905321001137e-29 %
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) = 1.9982479743776324551116699849331
y[1] (numeric) = 1.9982479743776324551116699849341
absolute error = 1.0e-30
relative error = 5.0043839044123470833332322765080e-29 %
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) = 1.9976063813191736721375819743679
y[1] (numeric) = 1.9976063813191736721375819743689
absolute error = 1.0e-30
relative error = 5.0059912170465876182875276265409e-29 %
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) = 1.9968650284539188517717030402022
y[1] (numeric) = 1.9968650284539188517717030402032
absolute error = 1.0e-30
relative error = 5.0078497332103322304545545822587e-29 %
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) = 1.996023989916536727501000590613
y[1] (numeric) = 1.996023989916536727501000590614
absolute error = 1.0e-30
relative error = 5.0099598253917517504966016349489e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (closed_form) = 1.9950833498101801744262972465342
y[1] (numeric) = 1.9950833498101801744262972465354
absolute error = 1.2e-30
relative error = 6.0147863001020612428791359564700e-29 %
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) = 1.9940432021980759640604878691936
y[1] (numeric) = 1.9940432021980759640604878691949
absolute error = 1.3e-30
relative error = 6.5194174256956044166452312983269e-29 %
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) = 1.9929036510941185200371492939456
y[1] (numeric) = 1.9929036510941185200371492939469
absolute error = 1.3e-30
relative error = 6.5231452573549684476895973203480e-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) = 1.9916648104524686153461333986479
y[1] (numeric) = 1.9916648104524686153461333986493
absolute error = 1.4e-30
relative error = 7.0292952541645120041504556255667e-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) = 1.9903268041561580512177522238611
y[1] (numeric) = 1.9903268041561580512177522238626
absolute error = 1.5e-30
relative error = 7.5364507821918086034852107345044e-29 %
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) = 1.9888897660047014571781706570855
y[1] (numeric) = 1.9888897660047014571781706570871
absolute error = 1.6e-30
relative error = 8.0446891896582760325104559925464e-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) = 1.9873538397007164510856776762221
y[1] (numeric) = 1.9873538397007164510856776762237
absolute error = 1.6e-30
relative error = 8.0509065272490699881871986672882e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=570.1MB, alloc=44.3MB, time=6.89
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (closed_form) = 1.9857191788355534971206826956656
y[1] (numeric) = 1.9857191788355534971206826956674
absolute error = 1.8e-30
relative error = 9.0647258644877410774984035916229e-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) = 1.983985946873936898731662936968
y[1] (numeric) = 1.9839859468739368987316629369699
absolute error = 1.9e-30
relative error = 9.5766807370472095756073998063820e-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) = 1.982154317137618462424968099456
y[1] (numeric) = 1.9821543171376184624249680994578
absolute error = 1.8e-30
relative error = 9.0810285780339083507663036777605e-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) = 1.9802244727880454670184814488984
y[1] (numeric) = 1.9802244727880454670184814489002
absolute error = 1.8e-30
relative error = 9.0898785705122638221589337578624e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (closed_form) = 1.9781966068080446715477686473056
y[1] (numeric) = 1.9781966068080446715477686473073
absolute error = 1.7e-30
relative error = 8.5936857547393436468806219106704e-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) = 1.9760709219825241934086604331086
y[1] (numeric) = 1.9760709219825241934086604331102
absolute error = 1.6e-30
relative error = 8.0968753813490401779003732668740e-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) = 1.9738476308781951865323731788434
y[1] (numeric) = 1.9738476308781951865323731788449
absolute error = 1.5e-30
relative error = 7.5993707747979863901134136950176e-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) = 1.9715269558223153474084512690904
y[1] (numeric) = 1.9715269558223153474084512690919
absolute error = 1.5e-30
relative error = 7.6083159581977741814041459659497e-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) = 1.969109128880456374587215318498
y[1] (numeric) = 1.9691091288804563745872153184997
absolute error = 1.7e-30
relative error = 8.6333457860029358762375521472989e-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) = 1.9665943918332976048972389297428
y[1] (numeric) = 1.9665943918332976048972389297445
absolute error = 1.7e-30
relative error = 8.6443854770440328618687345986640e-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) = 1.9639829961524481469948936717271
y[1] (numeric) = 1.9639829961524481469948936717289
absolute error = 1.8e-30
relative error = 9.1650487989269767045813091962630e-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) = 1.9612752029752999300124591686361
y[1] (numeric) = 1.9612752029752999300124591686379
absolute error = 1.8e-30
relative error = 9.1777023299400221346062340959020e-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) = 1.9584712830789141819789777659032
y[1] (numeric) = 1.9584712830789141819789777659051
absolute error = 1.9e-30
relative error = 9.7014442663310771974734331267835e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=611.2MB, alloc=44.3MB, time=7.38
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (closed_form) = 1.9555715168529439493442504921726
y[1] (numeric) = 1.9555715168529439493442504921745
absolute error = 1.9e-30
relative error = 9.7158297900433019846275700904331e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (closed_form) = 1.9525761942715953653314574258151
y[1] (numeric) = 1.9525761942715953653314574258169
absolute error = 1.8e-30
relative error = 9.2185903181693065313976530251110e-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) = 1.9494856148646304709682016721383
y[1] (numeric) = 1.9494856148646304709682016721402
absolute error = 1.9e-30
relative error = 9.7461606564967308968515804429235e-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) = 1.946300087687414488489709611635
y[1] (numeric) = 1.9463000876874144884897096116367
absolute error = 1.7e-30
relative error = 8.7345215198542830652542672525636e-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) = 1.9430199312900105423618865769482
y[1] (numeric) = 1.94301993129001054236188657695
absolute error = 1.8e-30
relative error = 9.2639296746942956246183415205185e-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) = 1.939645473685324918426371339687
y[1] (numeric) = 1.9396454736853249184263713396889
absolute error = 1.9e-30
relative error = 9.7956045358639764786139488655098e-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) = 1.9361770523163060466151293727488
y[1] (numeric) = 1.9361770523163060466151293727507
absolute error = 1.9e-30
relative error = 9.8131521480795035469763472921671e-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) = 1.9326150140222004873089793388657
y[1] (numeric) = 1.9326150140222004873089793388677
absolute error = 2.0e-30
relative error = 1.0348672578288401119583212477991e-28 %
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) = 1.9289597150038692957132970350915
y[1] (numeric) = 1.9289597150038692957132970350935
absolute error = 2.0e-30
relative error = 1.0368282885555171922020502309869e-28 %
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) = 1.92521152078816823258555628949
y[1] (numeric) = 1.925211520788168232585556289492
absolute error = 2.0e-30
relative error = 1.0388468894998165620658279075686e-28 %
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) = 1.9213708061913953832639509971532
y[1] (numeric) = 1.9213708061913953832639509971552
absolute error = 2.0e-30
relative error = 1.0409234873118874952852244284338e-28 %
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) = 1.917437955281809840204735217402
y[1] (numeric) = 1.9174379552818098402047352174039
absolute error = 1.9e-30
relative error = 9.9090559606699401770962780068295e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=652.2MB, alloc=44.3MB, time=7.88
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (closed_form) = 1.9134133613412251971287932710576
y[1] (numeric) = 1.9134133613412251971287932710595
absolute error = 1.9e-30
relative error = 9.9298982561101017158048213350282e-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) = 1.9092974268256816953960198659117
y[1] (numeric) = 1.9092974268256816953960198659136
absolute error = 1.9e-30
relative error = 9.9513044605044107264452695796580e-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) = 1.9050905633252009553600997102737
y[1] (numeric) = 1.9050905633252009553600997102756
absolute error = 1.9e-30
relative error = 9.9732791531111479718853074413568e-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) = 1.9007931915226273171970135245537
y[1] (numeric) = 1.9007931915226273171970135245557
absolute error = 2.0e-30
relative error = 1.0521923210372524688200032422639e-28 %
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) = 1.8964057411515599070388888319676
y[1] (numeric) = 1.8964057411515599070388888319695
absolute error = 1.9e-30
relative error = 1.0018953005522212460891330750865e-28 %
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) = 1.8919286509533796351715256485842
y[1] (numeric) = 1.8919286509533796351715256485859
absolute error = 1.7e-30
relative error = 8.9855396985681090248090886887364e-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) = 1.8873623686333754235599666046803
y[1] (numeric) = 1.8873623686333754235599666046821
absolute error = 1.8e-30
relative error = 9.5371192618583688153617671336267e-29 %
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) = 1.8827073508159740500427975851999
y[1] (numeric) = 1.8827073508159740500427975852017
absolute error = 1.8e-30
relative error = 9.5606999102641825735571295807258e-29 %
