|\^/| 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) / (c(x) * c(x) + c(1.0)));
> end;
exact_soln_y := proc(x) return c(1.0)/(c(x)*c(x) + c(1.0)) end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]);
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if (rad_given < glob_least_given_sing) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])*
(array_x[1] - array_given_rad_poles[1, 1])
+ array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if rad_given < glob_least_given_sing then
glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if array_rad_test_poles[1, 1] < glob_least_ratio_sing then
glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_float(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if array_rad_test_poles[1, 2] < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if array_rad_test_poles[1, 3] < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_1D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y[1]) < min_size) then # if number 3
> min_size := float_abs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < glob__1) then # if number 3
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_1D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y[1]) < min_size then
min_size := float_abs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_1D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_1D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := float_abs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_1D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
> est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
> fi;# end if 3;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 3
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_1D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y[no_terms - 3]))
+ c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_1D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_1D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_1D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> 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)*35*ATS_MAX_TERMS/float_abs(numeric_val));
> if (evalf(est_rel_err) > glob_prec) then # if number 6
> glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
> else
> glob_est_digits := Digits;
> fi;# end if 6;
> else
> relerr := glob__m1 ;
> glob_est_digits := -16;
> fi;# end if 5;
> array_est_digits[1] := glob_est_digits;
> if (glob_iter = 1) then # if number 5
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 5;
> array_est_rel_error[1] := est_rel_err;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," ");
> omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," ");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 4;
> #BOTTOM DISPLAY ALOT
> fi;# end if 3;
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_1D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, 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)*35*ATS_MAX_TERMS/float_abs(numeric_val))
;
if glob_prec < evalf(est_rel_err) then
glob_est_digits := -int_trunc(log10(est_rel_err)) + 3
else glob_est_digits := Digits
end if
else relerr := glob__m1; glob_est_digits := -16
end if;
array_est_digits[1] := glob_est_digits;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
array_est_rel_error[1] := est_rel_err;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Desired digits ", 32,
glob_desired_digits_correct, 4, " ");
omniout_int(INFO, "Estimated correct digits ", 32,
glob_est_digits, 4, " ");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_1D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr((glob_clock_sec));
> if (c(percent_done) < glob__100) then # if number 3
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 3;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr((left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_1D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(glob_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(left_sec);
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_1D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 3;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 4
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_rad_test_poles[1,1]) then # if number 6
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,2]) then # if number 8
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 9
> glob_min_pole_est := rad_c;
> fi;# end if 9;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[1,3]) then # if number 10
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 11
> glob_min_pole_est := rad_c;
> fi;# end if 11;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test1
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 10;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 9;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 9
> display_poles();
> fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_1D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4],
array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
if
float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_poles() end if
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_1D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> 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 neg ID_CONST $eq_no = 1