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) = 1.8779640629990780861734511204438
y[1] (numeric) = 1.8779640629990780861734511204457
absolute error = 1.9e-30
relative error = 1.0117339503109185596367722149008e-28 %
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) = 1.8731329795075164948766768050246
y[1] (numeric) = 1.8731329795075164948766768050266
absolute error = 2.0e-30
relative error = 1.0677298525414033019184784801202e-28 %
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) = 1.8682145834456125428216220587275
y[1] (numeric) = 1.8682145834456125428216220587296
absolute error = 2.1e-30
relative error = 1.1240678766819695974761835156454e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (closed_form) = 1.863209366648873770680759313269
y[1] (numeric) = 1.8632093666488737706807593132709
absolute error = 1.9e-30
relative error = 1.0197458396300878577180832016254e-28 %
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) = 1.8581178296348088522373755083107
y[1] (numeric) = 1.8581178296348088522373755083126
absolute error = 1.9e-30
relative error = 1.0225401046678630678964913088199e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=693.2MB, alloc=44.3MB, time=8.38
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (closed_form) = 1.8529404815528762606147273336542
y[1] (numeric) = 1.8529404815528762606147273336561
absolute error = 1.9e-30
relative error = 1.0253972099566225758950365633436e-28 %
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) = 1.8476778401335697467185299963159
y[1] (numeric) = 1.8476778401335697467185299963178
absolute error = 1.9e-30
relative error = 1.0283177936813096447332127365343e-28 %
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) = 1.8423304316366457213025066370689
y[1] (numeric) = 1.8423304316366457213025066370707
absolute error = 1.8e-30
relative error = 9.7702343135099754144922664722533e-29 %
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) = 1.8368987907984977178756481370438
y[1] (numeric) = 1.8368987907984977178756481370455
absolute error = 1.7e-30
relative error = 9.2547287227567503788929617135778e-29 %
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) = 1.8313834607786831989610381203463
y[1] (numeric) = 1.831383460778683198961038120348
absolute error = 1.7e-30
relative error = 9.2825999382847955749151848026043e-29 %
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) = 1.8257849931056080529810564239434
y[1] (numeric) = 1.8257849931056080529810564239451
absolute error = 1.7e-30
relative error = 9.3110634955343160239534467076864e-29 %
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) = 1.8201039476213742132740097460839
y[1] (numeric) = 1.8201039476213742132740097460857
absolute error = 1.8e-30
relative error = 9.8895450578652537365389861270499e-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) = 1.814340892425795914434327645905
y[1] (numeric) = 1.8143408924257959144343276459069
absolute error = 1.9e-30
relative error = 1.0472122454671000736803712727328e-28 %
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) = 1.8084964038195901843040369104161
y[1] (numeric) = 1.808496403819590184304036910418
absolute error = 1.9e-30
relative error = 1.0505965043597277297778699715124e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (closed_form) = 1.802571066246747252518974042556
y[1] (numeric) = 1.8025710662467472525189740425579
absolute error = 1.9e-30
relative error = 1.0540499820382205463151460243134e-28 %
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) = 1.7965654722360866385208567496092
y[1] (numeric) = 1.7965654722360866385208567496111
absolute error = 1.9e-30
relative error = 1.0575734808234815234852640482955e-28 %
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) = 1.7904802223420047633777101271885
y[1] (numeric) = 1.7904802223420047633777101271905
absolute error = 2.0e-30
relative error = 1.1170187612482737957162540709450e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=734.2MB, alloc=44.3MB, time=8.87
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (closed_form) = 1.7843159250844200106020886706045
y[1] (numeric) = 1.7843159250844200106020886706064
absolute error = 1.9e-30
relative error = 1.0648338521722865388370911110931e-28 %
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) = 1.7780731968879212414109666755878
y[1] (numeric) = 1.7780731968879212414109666755897
absolute error = 1.9e-30
relative error = 1.0685724318467212526255998314069e-28 %
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) = 1.7717526620201258495250616377403
y[1] (numeric) = 1.7717526620201258495250616377424
absolute error = 2.1e-30
relative error = 1.1852670211911020649475337638246e-28 %
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) = 1.7653549525292535196507426019347
y[1] (numeric) = 1.7653549525292535196507426019369
absolute error = 2.2e-30
relative error = 1.2462083032355749549536438127613e-28 %
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) = 1.7588807081809219322166535763009
y[1] (numeric) = 1.7588807081809219322166535763031
absolute error = 2.2e-30
relative error = 1.2507954574561765385109991360714e-28 %
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) = 1.7523305763941707347419082779736
y[1] (numeric) = 1.7523305763941707347419082779759
absolute error = 2.3e-30
relative error = 1.3125377317405411967789308097865e-28 %
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) = 1.7457052121767201773854062116435
y[1] (numeric) = 1.7457052121767201773854062116457
absolute error = 2.2e-30
relative error = 1.2602356827799233989980854938322e-28 %
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) = 1.7390052780594708867587641920983
y[1] (numeric) = 1.7390052780594708867587641921004
absolute error = 2.1e-30
relative error = 1.2075869041313994999692202829617e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (closed_form) = 1.7322314440302513279708986777247
y[1] (numeric) = 1.7322314440302513279708986777268
absolute error = 2.1e-30
relative error = 1.2123091329609451650253513325546e-28 %
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) = 1.7253843874668195801028441924754
y[1] (numeric) = 1.7253843874668195801028441924774
absolute error = 2.0e-30
relative error = 1.1591619899472757235409221573002e-28 %
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) = 1.718464793069126124879428686794
y[1] (numeric) = 1.718464793069126124879428686796
absolute error = 2.0e-30
relative error = 1.1638294878465682814164913705365e-28 %
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) = 1.7114733527908444222024911820132
y[1] (numeric) = 1.7114733527908444222024911820153
absolute error = 2.1e-30
relative error = 1.2270129690161974765490956306628e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=775.2MB, alloc=44.3MB, time=9.36
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (closed_form) = 1.7044107657701761194310307129327
y[1] (numeric) = 1.7044107657701761194310307129348
absolute error = 2.1e-30
relative error = 1.2320973571479807208977229719845e-28 %
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) = 1.6972777382599378138296964202892
y[1] (numeric) = 1.6972777382599378138296964202914
absolute error = 2.2e-30
relative error = 1.2961932808094548591113663149395e-28 %
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) = 1.6900749835569363594511131070202
y[1] (numeric) = 1.6900749835569363594511131070224
absolute error = 2.2e-30
relative error = 1.3017173920708973979445249004830e-28 %
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) = 1.682803221930639780862500311013
y[1] (numeric) = 1.6828032219306397808625003110153
absolute error = 2.3e-30
relative error = 1.3667670527521721504576518202985e-28 %
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) = 1.6754631805511509265657715253413
y[1] (numeric) = 1.6754631805511509265657715253436
absolute error = 2.3e-30
relative error = 1.3727547263935725287622496871900e-28 %
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) = 1.6680555934164910646857498006547
y[1] (numeric) = 1.6680555934164910646857498006572
absolute error = 2.5e-30
relative error = 1.4987510067812131951449013228494e-28 %
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) = 1.6605812012792006925063341065602
y[1] (numeric) = 1.6605812012792006925063341065627
absolute error = 2.5e-30
relative error = 1.5054969898937596113708268077140e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (closed_form) = 1.6530407515722648997124970471899
y[1] (numeric) = 1.6530407515722648997124970471923
absolute error = 2.4e-30
relative error = 1.4518698330439077334019869601094e-28 %
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) = 1.6454349983343706927400610729825
y[1] (numeric) = 1.645434998334370692740061072985
absolute error = 2.5e-30
relative error = 1.5193550657003663624296190487236e-28 %
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) = 1.6377647021345037544385328556338
y[1] (numeric) = 1.6377647021345037544385328556361
absolute error = 2.3e-30
relative error = 1.4043531387643188015653430584658e-28 %
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) = 1.6300306299958921793081937186159
y[1] (numeric) = 1.6300306299958921793081937186181
absolute error = 2.2e-30
relative error = 1.3496678893730630041492123245073e-28 %
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) = 1.6222335553193047898745424048558
y[1] (numeric) = 1.622233555319304789874542404858
absolute error = 2.2e-30
relative error = 1.3561549092522458898736578671394e-28 %
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) = 1.6143742578057117043045348806656
y[1] (numeric) = 1.614374257805711704304534880668
absolute error = 2.4e-30
relative error = 1.4866441213341234735171855708818e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=815.9MB, alloc=44.3MB, time=9.84
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (closed_form) = 1.6064535233783148891434102397918
y[1] (numeric) = 1.6064535233783148891434102397941
absolute error = 2.3e-30
relative error = 1.4317252049490864964201395302351e-28 %
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) = 1.5984721441039564940518547021862
y[1] (numeric) = 1.5984721441039564940518547021885
absolute error = 2.3e-30
relative error = 1.4388739950731476144446405304138e-28 %
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) = 1.590430918113912827644537155024
y[1] (numeric) = 1.5904309181139128276445371550262
absolute error = 2.2e-30
relative error = 1.3832729073256280042478763734498e-28 %
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) = 1.5823306495240818949664275822971
y[1] (numeric) = 1.5823306495240818949664275822994
absolute error = 2.3e-30
relative error = 1.4535520756624234949988970174372e-28 %
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) = 1.5741721483545724777866405874022
y[1] (numeric) = 1.5741721483545724777866405874045
absolute error = 2.3e-30
relative error = 1.4610854361793341274615913077725e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (closed_form) = 1.565956230448702798734765747982
y[1] (numeric) = 1.5659562304487027987347657479842
absolute error = 2.2e-30
relative error = 1.4048923956001125588120938692257e-28 %
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) = 1.5576837173914168693457702817662
y[1] (numeric) = 1.5576837173914168693457702817684
absolute error = 2.2e-30
relative error = 1.4123534678042609514049468728098e-28 %
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) = 1.5493554364271266803106833831373
y[1] (numeric) = 1.5493554364271266803106833831394
absolute error = 2.1e-30
relative error = 1.3554023503107078482064262758613e-28 %
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) = 1.5409722203769884496455725487458
y[1] (numeric) = 1.540972220376988449645572548748
absolute error = 2.2e-30
relative error = 1.4276701233859912501079428219489e-28 %
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) = 1.5325349075556212010850587644716
y[1] (numeric) = 1.5325349075556212010850587644739
absolute error = 2.3e-30
relative error = 1.5007814756196832219691716104656e-28 %
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) = 1.5240443416872760007731302488759
y[1] (numeric) = 1.5240443416872760007731302488783
absolute error = 2.4e-30
relative error = 1.5747573311042576019712393164759e-28 %
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) = 1.5155013718214642352577269352094
y[1] (numeric) = 1.5155013718214642352577269352119
absolute error = 2.5e-30
relative error = 1.6496190940396694055172574560304e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=856.5MB, alloc=44.3MB, time=10.32
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (closed_form) = 1.5069068522480533678909866995555
y[1] (numeric) = 1.506906852248053367890986699558
absolute error = 2.5e-30
relative error = 1.6590275611730197547917596761085e-28 %
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) = 1.4982616424118386639887600099976
y[1] (numeric) = 1.4982616424118386639887600100002
absolute error = 2.6e-30
relative error = 1.7353444327751921898602088688191e-28 %
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) = 1.4895666068265994275056870536116
y[1] (numeric) = 1.4895666068265994275056870536142
absolute error = 2.6e-30
relative error = 1.7454741453549960093047238395204e-28 %
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) = 1.4808226149886483435305502695329
y[1] (numeric) = 1.4808226149886483435305502695355
absolute error = 2.6e-30
relative error = 1.7557808569934157989100033433032e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (closed_form) = 1.4720305412898825715956107783974
y[1] (numeric) = 1.4720305412898825715956107784
absolute error = 2.6e-30
relative error = 1.7662677010231880621701929985004e-28 %
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) = 1.4631912649303452846181405937964
y[1] (numeric) = 1.4631912649303452846181405937991
absolute error = 2.7e-30
relative error = 1.8452816557297672006873436390530e-28 %
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) = 1.4543056698303063972473913211913
y[1] (numeric) = 1.4543056698303063972473913211941
absolute error = 2.8e-30
relative error = 1.9253173924067242650300298069665e-28 %
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) = 1.4453746445418712754708988319294
y[1] (numeric) = 1.4453746445418712754708988319322
absolute error = 2.8e-30
relative error = 1.9372140023166750514163430455475e-28 %
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) = 1.436399082160126266535504118761
y[1] (numeric) = 1.4363990821601262665355041187638
absolute error = 2.8e-30
relative error = 1.9493189843794837713106618316387e-28 %
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) = 1.4273798802338299345560530858579
y[1] (numeric) = 1.4273798802338299345560530858606
absolute error = 2.7e-30
relative error = 1.8915777344134152305372441928831e-28 %
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) = 1.4183179406756589326137906811086
y[1] (numeric) = 1.4183179406756589326137906811112
absolute error = 2.6e-30
relative error = 1.8331573799041213857739740394872e-28 %
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) = 1.4092141696720174866824446740074
y[1] (numeric) = 1.40921416967201748668244467401
absolute error = 2.6e-30
relative error = 1.8449998984931635365108642316924e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=897.1MB, alloc=44.3MB, time=10.80
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (closed_form) = 1.4000694775924195103584479578944
y[1] (numeric) = 1.400069477592419510358447957897
absolute error = 2.6e-30
relative error = 1.8570506975632373814251595788732e-28 %
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) = 1.3908847788984524121083117016403
y[1] (numeric) = 1.3908847788984524121083117016428
absolute error = 2.5e-30
relative error = 1.7974170383688722246645429216476e-28 %
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) = 1.3816609920523316985765613723778
y[1] (numeric) = 1.3816609920523316985765613723801
absolute error = 2.3e-30
relative error = 1.6646630492068530187449682418879e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (closed_form) = 1.3723990394250555184177005924498
y[1] (numeric) = 1.372399039425055518417700592452
absolute error = 2.2e-30
relative error = 1.6030323082429834543038145140352e-28 %
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) = 1.3630998472041683311212820091725
y[1] (numeric) = 1.3630998472041683311212820091749
absolute error = 2.4e-30
relative error = 1.7606927364291034964703555473951e-28 %
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) = 1.3537643453011429243863393172273
y[1] (numeric) = 1.3537643453011429243863393172299
absolute error = 2.6e-30
relative error = 1.9205705993251238665388309057129e-28 %
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) = 1.3443934672583900417662615955623
y[1] (numeric) = 1.3443934672583900417662615955648
absolute error = 2.5e-30
relative error = 1.8595746415654848095884219615539e-28 %
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) = 1.3349881501559049195438537527124
y[1] (numeric) = 1.334988150155904919543853752715
absolute error = 2.6e-30
relative error = 1.9475828303767057823885018863211e-28 %
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) = 1.3255493345175600681051012812063
y[1] (numeric) = 1.325549334517560068105101281209
absolute error = 2.7e-30
relative error = 2.0368913700090066687894737045093e-28 %
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) = 1.3160779642170536684554128560246
y[1] (numeric) = 1.3160779642170536684554128560273
absolute error = 2.7e-30
relative error = 2.0515501918659155551631870742409e-28 %
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) = 1.3065749863835229889603130778681
y[1] (numeric) = 1.3065749863835229889603130778707
absolute error = 2.6e-30
relative error = 1.9899355391737263629029404147969e-28 %
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) = 1.2970413513068322608902560680973
y[1] (numeric) = 1.2970413513068322608902560680999
absolute error = 2.6e-30
relative error = 2.0045621501429954513274355618108e-28 %
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) = 1.2874780123425444839030789266917
y[1] (numeric) = 1.2874780123425444839030789266943
absolute error = 2.6e-30
relative error = 2.0194519635091429191667634175252e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=937.9MB, alloc=44.3MB, time=11.28
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (closed_form) = 1.2778859258165866642043569097532
y[1] (numeric) = 1.2778859258165866642043569097558
absolute error = 2.6e-30
relative error = 2.0346104041630823010348049784601e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (closed_form) = 1.2682660509296180187823989209871
y[1] (numeric) = 1.2682660509296180187823989209899
absolute error = 2.8e-30
relative error = 2.2077386664632758677827211944546e-28 %
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) = 1.2586193496611107088177669201177
y[1] (numeric) = 1.2586193496611107088177669201205
absolute error = 2.8e-30
relative error = 2.2246599027370057655319533019339e-28 %
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) = 1.2489467866731526941140458405805
y[1] (numeric) = 1.2489467866731526941140458405833
absolute error = 2.8e-30
relative error = 2.2418889498554395683438684426389e-28 %
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) = 1.2392493292139823281842569187396
y[1] (numeric) = 1.2392493292139823281842569187425
absolute error = 2.9e-30
relative error = 2.3401263423232035633600665873723e-28 %
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) = 1.229527947021264340453018223827
y[1] (numeric) = 1.2295279470212643404530182238299
absolute error = 2.9e-30
relative error = 2.3586287786509706026620956504401e-28 %
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) = 1.2197836122251168778956290930646
y[1] (numeric) = 1.2197836122251168778956290930676
absolute error = 3.0e-30
relative error = 2.4594526192456631439176843920714e-28 %
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) = 1.2100172992508993033291040342591
y[1] (numeric) = 1.210017299250899303329104034262
absolute error = 2.9e-30
relative error = 2.3966599500646310083968632722230e-28 %