> array_tmp1[1] := neg(array_const_2D0[1]);
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] * array_x[1];
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_x[1] * array_x[1];
> #emit pre add FULL - CONST $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp3[1] + array_const_1D0[1];
> #emit pre div LINEAR - FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_tmp2[1] / array_tmp4[1];
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 1
> array_tmp6[1] := array_x[1] * array_x[1];
> #emit pre add FULL - CONST $eq_no = 1 i = 1
> array_tmp7[1] := array_tmp6[1] + array_const_1D0[1];
> #emit pre div FULL - FULL $eq_no = 1 i = 1
> array_tmp8[1] := (array_tmp5[1] / (array_tmp7[1]));
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp9[1] := array_const_0D0[1] + array_tmp8[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_tmp9[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[1] * array_x[2];
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := array_x[1] * array_x[2] + array_x[2] * array_x[1];
> #emit pre add FULL CONST $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[2];
> #emit pre div LINEAR - FULL $eq_no = 1 i = 2
> array_tmp5[2] := (array_tmp2[2] - array_tmp5[1] * array_tmp4[2]) / array_tmp4[1];
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 2
> array_tmp6[2] := array_x[1] * array_x[2] + array_x[2] * array_x[1];
> #emit pre add FULL CONST $eq_no = 1 i = 2
> array_tmp7[2] := array_tmp6[2];
> #emit pre div FULL - FULL $eq_no = 1 i = 2
> array_tmp8[2] := ((array_tmp5[2] - ats(2,array_tmp7,array_tmp8,2))/array_tmp7[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp9[2] := array_tmp8[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_tmp9[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 mult LINEAR - LINEAR $eq_no = 1 i = 3
> array_tmp3[3] := array_x[2] * array_x[2];
> #emit pre add FULL CONST $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp3[3];
> #emit pre div LINEAR FULL $eq_no = 1 i = 3
> array_tmp5[3] := neg( ats(3,array_tmp4,array_tmp5,2)) / array_tmp4[1];
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 3
> array_tmp6[3] := array_x[2] * array_x[2];
> #emit pre add FULL CONST $eq_no = 1 i = 3
> array_tmp7[3] := array_tmp6[3];
> #emit pre div FULL - FULL $eq_no = 1 i = 3
> array_tmp8[3] := ((array_tmp5[3] - ats(3,array_tmp7,array_tmp8,2))/array_tmp7[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp9[3] := array_tmp8[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_tmp9[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 add FULL CONST $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp3[4];
> #emit pre div LINEAR FULL $eq_no = 1 i = 4
> array_tmp5[4] := neg( ats(4,array_tmp4,array_tmp5,2)) / array_tmp4[1];
> #emit pre add FULL CONST $eq_no = 1 i = 4
> array_tmp7[4] := array_tmp6[4];
> #emit pre div FULL - FULL $eq_no = 1 i = 4
> array_tmp8[4] := ((array_tmp5[4] - ats(4,array_tmp7,array_tmp8,2))/array_tmp7[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp9[4] := array_tmp8[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_tmp9[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 add FULL CONST $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp3[5];
> #emit pre div LINEAR FULL $eq_no = 1 i = 5
> array_tmp5[5] := neg( ats(5,array_tmp4,array_tmp5,2)) / array_tmp4[1];
> #emit pre add FULL CONST $eq_no = 1 i = 5
> array_tmp7[5] := array_tmp6[5];
> #emit pre div FULL - FULL $eq_no = 1 i = 5
> array_tmp8[5] := ((array_tmp5[5] - ats(5,array_tmp7,array_tmp8,2))/array_tmp7[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp9[5] := array_tmp8[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_tmp9[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 mult LINEAR - LINEAR $eq_no = 1 i = 1
> #emit FULL - NOT FULL add $eq_no = 1
> array_tmp4[kkk] := array_tmp3[kkk];
> #emit div LINEAR FULL $eq_no = 1 i = 1
> array_tmp5[kkk] := neg(ats(kkk,array_tmp4,array_tmp5,2)) / array_tmp4[1];
> #emit mult LINEAR - LINEAR $eq_no = 1 i = 1
> #emit FULL - NOT FULL add $eq_no = 1
> array_tmp7[kkk] := array_tmp6[kkk];
> #emit div FULL FULL $eq_no = 1
> array_tmp8[kkk] := ((array_tmp5[kkk] - ats(kkk,array_tmp7,array_tmp8,2)) /array_tmp7[1]);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp9[kkk] := array_tmp8[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_tmp9[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_1D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, 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] := neg(array_const_2D0[1]);
array_tmp2[1] := array_tmp1[1]*array_x[1];
array_tmp3[1] := array_x[1]*array_x[1];
array_tmp4[1] := array_tmp3[1] + array_const_1D0[1];
array_tmp5[1] := array_tmp2[1]/array_tmp4[1];
array_tmp6[1] := array_x[1]*array_x[1];
array_tmp7[1] := array_tmp6[1] + array_const_1D0[1];
array_tmp8[1] := array_tmp5[1]/array_tmp7[1];
array_tmp9[1] := array_const_0D0[1] + array_tmp8[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp9[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_tmp2[2] := array_tmp1[1]*array_x[2];
array_tmp3[2] := array_x[1]*array_x[2] + array_x[1]*array_x[2];
array_tmp4[2] := array_tmp3[2];
array_tmp5[2] :=
(-array_tmp4[2]*array_tmp5[1] + array_tmp2[2])/array_tmp4[1];
array_tmp6[2] := array_x[1]*array_x[2] + array_x[1]*array_x[2];