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) = 1.2002299847217704714943170944231
y[1] (numeric) = 1.2002299847217704714943170944259
absolute error = 2.8e-30
relative error = 2.3328862265085618860445974834683e-28 %
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) = 1.1904226473610272270204473140574
y[1] (numeric) = 1.19042264736102722702044731406
absolute error = 2.6e-30
relative error = 2.1840982324754789981655292965070e-28 %
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) = 1.1805962678942328903405445088014
y[1] (numeric) = 1.180596267894232890340544508804
absolute error = 2.6e-30
relative error = 2.2022769940120871806162379203721e-28 %
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) = 1.170751828951145518628064498668
y[1] (numeric) = 1.1707518289511455186280644986707
absolute error = 2.7e-30
relative error = 2.3062103626341366246980033930710e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=978.6MB, alloc=44.3MB, time=11.76
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (closed_form) = 1.1608903149674557488465539545413
y[1] (numeric) = 1.1608903149674557488465539545442
absolute error = 2.9e-30
relative error = 2.4980826893032510400801827060352e-28 %
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) = 1.1510127120863440490462950356105
y[1] (numeric) = 1.1510127120863440490462950356132
absolute error = 2.7e-30
relative error = 2.3457603653272749883976318827301e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (closed_form) = 1.1411200080598672221007448028081
y[1] (numeric) = 1.1411200080598672221007448028108
absolute error = 2.7e-30
relative error = 2.3660964499172539075495904883078e-28 %
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) = 1.1312131921501840231502181246848
y[1] (numeric) = 1.1312131921501840231502181246875
absolute error = 2.7e-30
relative error = 2.3868179921663590990098092690037e-28 %
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) = 1.1212932550306297681087579963391
y[1] (numeric) = 1.1212932550306297681087579963418
absolute error = 2.7e-30
relative error = 2.4079338637654121482534377299312e-28 %
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) = 1.1113611886866498256909050329173
y[1] (numeric) = 1.1113611886866498256909050329201
absolute error = 2.8e-30
relative error = 2.5194329516841394346822945696422e-28 %
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) = 1.1014179863166018995266083126088
y[1] (numeric) = 1.1014179863166018995266083126116
absolute error = 2.8e-30
relative error = 2.5421774792001097584686441254344e-28 %
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) = 1.0914646422324370200534015886964
y[1] (numeric) = 1.0914646422324370200534015886992
absolute error = 2.8e-30
relative error = 2.5653602431618809230432062938870e-28 %
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) = 1.0815021517602691780038900888357
y[1] (numeric) = 1.0815021517602691780038900888385
absolute error = 2.8e-30
relative error = 2.5889916126774947808409076909017e-28 %
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) = 1.0715315111408435424423407903189
y[1] (numeric) = 1.0715315111408435424423407903217
absolute error = 2.8e-30
relative error = 2.6130822760582019277141614206711e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (closed_form) = 1.0615537174299132164456296371357
y[1] (numeric) = 1.0615537174299132164456296371385
absolute error = 2.8e-30
relative error = 2.6376432525515261376636121626627e-28 %
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) = 1.0515697683985344926699585105746
y[1] (numeric) = 1.0515697683985344926699585105775
absolute error = 2.9e-30
relative error = 2.7577818297462967931079107549343e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1019.3MB, alloc=44.3MB, time=12.24
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (closed_form) = 1.0415806624332905791946982715967
y[1] (numeric) = 1.0415806624332905791946982715994
absolute error = 2.7e-30
relative error = 2.5922140237246628953483023549709e-28 %
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) = 1.0315873984364537731876268727034
y[1] (numeric) = 1.0315873984364537731876268727061
absolute error = 2.7e-30
relative error = 2.6173254966979137247138181071769e-28 %
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) = 1.0215909757260960660909981042019
y[1] (numeric) = 1.0215909757260960660909981042047
absolute error = 2.8e-30
relative error = 2.7408229580433590188214263207182e-28 %
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) = 1.0115923939361581691846814831183
y[1] (numeric) = 1.0115923939361581691846814831211
absolute error = 2.8e-30
relative error = 2.7679132591191750795233472845283e-28 %
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) = 1.0015926529164869525405414363244
y[1] (numeric) = 1.0015926529164869525405414363271
absolute error = 2.7e-30
relative error = 2.6957066749022236283095904850021e-28 %
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) = 0.99159275263285129354085848342893
y[1] (numeric) = 0.99159275263285129354085848343158
absolute error = 2.65e-30
relative error = 2.6724681004008842389306003592637e-28 %
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) = 0.98159369306694633329262072881263
y[1] (numeric) = 0.98159369306694633329262072881528
absolute error = 2.65e-30
relative error = 2.6996913475678429845601287841297e-28 %
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) = 0.97159647411639614042871472510327
y[1] (numeric) = 0.97159647411639614042871472510592
absolute error = 2.65e-30
relative error = 2.7274697578642438003007418593779e-28 %
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) = 0.96160209549476478194630475327388
y[1] (numeric) = 0.96160209549476478194630475327654
absolute error = 2.66e-30
relative error = 2.7662169336594189533268662648467e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (closed_form) = 0.95161155663158579989199285154883
y[1] (numeric) = 0.95161155663158579989199285155151
absolute error = 2.68e-30
relative error = 2.8162751716534226208948156171699e-28 %
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) = 0.9416258565724200908627825853809
y[1] (numeric) = 0.9416258565724200908627825853836
absolute error = 2.70e-30
relative error = 2.8673809041609978499804002052176e-28 %
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) = 0.93164599387895218245161163932314
y[1] (numeric) = 0.93164599387895218245161163932584
absolute error = 2.70e-30
relative error = 2.8980965063332932198882553354057e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=1060.1MB, alloc=44.3MB, time=12.72
x[1] = 3.22
y[1] (closed_form) = 0.92167296652913489692655585208396
y[1] (numeric) = 0.92167296652913489692655585208665
absolute error = 2.69e-30
relative error = 2.9186057285916573782119567223585e-28 %
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) = 0.91170777181739238759412427147028
y[1] (numeric) = 0.91170777181739238759412427147297
absolute error = 2.69e-30
relative error = 2.9505068215419194716144409245346e-28 %
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) = 0.90175140625489152745984504056236
y[1] (numeric) = 0.90175140625489152745984504056506
absolute error = 2.70e-30
relative error = 2.9941733179141952893360263381701e-28 %
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) = 0.89180486546989162296416915743917
y[1] (numeric) = 0.89180486546989162296416915744189
absolute error = 2.72e-30
relative error = 3.0499945731590431500801342370386e-28 %
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) = 0.88186914410818241773927688966392
y[1] (numeric) = 0.88186914410818241773927688966663
absolute error = 2.71e-30
relative error = 3.0730182795323582075156452733628e-28 %
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) = 0.87194523573362034250344310924638
y[1] (numeric) = 0.87194523573362034250344310924909
absolute error = 2.71e-30
relative error = 3.1079933566239545413825315129827e-28 %
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) = 0.86203413272877295738508592941475
y[1] (numeric) = 0.86203413272877295738508592941747
absolute error = 2.72e-30
relative error = 3.1553274942719816232066959147580e-28 %
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) = 0.85213682619568152214947021625736
y[1] (numeric) = 0.85213682619568152214947021626008
absolute error = 2.72e-30
relative error = 3.1919756503697791674498016108044e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (closed_form) = 0.84225430585675161798834572239752
y[1] (numeric) = 0.84225430585675161798834572240024
absolute error = 2.72e-30
relative error = 3.2294284292594764096271157671685e-28 %
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) = 0.83238755995578173172775000568302
y[1] (numeric) = 0.83238755995578173172775000568575
absolute error = 2.73e-30
relative error = 3.2797222487863990161689874726687e-28 %
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) = 0.82253757515913969951307944769159
y[1] (numeric) = 0.82253757515913969951307944769434
absolute error = 2.75e-30
relative error = 3.3433123094321208167281508071049e-28 %
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) = 0.81270533645709689224470717586405
y[1] (numeric) = 0.8127053364570968922447071758668
absolute error = 2.75e-30
relative error = 3.3837602346606146961921902980297e-28 %
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) = 0.80289182706533000926338308940728
y[1] (numeric) = 0.80289182706533000926338308941003
absolute error = 2.75e-30
relative error = 3.4251189354506120140376303659410e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1100.8MB, alloc=44.3MB, time=13.20
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (closed_form) = 0.79309802832660033002396588397449
y[1] (numeric) = 0.79309802832660033002396588397724
absolute error = 2.75e-30
relative error = 3.4674150001385971377357711239874e-28 %
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) = 0.78332491961262025575038601809447
y[1] (numeric) = 0.78332491961262025575038601809721
absolute error = 2.74e-30
relative error = 3.4979099111962625251439697999491e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (closed_form) = 0.77357347822611695433589651569143
y[1] (numeric) = 0.77357347822611695433589651569416
absolute error = 2.73e-30
relative error = 3.5290765219357946566538821039328e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (closed_form) = 0.76384467930310290204250822241037
y[1] (numeric) = 0.7638446793031029020425082224131
absolute error = 2.73e-30
relative error = 3.5740250262536719753335617402450e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (closed_form) = 0.75413949571536309486399862844206
y[1] (numeric) = 0.75413949571536309486399862844478
absolute error = 2.72e-30
relative error = 3.6067597778045786647452121280007e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (closed_form) = 0.74445889797316868075009757063626
y[1] (numeric) = 0.74445889797316868075009757063899
absolute error = 2.73e-30
relative error = 3.6670929818054145180139921139286e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (closed_form) = 0.73480385412822674124755569242589
y[1] (numeric) = 0.73480385412822674124755569242862
absolute error = 2.73e-30
relative error = 3.7152771922227861815350570604480e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (closed_form) = 0.7251753296768759274990566423338
y[1] (numeric) = 0.72517532967687592749905664233653
absolute error = 2.73e-30
relative error = 3.7646068313113121080638292733851e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (closed_form) = 0.71557428746353763095570308540863
y[1] (numeric) = 0.71557428746353763095570308541137
absolute error = 2.74e-30
relative error = 3.8290923080989236590513764343349e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (closed_form) = 0.70600168758443234360554818943968
y[1] (numeric) = 0.70600168758443234360554818944241
absolute error = 2.73e-30
relative error = 3.8668462809779234502674412198647e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (closed_form) = 0.69645848729157083600191363378011
y[1] (numeric) = 0.69645848729157083600191363378283
absolute error = 2.72e-30
relative error = 3.9054732616981920648251612366517e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (closed_form) = 0.68694564089702975389368422402507
y[1] (numeric) = 0.68694564089702975389368422402781
absolute error = 2.74e-30
relative error = 3.9886707722929046303680803210867e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1141.5MB, alloc=44.3MB, time=13.69
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (closed_form) = 0.67746409967752120581814601284274
y[1] (numeric) = 0.67746409967752120581814601284547
absolute error = 2.73e-30
relative error = 4.0297338284043445340611541387689e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (closed_form) = 0.66801481177926588461808356455725
y[1] (numeric) = 0.66801481177926588461808356455998
absolute error = 2.73e-30
relative error = 4.0867357307970620213390706563898e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (closed_form) = 0.6585987221231792354917125192625
y[1] (numeric) = 0.65859872212317923549171251926523
absolute error = 2.73e-30
relative error = 4.1451644351800029971620426198340e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (closed_form) = 0.64921677231038015187963119995636
y[1] (numeric) = 0.6492167723103801518796311999591
absolute error = 2.74e-30
relative error = 4.2204701370377563780234150692357e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (closed_form) = 0.63986990052803164824046007658263
y[1] (numeric) = 0.63986990052803164824046007658535
absolute error = 2.72e-30
relative error = 4.2508641174642051667208397419202e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (closed_form) = 0.63055904145552292556942567856704
y[1] (numeric) = 0.63055904145552292556942567856976
absolute error = 2.72e-30
relative error = 4.3136325406125474700293734242464e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (closed_form) = 0.62128512617100221137515574599336
y[1] (numeric) = 0.62128512617100221137515574599608
absolute error = 2.72e-30
relative error = 4.3780220794330565431365076096326e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (closed_form) = 0.61204908205826972075279889951549
y[1] (numeric) = 0.61204908205826972075279889951821
absolute error = 2.72e-30
relative error = 4.4440880310658553220882646952243e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (closed_form) = 0.60285183271404004917977257656305
y[1] (numeric) = 0.60285183271404004917977257656576
absolute error = 2.71e-30
relative error = 4.4953002594345198600566432661527e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (closed_form) = 0.59369429785558327071757857731409
y[1] (numeric) = 0.59369429785558327071757857731679
absolute error = 2.70e-30
relative error = 4.5477950685266269632310685738981e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (closed_form) = 0.58457739322875397743290054393371
y[1] (numeric) = 0.58457739322875397743290054393641
absolute error = 2.70e-30
relative error = 4.6187212014602301846323831711015e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (closed_form) = 0.57550203051641745705739905165624
y[1] (numeric) = 0.57550203051641745705739905165893
absolute error = 2.69e-30
relative error = 4.6741798592546614010289352979218e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1182.2MB, alloc=44.3MB, time=14.17
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (closed_form) = 0.56646911724728216619212706795597
y[1] (numeric) = 0.56646911724728216619212706795866
absolute error = 2.69e-30
relative error = 4.7487143042711146426227842604485e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (closed_form) = 0.55747955670514761573327265250731
y[1] (numeric) = 0.55747955670514761573327265250999
absolute error = 2.68e-30
relative error = 4.8073511714752599527464380555223e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (closed_form) = 0.54853424783857674365505981360747
y[1] (numeric) = 0.54853424783857674365505981361015
absolute error = 2.68e-30
relative error = 4.8857478098408056394405157509418e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (closed_form) = 0.53963408517100180783725645920515
y[1] (numeric) = 0.53963408517100180783725645920782
absolute error = 2.67e-30
relative error = 4.9477971710291757032766893602320e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (closed_form) = 0.53077995871127278827309518546809
y[1] (numeric) = 0.53077995871127278827309518547076
absolute error = 2.67e-30
relative error = 5.0303331091903453963567231259884e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (closed_form) = 0.52197275386465724374284336112709
y[1] (numeric) = 0.52197275386465724374284336112976
absolute error = 2.67e-30
relative error = 5.1152095204806543510405148311069e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (closed_form) = 0.51321335134430052289318861170468
y[1] (numeric) = 0.51321335134430052289318861170734
absolute error = 2.66e-30
relative error = 5.1830296172779811268010209084672e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (closed_form) = 0.50450262708315518362754885358965
y[1] (numeric) = 0.50450262708315518362754885359231
absolute error = 2.66e-30
relative error = 5.2725196207185709317610609769135e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (closed_form) = 0.49584145214638842779197594108609
y[1] (numeric) = 0.49584145214638842779197594108874
absolute error = 2.65e-30
relative error = 5.3444503046865761487092961520545e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (closed_form) = 0.48723069264427631034019077495596
y[1] (numeric) = 0.48723069264427631034019077495859
absolute error = 2.63e-30
relative error = 5.3978537060680297424661522619915e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (closed_form) = 0.47867120964559343348424545187534
y[1] (numeric) = 0.47867120964559343348424545187798
absolute error = 2.64e-30
relative error = 5.5152679893880544675608741434908e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (closed_form) = 0.47016385909150678678922237429879
y[1] (numeric) = 0.47016385909150678678922237430143
absolute error = 2.64e-30
relative error = 5.6150636612121723433990007518565e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (closed_form) = 0.46170949170998234375620595674963
y[1] (numeric) = 0.46170949170998234375620595675226
absolute error = 2.63e-30
relative error = 5.6962225105218436833537863651687e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1223.0MB, alloc=44.3MB, time=14.65
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (closed_form) = 0.45330895293071297416254103294378
y[1] (numeric) = 0.4533089529307129741625410329464
absolute error = 2.62e-30
relative error = 5.7797225999206324722954377177827e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (closed_form) = 0.44496308280057617929725076783427
y[1] (numeric) = 0.44496308280057617929725076783689
absolute error = 2.62e-30
relative error = 5.8881289286064955814167907253787e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (closed_form) = 0.43667271589963010424763888032052
y[1] (numeric) = 0.43667271589963010424763888032313
absolute error = 2.61e-30
relative error = 5.9770164358056950747799105292466e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (closed_form) = 0.42843868125765622756584442664971
y[1] (numeric) = 0.42843868125765622756584442665232
absolute error = 2.61e-30
relative error = 6.0918869237915224476619549856702e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (closed_form) = 0.42026180227125707397683496224605
y[1] (numeric) = 0.42026180227125707397683496224867
absolute error = 2.62e-30
relative error = 6.2342092139721198122557389928047e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (closed_form) = 0.41214289662151724028748227352559
y[1] (numeric) = 0.41214289662151724028748227352821
absolute error = 2.62e-30
relative error = 6.3570184551937622946954278572391e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (closed_form) = 0.40408277619223596832551418909979
y[1] (numeric) = 0.4040827761922359683255141891024
absolute error = 2.61e-30