array_tmp7[2] := array_tmp6[2];
array_tmp8[2] :=
(array_tmp5[2] - ats(2, array_tmp7, array_tmp8, 2))/array_tmp7[1];
array_tmp9[2] := array_tmp8[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp9[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp3[3] := array_x[2]*array_x[2];
array_tmp4[3] := array_tmp3[3];
array_tmp5[3] := neg(ats(3, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp6[3] := array_x[2]*array_x[2];
array_tmp7[3] := array_tmp6[3];
array_tmp8[3] :=
(array_tmp5[3] - ats(3, array_tmp7, array_tmp8, 2))/array_tmp7[1];
array_tmp9[3] := array_tmp8[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp9[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_tmp4[4] := array_tmp3[4];
array_tmp5[4] := neg(ats(4, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp7[4] := array_tmp6[4];
array_tmp8[4] :=
(array_tmp5[4] - ats(4, array_tmp7, array_tmp8, 2))/array_tmp7[1];
array_tmp9[4] := array_tmp8[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp9[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_tmp4[5] := array_tmp3[5];
array_tmp5[5] := neg(ats(5, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp7[5] := array_tmp6[5];
array_tmp8[5] :=
(array_tmp5[5] - ats(5, array_tmp7, array_tmp8, 2))/array_tmp7[1];
array_tmp9[5] := array_tmp8[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp9[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_tmp4[kkk] := array_tmp3[kkk];
array_tmp5[kkk] :=
neg(ats(kkk, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp7[kkk] := array_tmp6[kkk];
array_tmp8[kkk] := (
array_tmp5[kkk] - ats(kkk, array_tmp7, array_tmp8, 2))/
array_tmp7[1];
array_tmp9[kkk] := array_tmp8[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_tmp9[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_1D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> 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:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_tmp3:= Array(0..(40),[]);
> array_tmp4:= Array(0..(40),[]);
> array_tmp5:= Array(0..(40),[]);
> array_tmp6:= Array(0..(40),[]);
> array_tmp7:= Array(0..(40),[]);
> array_tmp8:= Array(0..(40),[]);
> array_tmp9:= 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[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp6[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp7[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp8[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp9[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);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> zero_ats_ar(array_tmp6);
> zero_ats_ar(array_tmp7);
> zero_ats_ar(array_tmp8);
> zero_ats_ar(array_tmp9);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_2D0);
> array_const_2D0[1] := c(2.0);
> zero_ats_ar(array_const_1D0);
> array_const_1D0[1] := c(1.0);
> 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/sing4_backpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; ");
> 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(-1.0);");
> omniout_str(ALWAYS,"x_end := c(-2.0);");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_h := c(0.1);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 2;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(1.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(1.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=100000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=false;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"return(c(1.0) / (c(x) * c(x) + c(1.0)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := c(-1.0);
> x_end := c(-2.0);
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_h := c(0.1);
> glob_type_given_pole := 2;
> array_given_rad_poles[1,1] := c(0.0);
> array_given_rad_poles[1,2] := c(1.0);
> array_given_ord_poles[1,1] := c(1.0);
> array_given_ord_poles[1,2] := c(0.0);
> #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 ) = neg ( 2.0 ) * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2016-08-26T17:08:47-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sing4_back")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; ")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 308.maple.seems.ok | ")
> ;
> logitem_str(html_log_file,"sing4_back diffeq.mxt")
> ;
> logitem_str(html_log_file,"sing4_back maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> fi;# end if 14
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_1D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, 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 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_tmp3 := Array(0 .. 40, []);
array_tmp4 := Array(0 .. 40, []);
array_tmp5 := Array(0 .. 40, []);
array_tmp6 := Array(0 .. 40, []);
array_tmp7 := Array(0 .. 40, []);
array_tmp8 := Array(0 .. 40, []);
array_tmp9 := 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[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp6[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp7[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp8[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp9[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);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
zero_ats_ar(array_tmp6);
zero_ats_ar(array_tmp7);
zero_ats_ar(array_tmp8);
zero_ats_ar(array_tmp9);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_2D0);