relative error = 6.4590726301047137888079511063356e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (closed_form) = 0.39608224698873944158290927976732
y[1] (numeric) = 0.39608224698873944158290927976992
absolute error = 2.60e-30
relative error = 6.5642931986141696651955879132478e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (closed_form) = 0.38814210905728092426641391388112
y[1] (numeric) = 0.38814210905728092426641391388373
absolute error = 2.61e-30
relative error = 6.7243412634077884019257916107330e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (closed_form) = 0.38026315640503680267411028948219
y[1] (numeric) = 0.3802631564050368026741102894848
absolute error = 2.61e-30
relative error = 6.8636678469579680253088997225600e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (closed_form) = 0.37244617692070652922722804311009
y[1] (numeric) = 0.37244617692070652922722804311271
absolute error = 2.62e-30
relative error = 7.0345734829701198594147680734272e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (closed_form) = 0.36469195229572440909662976137772
y[1] (numeric) = 0.36469195229572440909662976138033
absolute error = 2.61e-30
relative error = 7.1567249662904042869492021149188e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1263.7MB, alloc=44.3MB, time=15.13
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (closed_form) = 0.35700125794609110817965112113726
y[1] (numeric) = 0.3570012579460911081796511211399
absolute error = 2.64e-30
relative error = 7.3949319259784025332941932805854e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (closed_form) = 0.349374862934832699211357781338
y[1] (numeric) = 0.34937486293483269921135778134063
absolute error = 2.63e-30
relative error = 7.5277310391118834238564047718095e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (closed_form) = 0.3418135298950950000409906547043
y[1] (numeric) = 0.34181352989509500004099065470692
absolute error = 2.62e-30
relative error = 7.6649979326567225346848037113522e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (closed_form) = 0.33431801495388089457568407689649
y[1] (numeric) = 0.33431801495388089457568407689911
absolute error = 2.62e-30
relative error = 7.8368495947232412607305911398533e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (closed_form) = 0.32688906765643826259581048063146
y[1] (numeric) = 0.32688906765643826259581048063408
absolute error = 2.62e-30
relative error = 8.0149514291913568618427289675181e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (closed_form) = 0.31952743089130607958596019184132
y[1] (numeric) = 0.31952743089130607958596019184393
absolute error = 2.61e-30
relative error = 8.1683127884186129238505231795041e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (closed_form) = 0.31223384081602618190911187462131
y[1] (numeric) = 0.31223384081602618190911187462392
absolute error = 2.61e-30
relative error = 8.3591195405941252145095057423464e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (closed_form) = 0.30500902678352812608556955192351
y[1] (numeric) = 0.30500902678352812608556955192612
absolute error = 2.61e-30
relative error = 8.5571237924455810374046821949053e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (closed_form) = 0.29785371126919450362939256217935
y[1] (numeric) = 0.29785371126919450362939256218197
absolute error = 2.62e-30
relative error = 8.7962644105921311425183482988041e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (closed_form) = 0.29076860979861400485005610714845
y[1] (numeric) = 0.29076860979861400485005610715107
absolute error = 2.62e-30
relative error = 9.0106012537412786764844372566734e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (closed_form) = 0.28375443087602945625275664545921
y[1] (numeric) = 0.28375443087602945625275664546184
absolute error = 2.63e-30
relative error = 9.2685777342064858239100796267124e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (closed_form) = 0.27681187591348798667399566455718
y[1] (numeric) = 0.2768118759134879866739956645598
absolute error = 2.62e-30
relative error = 9.4649118335473026405604807738653e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1304.3MB, alloc=44.3MB, time=15.62
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (closed_form) = 0.26994163916070040707678694126831
y[1] (numeric) = 0.26994163916070040707678694127093
absolute error = 2.62e-30
relative error = 9.7058016249218733085802846324645e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (closed_form) = 0.26314440763561681800905744824866
y[1] (numeric) = 0.26314440763561681800905744825128
absolute error = 2.62e-30
relative error = 9.9565102809556374752989187878956e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (closed_form) = 0.2564208610557253871066425986234
y[1] (numeric) = 0.25642086105572538710664259862603
absolute error = 2.63e-30
relative error = 1.0256575807334366382724481600781e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (closed_form) = 0.24977167177008116670587470137992
y[1] (numeric) = 0.24977167177008116670587470138254
absolute error = 2.62e-30
relative error = 1.0489580269181815210955387075268e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (closed_form) = 0.24319750469207174862736090548817
y[1] (numeric) = 0.24319750469207174862736090549078
absolute error = 2.61e-30
relative error = 1.0732018008592199739407147746046e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (closed_form) = 0.2366990172329264795094438207023
y[1] (numeric) = 0.23669901723292647950944382070491
absolute error = 2.61e-30
relative error = 1.1026661751753698653605199403863e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (closed_form) = 0.23027685923597588571440266645551
y[1] (numeric) = 0.23027685923597588571440266645812
absolute error = 2.61e-30
relative error = 1.1334182725348907909747497299026e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (closed_form) = 0.2239316729116678818101206987675
y[1] (numeric) = 0.22393167291166788181012069877012
absolute error = 2.62e-30
relative error = 1.1699997440886736717988493708551e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (closed_form) = 0.21766409277334726095221776933351
y[1] (numeric) = 0.21766409277334726095221776933613
absolute error = 2.62e-30
relative error = 1.2036895781097874505275095669637e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (closed_form) = 0.21147474557380488916409289058062
y[1] (numeric) = 0.21147474557380488916409289058323
absolute error = 2.61e-30
relative error = 1.2341899232072169558906079239000e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (closed_form) = 0.20536425024260294854257330725366
y[1] (numeric) = 0.20536425024260294854257330725626
absolute error = 2.60e-30
relative error = 1.2660431389243950761383590006544e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (closed_form) = 0.19933321782418249681262071972431
y[1] (numeric) = 0.19933321782418249681262071972691
absolute error = 2.60e-30
relative error = 1.3043485819274101668316822201673e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (closed_form) = 0.19338225141675953242356232661989
y[1] (numeric) = 0.19338225141675953242356232662248
absolute error = 2.59e-30
relative error = 1.3393162924855351289528082800265e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1345.1MB, alloc=44.3MB, time=16.09
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (closed_form) = 0.18751194611201567552941728764728
y[1] (numeric) = 0.18751194611201567552941728764989
absolute error = 2.61e-30
relative error = 1.3919113177145743742063269913778e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (closed_form) = 0.18172288893558949573496297564155
y[1] (numeric) = 0.18172288893558949573496297564414
absolute error = 2.59e-30
relative error = 1.4252469874161029718259435697823e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (closed_form) = 0.17601565878837443742517601630396
y[1] (numeric) = 0.17601565878837443742517601630654
absolute error = 2.58e-30
relative error = 1.4657786800104883723294329611267e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (closed_form) = 0.17039082638862921283659693902778
y[1] (numeric) = 0.17039082638862921283659693903039
absolute error = 2.61e-30
relative error = 1.5317726049682300283381055177771e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (closed_form) = 0.16484895421490645178307012404365
y[1] (numeric) = 0.16484895421490645178307012404625
absolute error = 2.60e-30
relative error = 1.5772013916512278577934701477519e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (closed_form) = 0.15939059644980531512332717185912
y[1] (numeric) = 0.15939059644980531512332717186173
absolute error = 2.61e-30
relative error = 1.6374868142374580713132352530833e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (closed_form) = 0.15401629892455369666219427078778
y[1] (numeric) = 0.15401629892455369666219427079039
absolute error = 2.61e-30
relative error = 1.6946258403979260350798709036095e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (closed_form) = 0.14872659906442555521905209735327
y[1] (numeric) = 0.14872659906442555521905209735587
absolute error = 2.60e-30
relative error = 1.7481741775549705671102669272563e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (closed_form) = 0.14352202583499883508485599858706
y[1] (numeric) = 0.14352202583499883508485599858967
absolute error = 2.61e-30
relative error = 1.8185362036351172470221251973134e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (closed_form) = 0.13840309968925934903088583719909
y[1] (numeric) = 0.13840309968925934903088583720171
absolute error = 2.62e-30
relative error = 1.8930211865791924878557141606473e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (closed_form) = 0.13337033251555591343684467407746
y[1] (numeric) = 0.13337033251555591343684467408006
absolute error = 2.60e-30
relative error = 1.9494590370738888573334254279208e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (closed_form) = 0.12842422758641193998142290209118
y[1] (numeric) = 0.12842422758641193998142290209379
absolute error = 2.61e-30
relative error = 2.0323268039465738518437389948758e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1385.8MB, alloc=44.3MB, time=16.57