array_const_2D0[1] := c(2.0);
zero_ats_ar(array_const_1D0);
array_const_1D0[1] := c(1.0);
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/sing4_backpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = neg ( 2.0 ) * \
x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; ");
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(-1.0);");
omniout_str(ALWAYS, "x_end := c(-2.0);");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_h := c(0.1);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 2;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(1.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(1.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=100000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=false;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "return(c(1.0) / (c(x) * c(x) + c(1.0)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := c(-1.0);
x_end := c(-2.0);
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := c(0.1);
glob_type_given_pole := 2;
array_given_rad_poles[1, 1] := c(0.);
array_given_rad_poles[1, 2] := c(1.0);
array_given_ord_poles[1, 1] := c(1.0);
array_given_ord_poles[1, 2] := c(0.);
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 ) = neg ( 2.0 ) *\
x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2016-08-26T17:08:47-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sing4_back");
logitem_str(html_log_file, "diff ( y , x , 1 ) = ne\
g ( 2.0 ) * x / ( x * x + 1.0 ) / ( x * \
x + 1.0 ) ; ");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 308.maple.seems.ok | ");
logitem_str(html_log_file, "sing4_back diffeq.mxt");
logitem_str(html_log_file, "sing4_back 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/sing4_backpostode.ode#################
diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(-1.0);
x_end := c(-2.0);
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := c(0.1);
glob_type_given_pole := 2;
array_given_rad_poles[1,1] := c(0.0);
array_given_rad_poles[1,2] := c(1.0);
array_given_ord_poles[1,1] := c(1.0);
array_given_ord_poles[1,2] := c(0.0);
#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) / (c(x) * c(x) + c(1.0)));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
memory used=4.1MB, alloc=40.3MB, time=0.09
x[1] = -1.001
y[1] (closed_form) = 0.49950024999987512493750003121877
y[1] (numeric) = 0.49950024999987512493750003121877
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] = -1.002
y[1] (closed_form) = 0.499000999998003996000007984016
y[1] (numeric) = 0.499000999998003996000007984016
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] = -1.003
y[1] (closed_form) = 0.49850224998990532943770441707889
y[1] (numeric) = 0.49850224998990532943770441707889
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] = -1.004
y[1] (closed_form) = 0.49800399996812774400203982438387
y[1] (numeric) = 0.49800399996812774400203982438387
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] = -1.005
y[1] (closed_form) = 0.49750624992226464844964614867974
y[1] (numeric) = 0.49750624992226464844964614867974
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] = -1.006
y[1] (closed_form) = 0.4970089998389690840521740167671
y[1] (numeric) = 0.49700899983896908405217401676709
absolute error = 1e-32
relative error = 2.0120360000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.007
y[1] (closed_form) = 0.49651224970196852211639339459963
y[1] (numeric) = 0.49651224970196852211639339459963
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] = -1.008
y[1] (closed_form) = 0.49601599949207961652011047268341
y[1] (numeric) = 0.4960159994920796165201104726834
absolute error = 1e-32
relative error = 2.0160640000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.009
y[1] (closed_form) = 0.4955202491872229112706576197883
y[1] (numeric) = 0.4955202491872229112706576197883
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] = -1.01
y[1] (closed_form) = 0.49502499876243750309390624226523
y[1] (numeric) = 0.49502499876243750309390624226523
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] = -1.011
y[1] (closed_form) = 0.49453024818989565906293441391489
y[1] (numeric) = 0.49453024818989565906293441391489
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] = -1.012
y[1] (closed_form) = 0.49403599743891738927665225398983
y[1] (numeric) = 0.49403599743891738927665225398983
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] = -1.013
y[1] (closed_form) = 0.49354224647598497459984828511343
y[1] (numeric) = 0.49354224647598497459984828511343
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] = -1.014
y[1] (closed_form) = 0.4930489952647574494772694552203
y[1] (numeric) = 0.4930489952647574494772694552203
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] = -1.015
y[1] (closed_form) = 0.49255624376608503983548621458213
y[1] (numeric) = 0.49255624376608503983548621458212
absolute error = 1e-32
relative error = 2.0302250000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.016
y[1] (closed_form) = 0.49206399193802355608742205706368
y[1] (numeric) = 0.49206399193802355608742205706367
absolute error = 1e-32
relative error = 2.0322560000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.017
y[1] (closed_form) = 0.49157223973584874125554432039892