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (closed_form) = 0.1235652795081986026935019100478
y[1] (numeric) = 0.12356527950819860269350191005041
absolute error = 2.61e-30
relative error = 2.1122438361229341288855313532237e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (closed_form) = 0.11879397417167461300535326877877
y[1] (numeric) = 0.11879397417167461300535326878138
absolute error = 2.61e-30
relative error = 2.1970811383312839238429366856512e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (closed_form) = 0.11411078870339754878911140270074
y[1] (numeric) = 0.11411078870339754878911140270335
absolute error = 2.61e-30
relative error = 2.2872508635305660068425915215456e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (closed_form) = 0.10951619141801159620312567541779
y[1] (numeric) = 0.1095161914180115962031256754204
absolute error = 2.61e-30
relative error = 2.3832092462363934744103470752928e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (closed_form) = 0.10501064177141647553424717156172
y[1] (numeric) = 0.10501064177141647553424717156433
absolute error = 2.61e-30
relative error = 2.4854623835947574872377276723476e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (closed_form) = 0.10059459031482223410444018114688
y[1] (numeric) = 0.10059459031482223410444018114949
absolute error = 2.61e-30
relative error = 2.5945729207025025556300356729809e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (closed_form) = 0.09626847864969450072414018033867
y[1] (numeric) = 0.096268478649694500724140180341284
absolute error = 2.614e-30
relative error = 2.7153228519502476750212611880281e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (closed_form) = 0.09203273938359470712936747670058
y[1] (numeric) = 0.092032739383594707129367476703186
absolute error = 2.606e-30
relative error = 2.8316010339952267492265646352344e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (closed_form) = 0.08788779608691969234365311475198
y[1] (numeric) = 0.087887796086919692343653114754586
absolute error = 2.606e-30
relative error = 2.9651443272314004474809947064101e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (closed_form) = 0.08383406325054501596829063971536
y[1] (numeric) = 0.083834063250545015968290639717975
absolute error = 2.615e-30
relative error = 3.1192571355927920510508884010277e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (closed_form) = 0.07987194624437621603428757300901
y[1] (numeric) = 0.079871946244376216034287573011617
absolute error = 2.607e-30
relative error = 3.2639745524963452077245750158418e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (closed_form) = 0.07600184127681215625569090101602
y[1] (numeric) = 0.076001841276812156255690901018628
absolute error = 2.608e-30
relative error = 3.4314958113990981516387742283759e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
memory used=1426.6MB, alloc=44.3MB, time=17.06
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (closed_form) = 0.07222413535512451631578081322702
y[1] (numeric) = 0.072224135355124516315780813229632
absolute error = 2.612e-30
relative error = 3.6165195847023329768648042930705e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (closed_form) = 0.06853920624675738720408708901116
y[1] (numeric) = 0.068539206246757387204087089013772
absolute error = 2.612e-30
relative error = 3.8109574695046524478140666137525e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (closed_form) = 0.06494742244155084161244420165858
y[1] (numeric) = 0.064947422441550841612444201661193
absolute error = 2.613e-30
relative error = 4.0232543521670291205664686669171e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (closed_form) = 0.06144914311489225700156528111504
y[1] (numeric) = 0.061449143114892257001565281117651
absolute error = 2.611e-30
relative error = 4.2490421634003578496142598212439e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (closed_form) = 0.05804471809179907617512114959174
y[1] (numeric) = 0.058044718091799076175121149594348
absolute error = 2.608e-30
relative error = 4.4930875465281563441271879942848e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (closed_form) = 0.05473448781193659705533608906184
y[1] (numeric) = 0.054734487811936597055336089064448
absolute error = 2.608e-30
relative error = 4.7648203249126642917163087856731e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (closed_form) = 0.05151878329557428985197103638587
y[1] (numeric) = 0.05151878329557428985197103638848
absolute error = 2.610e-30
relative error = 5.0661134309517194988265348890442e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (closed_form) = 0.04839792611048404596460766661961
y[1] (numeric) = 0.048397926110484045964607666622223
absolute error = 2.613e-30
relative error = 5.3989916717401806841252637646285e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (closed_form) = 0.04537222833978366876575843546385
y[1] (numeric) = 0.045372228339783668765758435466457
absolute error = 2.607e-30
relative error = 5.7458055189105794136893810498090e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (closed_form) = 0.04244199255072882188892726816111
y[1] (numeric) = 0.042441992550728821888927268163718
absolute error = 2.608e-30
relative error = 6.1448575885846691541605923820549e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (closed_form) = 0.03960751176445655580078546569952
y[1] (numeric) = 0.039607511764456555800785465702133
absolute error = 2.613e-30
relative error = 6.5972334125388911117554664467279e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (closed_form) = 0.03686906942668343827959196692216
y[1] (numeric) = 0.036869069426683438279591966924767
absolute error = 2.607e-30
relative error = 7.0709677258987792382140558013183e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (closed_form) = 0.03422693937936121896239198130831
y[1] (numeric) = 0.034226939379361218962391981310916
absolute error = 2.606e-30
relative error = 7.6138855745057157292195924823479e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
memory used=1467.4MB, alloc=44.3MB, time=17.54
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (closed_form) = 0.03168138583329286237091907175356
y[1] (numeric) = 0.03168138583329286237091907175617
absolute error = 2.610e-30
relative error = 8.2382759824137557626614528410386e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (closed_form) = 0.02923266334171168779007820072841
y[1] (numeric) = 0.029232663341711687790078200731023
absolute error = 2.613e-30
relative error = 8.9386313161262525563699135708274e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (closed_form) = 0.02688101677482625806300458146732
y[1] (numeric) = 0.026881016774826258063004581469926
absolute error = 2.606e-30
relative error = 9.6945737649346916872442121616642e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (closed_form) = 0.02462668129533356279260630634082
y[1] (numeric) = 0.024626681295333562792606306343427
absolute error = 2.607e-30
relative error = 1.0586079255811024529713433539453e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (closed_form) = 0.02246988233490294461086498550137
y[1] (numeric) = 0.022469882334902944610864985503978
absolute error = 2.608e-30
relative error = 1.1606647338552985247485771507112e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (closed_form) = 0.02041083557163312010367080295234
y[1] (numeric) = 0.020410835571633120103670802954945
absolute error = 2.605e-30
relative error = 1.2762828796780942746689737674272e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (closed_form) = 0.01844974690848454967031375325789
y[1] (numeric) = 0.0184497469084845496703137532605
absolute error = 2.610e-30
relative error = 1.4146535521306962574462916405237e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (closed_form) = 0.01658681245268931306267214456304
y[1] (numeric) = 0.016586812452689313062672144565648
absolute error = 2.608e-30
relative error = 1.5723334470916684852164018200848e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (closed_form) = 0.01482221849614054959938606921746
y[1] (numeric) = 0.014822218496140549599386069220066
absolute error = 2.606e-30
relative error = 1.7581713565203194883593360315275e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (closed_form) = 0.01315614149676342409465234597491
y[1] (numeric) = 0.013156141496763424094652345977514
absolute error = 2.604e-30
relative error = 1.9793037347923148118613218936206e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (closed_form) = 0.01158874806086948138952391096191
y[1] (numeric) = 0.011588748060869481389523910964519
absolute error = 2.609e-30
relative error = 2.2513217012711999262251095917230e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (closed_form) = 0.01012019492649615403555587193493
y[1] (numeric) = 0.010120194926496154035555871937534
absolute error = 2.604e-30
relative error = 2.5730729683697556343850623693404e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
memory used=1508.1MB, alloc=44.3MB, time=18.02
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (closed_form) = 0.00875062894773308916614616390269
y[1] (numeric) = 0.0087506289477330891661461639052973
absolute error = 2.6073e-30
relative error = 2.9795572587675987141459251675883e-26 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (closed_form) = 0.00748018708003686190982232131219
y[1] (numeric) = 0.007480187080036861909822321314794
absolute error = 2.6040e-30
relative error = 3.4811963553018083678566326869897e-26 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (closed_form) = 0.00630899636653554386189534009117
y[1] (numeric) = 0.0063089963665355438618953400937788
absolute error = 2.6088e-30
relative error = 4.1350475550084507154826106554313e-26 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (closed_form) = 0.00523717392532449614622064259686
y[1] (numeric) = 0.0052371739253244961462206425994721
absolute error = 2.6121e-30
relative error = 4.9876136199508666501825896571528e-26 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (closed_form) = 0.00426482693775465747717316554853