y[1] (numeric) = 0.49157223973584874125554432039891
absolute error = 1e-32
relative error = 2.0342890000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.018
y[1] (closed_form) = 0.49108098711207057423081984988636
y[1] (numeric) = 0.49108098711207057423081984988635
absolute error = 1e-32
relative error = 2.0363240000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.019
y[1] (closed_form) = 0.49059023401644752818563541982995
y[1] (numeric) = 0.49059023401644752818563541982994
absolute error = 1e-32
relative error = 2.0383610000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.02
y[1] (closed_form) = 0.49009998039600078415996863360125
y[1] (numeric) = 0.49009998039600078415996863360124
absolute error = 1e-32
relative error = 2.0404000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.021
y[1] (closed_form) = 0.48961022619502839984117044262233
y[1] (numeric) = 0.48961022619502839984117044262232
absolute error = 1e-32
relative error = 2.0424410000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.022
y[1] (closed_form) = 0.48912097135511943355878549306329
y[1] (numeric) = 0.48912097135511943355878549306327
absolute error = 2e-32
relative error = 4.0889680000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.023
y[1] (closed_form) = 0.48863221581516802351689128275241
y[1] (numeric) = 0.48863221581516802351689128275239
absolute error = 2e-32
relative error = 4.0930580000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.024
y[1] (closed_form) = 0.48814395951138742228748164578712
y[1] (numeric) = 0.48814395951138742228748164578711
absolute error = 1e-32
relative error = 2.0485760000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.025
y[1] (closed_form) = 0.48765620237732398658945443462359
y[1] (numeric) = 0.48765620237732398658945443462358
absolute error = 1e-32
relative error = 2.0506250000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.026
y[1] (closed_form) = 0.4871689443438711223787874949578
y[1] (numeric) = 0.48716894434387112237878749495779
absolute error = 1e-32
relative error = 2.0526760000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.027
y[1] (closed_form) = 0.48668218533928318527650118336773
y[1] (numeric) = 0.48668218533928318527650118336772
absolute error = 1e-32
relative error = 2.0547290000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.028
y[1] (closed_form) = 0.48619592528918933636200981726812
y[1] (numeric) = 0.48619592528918933636200981726811
absolute error = 1e-32
relative error = 2.0567840000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.029
y[1] (closed_form) = 0.48571016411660735336045862696537
y[1] (numeric) = 0.48571016411660735336045862696535
absolute error = 2e-32
relative error = 4.1176820000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.03
y[1] (closed_form) = 0.48522490174195739725362705614052
y[1] (numeric) = 0.48522490174195739725362705614051
absolute error = 1e-32
relative error = 2.0609000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.031
y[1] (closed_form) = 0.48474013808307573434495368550351
y[1] (numeric) = 0.4847401380830757343449536855035
absolute error = 1e-32
relative error = 2.0629610000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.032
y[1] (closed_form) = 0.48425587305522841381020269013823
y[1] (numeric) = 0.48425587305522841381020269013822
absolute error = 1e-32
relative error = 2.0650240000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.033
y[1] (closed_form) = 0.483772106571124900766246639598
y[1] (numeric) = 0.483772106571124900766246639598
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] = -1.034
y[1] (closed_form) = 0.48328883854093166489138566642631
y[1] (numeric) = 0.48328883854093166489138566642631
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] = -1.035
y[1] (closed_form) = 0.48280606887228572463155861869184
y[1] (numeric) = 0.48280606887228572463155861869184
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] = -1.036
y[1] (closed_form) = 0.48232379747030814702772783046897
y[1] (numeric) = 0.48232379747030814702772783046898
absolute error = 1e-32
relative error = 2.0732960000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.037
y[1] (closed_form) = 0.48184202423761750320063564599837
y[1] (numeric) = 0.48184202423761750320063564599838
absolute error = 1e-32
relative error = 2.0753690000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.038
y[1] (closed_form) = 0.48136074907434327953003787346374
y[1] (numeric) = 0.48136074907434327953003787346374
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] = -1.039
y[1] (closed_form) = 0.48087997187813924456641697775594
y[1] (numeric) = 0.48087997187813924456641697775594
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] = -1.04
y[1] (closed_form) = 0.48039969254419677171406610299769
y[1] (numeric) = 0.4803996925441967717140661029977
absolute error = 1e-32
relative error = 2.0816000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.041
y[1] (closed_form) = 0.47991991096525811772531399959975
y[1] (numeric) = 0.47991991096525811772531399959975
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] = -1.042
y[1] (closed_form) = 0.47944062703162965704653067173467
y[1] (numeric) = 0.47944062703162965704653067173468
absolute error = 1e-32
relative error = 2.0857640000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.043
y[1] (closed_form) = 0.47896184063119507205741411376014
y[1] (numeric) = 0.47896184063119507205741411376015
absolute error = 1e-32
relative error = 2.0878490000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.044
y[1] (closed_form) = 0.4784835516494284992459099226005
y[1] (numeric) = 0.47848355164942849924590992260051
absolute error = 1e-32
relative error = 2.0899360000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.045
y[1] (closed_form) = 0.47800575996940763136195791159283
y[1] (numeric) = 0.47800575996940763136195791159284
absolute error = 1e-32
relative error = 2.0920250000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.046
y[1] (closed_form) = 0.4775284654718267755940931638935
y[1] (numeric) = 0.4775284654718267755940931638935
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.047
y[1] (closed_form) = 0.47705166803500986781375330417912
y[1] (numeric) = 0.47705166803500986781375330417912
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.048
y[1] (closed_form) = 0.47657536753492344293295918989813
y[1] (numeric) = 0.47657536753492344293295918989813
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.049
y[1] (closed_form) = 0.47609956384518956142184278144983
y[1] (numeric) = 0.47609956384518956142184278144983
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.05
y[1] (closed_form) = 0.4756242568370986920332936979786
y[1] (numeric) = 0.4756242568370986920332936979786
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.051
y[1] (closed_form) = 0.47514944637962255078278495543811
y[1] (numeric) = 0.47514944637962255078278495543811
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.052
y[1] (closed_form) = 0.47467513233942689623221866954256
y[1] (numeric) = 0.47467513233942689623221866954257
absolute error = 1e-32
relative error = 2.1067040000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.053
y[1] (closed_form) = 0.47420131458088428112740414138976
y[1] (numeric) = 0.47420131458088428112740414138977
absolute error = 1e-32
relative error = 2.1088090000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.054
y[1] (closed_form) = 0.47372799296608676043954378099365
y[1] (numeric) = 0.47372799296608676043954378099366
absolute error = 1e-32
relative error = 2.1109160000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
memory used=41.8MB, alloc=40.3MB, time=0.65
TOP MAIN SOLVE Loop
x[1] = -1.055
y[1] (closed_form) = 0.47325516735485855586185681664912
y[1] (numeric) = 0.47325516735485855586185681664912
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.056
y[1] (closed_form) = 0.47278283760476867681321673878181
y[1] (numeric) = 0.47278283760476867681321673878181
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.057
y[1] (closed_form) = 0.47231100357114349800141598838871
y[1] (numeric) = 0.47231100357114349800141598838871
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.058
y[1] (closed_form) = 0.47183966510707929359940057488945
y[1] (numeric) = 0.47183966510707929359940057488945
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.059
y[1] (closed_form) = 0.47136882206345472808853814858582
y[1] (numeric) = 0.47136882206345472808853814858582
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.06
y[1] (closed_form) = 0.47089847428894330382369561122622
y[1] (numeric) = 0.47089847428894330382369561122622
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.061
y[1] (closed_form) = 0.47042862163002576537560667651117
y[1] (numeric) = 0.47042862163002576537560667651117
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.062
y[1] (closed_form) = 0.46995926393100246070670594272888
y[1] (numeric) = 0.46995926393100246070670594272888
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.063
y[1] (closed_form) = 0.46949040103400565923729406390422
y[1] (numeric) = 0.46949040103400565923729406390421
absolute error = 1e-32
relative error = 2.1299690000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.064
y[1] (closed_form) = 0.46902203277901182685957855556223
y[1] (numeric) = 0.46902203277901182685957855556222
absolute error = 1e-32
relative error = 2.1320960000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.065
y[1] (closed_form) = 0.4685541590038538579578066979817
y[1] (numeric) = 0.4685541590038538579578066979817
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.066
y[1] (closed_form) = 0.46808677954423326449337095502809
y[1] (numeric) = 0.46808677954423326449337095502809
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.067
y[1] (closed_form) = 0.46761989423373232221442336154172
y[1] (numeric) = 0.46761989423373232221442336154172
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.068
y[1] (closed_form) = 0.46715350290382617405018349789594
y[1] (numeric) = 0.46715350290382617405018349789594
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.069
y[1] (closed_form) = 0.46668760538389489075076501765713
y[1] (numeric) = 0.46668760538389489075076501765712
absolute error = 1e-32
relative error = 2.1427610000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.07
y[1] (closed_form) = 0.46622220150123548883397827404541
y[1] (numeric) = 0.4662222015012354888339782740454
absolute error = 1e-32
relative error = 2.1449000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.071