y[1] (numeric) = 0.0042648269377546574771731655511425
absolute error = 2.6125e-30
relative error = 6.1256881888281891625722164736816e-26 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (closed_form) = 0.0033920526377144983832706460193
y[1] (numeric) = 0.003392052637714498383270646021904
absolute error = 2.6040e-30
relative error = 7.6767676628819253538389264699684e-26 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (closed_form) = 0.00261893830190671338809106811717
y[1] (numeric) = 0.002618938301906713388091068119777
absolute error = 2.6070e-30
relative error = 9.9544154900555628647264991106293e-26 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (closed_form) = 0.00194556124112062347116344910397
y[1] (numeric) = 0.0019455612411206234711634491065827
absolute error = 2.6127e-30
relative error = 1.3429029859245712535255104732244e-25 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (closed_form) = 0.00137198879250116156131290216748
y[1] (numeric) = 0.001371988792501161561312902170085
absolute error = 2.6050e-30
relative error = 1.8987035566457038237095734886219e-25 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (closed_form) = 0.00089827831281521415746815072662
y[1] (numeric) = 0.0008982783128152141574681507292259
absolute error = 2.60590e-30
relative error = 2.9009940046677522552326987818450e-25 %
Desired digits = 8
Estimated correct digits = 8
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (closed_form) = 0.00052447717271599243715805024033
y[1] (numeric) = 0.00052447717271599243715805024293554
absolute error = 2.60554e-30
relative error = 4.9678806543805781174394381780072e-25 %
Desired digits = 8
Estimated correct digits = 8
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (closed_form) = 0.00025062275200600641080659305708
y[1] (numeric) = 0.00025062275200600641080659305969169
absolute error = 2.61169e-30
relative error = 1.0420801699350138745821688340699e-24 %
Desired digits = 8
Estimated correct digits = 8
Correct digits = 32
h = 0.001
memory used=1549.0MB, alloc=44.3MB, time=18.50
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (closed_form) = 7.674243589911582046345842503e-05
y[1] (numeric) = 7.6742435899115820463458427636769e-05
absolute error = 2.606769e-30
relative error = 3.3967764633205154781785349024346e-24 %
Desired digits = 8
Estimated correct digits = 7
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (closed_form) = 2.85361228203157476528740643e-06
y[1] (numeric) = 2.8536122820315747652874090344934e-06
absolute error = 2.6044934e-30
relative error = 9.1270051520306068526192600500184e-23 %
Desired digits = 8
Estimated correct digits = 6
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (closed_form) = 2.896366997554156770211203836e-05
y[1] (numeric) = 2.8963669975541567702112040968693e-05
absolute error = 2.608693e-30
relative error = 9.0067764278591639624055424741931e-24 %
Desired digits = 8
Estimated correct digits = 7
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (closed_form) = 0.00015506999799563475715808844232
y[1] (numeric) = 0.00015506999799563475715808844492693
absolute error = 2.60693e-30
relative error = 1.6811311238124769022344164047191e-24 %
Desired digits = 8
Estimated correct digits = 8
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (closed_form) = 0.00038115998581459739020295192723
y[1] (numeric) = 0.00038115998581459739020295192983786
absolute error = 2.60786e-30
relative error = 6.8419039171349608618609506406369e-25 %
Desired digits = 8
Estimated correct digits = 8
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (closed_form) = 0.00070721102462205526572924440292
y[1] (numeric) = 0.00070721102462205526572924440552893
absolute error = 2.60893e-30
relative error = 3.6890403418049844057473258869260e-25 %
Desired digits = 8
Estimated correct digits = 8
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (closed_form) = 0.00113319050958583593125991543056
y[1] (numeric) = 0.0011331905095858359312599154331719
absolute error = 2.6119e-30
relative error = 2.3049081137774531155172696936772e-25 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (closed_form) = 0.00165905584311242472959066170051
y[1] (numeric) = 0.0016590558431124247295906617031226
absolute error = 2.6126e-30
relative error = 1.5747510916201022863050250393853e-25 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (closed_form) = 0.00228475443910668865237937835233
y[1] (numeric) = 0.0022847544391066886523793783549358
absolute error = 2.6058e-30
relative error = 1.1405164403658347976891023125959e-25 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (closed_form) = 0.00301022372823044203184712123726
y[1] (numeric) = 0.0030102237282304420318471212398702
absolute error = 2.6102e-30
relative error = 8.6711162878727432395815390437057e-26 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (closed_form) = 0.00383539116415932821840353349637
y[1] (numeric) = 0.0038353911641593282184035334989736
absolute error = 2.6036e-30
relative error = 6.7883558379388349027473484777684e-26 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (closed_form) = 0.00476017423083739156124302459597
y[1] (numeric) = 0.004760174230837391561243024598581
absolute error = 2.6110e-30
relative error = 5.4850933461330110010107659462565e-26 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (closed_form) = 0.00578448045072861424075909870166
y[1] (numeric) = 0.0057844804507286142407590987042682
absolute error = 2.6082e-30
relative error = 4.5089615605347419569823281413252e-26 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
memory used=1589.8MB, alloc=44.3MB, time=18.98
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (closed_form) = 0.0069082073940645928059698487306
y[1] (numeric) = 0.0069082073940645928059698487332071
absolute error = 2.6071e-30
relative error = 3.7739168083459296508567097265630e-26 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (closed_form) = 0.00813124268908742965700724495948
y[1] (numeric) = 0.008131242689087429657007244962092
absolute error = 2.6120e-30
relative error = 3.2123011203508243504652501112819e-26 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (closed_form) = 0.00945346403328681519205768370882
y[1] (numeric) = 0.0094534640332868151920576837114278
absolute error = 2.6078e-30
relative error = 2.7585655277447652080527230741508e-26 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (closed_form) = 0.01087473920563017691990330595709
y[1] (numeric) = 0.010874739205630176919903305959699
absolute error = 2.609e-30
relative error = 2.3991379937178105972515515714192e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (closed_form) = 0.01239492607978467253334458870749
y[1] (numeric) = 0.0123949260797846725333445887101
absolute error = 2.610e-30
relative error = 2.1057003351207896125425711461337e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (closed_form) = 0.01401387263832970475521515768158
y[1] (numeric) = 0.014013872638329704755215157684187
absolute error = 2.607e-30
relative error = 1.8602994812936482757617304448592e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (closed_form) = 0.0157314169879585367173479427511
y[1] (numeric) = 0.015731416987958536717347942753713
absolute error = 2.613e-30
relative error = 1.6610073981257352466560684588227e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (closed_form) = 0.01754738737566748772362275008167
y[1] (numeric) = 0.017547387375667487723622750084284
absolute error = 2.614e-30
relative error = 1.4896804544389136781418587473179e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (closed_form) = 0.01946160220593109049100989773031
y[1] (numeric) = 0.019461602205931090491009897732923
absolute error = 2.613e-30
relative error = 1.3426438236434951889405537014009e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (closed_form) = 0.02147387005886149236719839365887
y[1] (numeric) = 0.021473870058861492367198393661486
absolute error = 2.616e-30
relative error = 1.2182247507456025920085921823148e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (closed_form) = 0.02358398970935028459981967725086
y[1] (numeric) = 0.023583989709350284599819677253476
absolute error = 2.616e-30
relative error = 1.1092270783017010532383598083187e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (closed_form) = 0.02579175014719084549029147317684
y[1] (numeric) = 0.025791750147190845490291473179457
absolute error = 2.617e-30
relative error = 1.0146655364855243166840359763867e-26 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
memory used=1630.5MB, alloc=44.3MB, time=19.46
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (closed_form) = 0.02809693059817918521473493662265
y[1] (numeric) = 0.028096930598179185214734936625259
absolute error = 2.609e-30
relative error = 9.2857118000251444311570477553454e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (closed_form) = 0.03049930054619118224506697690327
y[1] (numeric) = 0.030499300546191182245066976905878
absolute error = 2.608e-30
relative error = 8.5510157718213397091962302989950e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (closed_form) = 0.03299861975623400366502328592209
y[1] (numeric) = 0.032998619756234003665023285924706
absolute error = 2.616e-30
relative error = 7.9276043038308984337159678943175e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (closed_form) = 0.03559463829846940425828992207108
y[1] (numeric) = 0.03559463829846940425828992207369
absolute error = 2.610e-30
relative error = 7.3325650287960137189787770239925e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (closed_form) = 0.03828709657320650205885398558889
y[1] (numeric) = 0.038287096573206502058853985591506
absolute error = 2.616e-30
relative error = 6.8325891335168246443001288239391e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
Finished!
diff ( y , x , 1 ) = cos ( x ) ;
Iterations = 5000
Total Elapsed Time = 19 Seconds
Elapsed Time(since restart) = 19 Seconds
Time to Timeout = 2 Minutes 40 Seconds
Percent Done = 100 %
> quit
memory used=1648.8MB, alloc=44.3MB, time=19.67