y[1] (closed_form) = 0.46575729108107390590119145372631
y[1] (numeric) = 0.4657572910810739059011914537263
absolute error = 1e-32
relative error = 2.1470410000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.072
y[1] (closed_form) = 0.46529287394657693338494982281647
y[1] (numeric) = 0.46529287394657693338494982281646
absolute error = 1e-32
relative error = 2.1491840000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.073
y[1] (closed_form) = 0.46482894991886410679166227015952
y[1] (numeric) = 0.4648289499188641067916622701595
absolute error = 2e-32
relative error = 4.3026580000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.074
y[1] (closed_form) = 0.46436551881701955350326634705936
y[1] (numeric) = 0.46436551881701955350326634705934
absolute error = 2e-32
relative error = 4.3069520000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.075
y[1] (closed_form) = 0.46390258045810379820237750072485
y[1] (numeric) = 0.46390258045810379820237750072483
absolute error = 2e-32
relative error = 4.3112500000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.076
y[1] (closed_form) = 0.46344013465716552598601523049659
y[1] (numeric) = 0.46344013465716552598601523049657
absolute error = 2e-32
relative error = 4.3155520000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.077
y[1] (closed_form) = 0.46297818122725330323357851114551
y[1] (numeric) = 0.46297818122725330323357851114549
absolute error = 2e-32
relative error = 4.3198580000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.078
y[1] (closed_form) = 0.46251671997942725629531507563998
y[1] (numeric) = 0.46251671997942725629531507563997
absolute error = 1e-32
relative error = 2.1620840000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.079
y[1] (closed_form) = 0.46205575072277070806809408009552
y[1] (numeric) = 0.4620557507227707080680940800955
absolute error = 2e-32
relative error = 4.3284820000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.08
y[1] (closed_form) = 0.46159527326440177252584933530281
y[1] (numeric) = 0.46159527326440177252584933530279
absolute error = 2e-32
relative error = 4.3328000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.081
y[1] (closed_form) = 0.46113528740948490727261073126373
y[1] (numeric) = 0.46113528740948490727261073126371
absolute error = 2e-32
relative error = 4.3371220000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.082
y[1] (closed_form) = 0.46067579296124242418658475236833
y[1] (numeric) = 0.46067579296124242418658475236832
absolute error = 1e-32
relative error = 2.1707240000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.083
y[1] (closed_form) = 0.46021678972096595822428112986904
y[1] (numeric) = 0.46021678972096595822428112986902
absolute error = 2e-32
relative error = 4.3457780000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.084
y[1] (closed_form) = 0.45975827748802789445421175362841
y[1] (numeric) = 0.4597582774880278944542117536284
absolute error = 1e-32
relative error = 2.1750560000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.085
y[1] (closed_form) = 0.45930025605989275339021001504208
y[1] (numeric) = 0.45930025605989275339021001504207
absolute error = 1e-32
relative error = 2.1772250000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.086
y[1] (closed_form) = 0.45884272523212853469493382570217
y[1] (numeric) = 0.45884272523212853469493382570215
absolute error = 2e-32
relative error = 4.3587920000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.087
y[1] (closed_form) = 0.45838568479841801932462369973171
y[1] (numeric) = 0.45838568479841801932462369973169
absolute error = 2e-32
relative error = 4.3631380000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.088
y[1] (closed_form) = 0.45792913455057003018668854957358
y[1] (numeric) = 0.45792913455057003018668854957356
absolute error = 2e-32
relative error = 4.3674880000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.089
y[1] (closed_form) = 0.45747307427853065138218627297144
y[1] (numeric) = 0.45747307427853065138218627297142
absolute error = 2e-32
relative error = 4.3718420000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.09
y[1] (closed_form) = 0.45701750377039440610575385037247
y[1] (numeric) = 0.45701750377039440610575385037245
absolute error = 2e-32
relative error = 4.3762000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.091
y[1] (closed_form) = 0.45656242281241539327602257427243
y[1] (numeric) = 0.45656242281241539327602257427241
absolute error = 2e-32
relative error = 4.3805620000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.092
y[1] (closed_form) = 0.45610783118901838297002824219691
y[1] (numeric) = 0.45610783118901838297002824219688
absolute error = 3e-32
relative error = 6.5773920000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.093
y[1] (closed_form) = 0.45565372868280987073559370997367
y[1] (numeric) = 0.45565372868280987073559370997364
absolute error = 3e-32
relative error = 6.5839470000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.094
y[1] (closed_form) = 0.45520011507458909085612216842768
y[1] (numeric) = 0.45520011507458909085612216842766
absolute error = 2e-32
relative error = 4.3936720000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.095
y[1] (closed_form) = 0.45474699014335898864269392116961
y[1] (numeric) = 0.45474699014335898864269392116959
absolute error = 2e-32
relative error = 4.3980500000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.096
y[1] (closed_form) = 0.45429435366633715182880735011921
y[1] (numeric) = 0.45429435366633715182880735011919
absolute error = 2e-32
relative error = 4.4024320000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.097
y[1] (closed_form) = 0.45384220541896670114354620499417
y[1] (numeric) = 0.45384220541896670114354620499415
absolute error = 2e-32
relative error = 4.4068180000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.098
y[1] (closed_form) = 0.45339054517492714013939038920858
y[1] (numeric) = 0.45339054517492714013939038920856
absolute error = 2e-32
relative error = 4.4112080000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.099
y[1] (closed_form) = 0.4529393727061451643513160832883
y[1] (numeric) = 0.45293937270614516435131608328828
absolute error = 2e-32
relative error = 4.4156020000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.1
y[1] (closed_form) = 0.45248868778280542986425339366516
y[1] (numeric) = 0.45248868778280542986425339366513
absolute error = 3e-32
relative error = 6.6300000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.101
y[1] (closed_form) = 0.45203849017336128136638578501682
y[1] (numeric) = 0.45203849017336128136638578501679
absolute error = 3e-32
relative error = 6.6366030000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.102
y[1] (closed_form) = 0.45158877964454543976618539345124
y[1] (numeric) = 0.45158877964454543976618539345121
absolute error = 3e-32
relative error = 6.6432120000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.103
y[1] (closed_form) = 0.45113955596138064945148197088436
y[1] (numeric) = 0.45113955596138064945148197088433
absolute error = 3e-32
relative error = 6.6498269999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.104
y[1] (closed_form) = 0.45069081888719028526926072283596
y[1] (numeric) = 0.45069081888719028526926072283594
absolute error = 2e-32
relative error = 4.4376320000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.105
y[1] (closed_form) = 0.45024256818360891930527571729269
y[1] (numeric) = 0.45024256818360891930527571729267
absolute error = 2e-32
relative error = 4.4420500000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.106
y[1] (closed_form) = 0.44979480361059284754295090579678
y[1] (numeric) = 0.44979480361059284754295090579675
absolute error = 3e-32
relative error = 6.6697079999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.107
y[1] (closed_form) = 0.44934752492643057648142015386558
y[1] (numeric) = 0.44934752492643057648142015386555
absolute error = 3e-32
relative error = 6.6763470000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.108
y[1] (closed_form) = 0.44890073188775326979293107039482
y[1] (numeric) = 0.44890073188775326979293107039479
absolute error = 3e-32
relative error = 6.6829920000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.109
y[1] (closed_form) = 0.44845442424954515510020489882644
y[1] (numeric) = 0.44845442424954515510020489882641
absolute error = 3e-32
relative error = 6.6896430000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.11
y[1] (closed_form) = 0.44800860176515389095470633036154
y[1] (numeric) = 0.44800860176515389095470633036151
absolute error = 3e-32
relative error = 6.6963000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.111
y[1] (closed_form) = 0.4475632641863008940971328649733
y[1] (numeric) = 0.44756326418630089409713286497326
absolute error = 4e-32
relative error = 8.9372839999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.112
y[1] (closed_form) = 0.44711841126309162708178332284095
y[1] (numeric) = 0.44711841126309162708178332284092
absolute error = 3e-32
relative error = 6.7096320000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.113
y[1] (closed_form) = 0.44667404274402584634680934031157
y[1] (numeric) = 0.44667404274402584634680934031154
absolute error = 3e-32
relative error = 6.7163070000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.114
y[1] (closed_form) = 0.44623015837600781081269221364072
y[1] (numeric) = 0.44623015837600781081269221364069
absolute error = 3e-32
relative error = 6.7229880000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.115
y[1] (closed_form) = 0.44578675790435645109162032341829
y[1] (numeric) = 0.44578675790435645109162032341826
absolute error = 3e-32
relative error = 6.7296750000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.116
y[1] (closed_form) = 0.44534384107281549939076962541239
y[1] (numeric) = 0.44534384107281549939076962541236
absolute error = 3e-32
relative error = 6.7363680000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.117
y[1] (closed_form) = 0.4449014076235635801928113720359
y[1] (numeric) = 0.44490140762356358019281137203587
absolute error = 3e-32
relative error = 6.7430670000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.118
y[1] (closed_form) = 0.44445945729722426179728737504022
y[1] (numeric) = 0.44445945729722426179728737504019
absolute error = 3e-32
relative error = 6.7497720000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.119
y[1] (closed_form) = 0.44401798983287606880680377646181
y[1] (numeric) = 0.44401798983287606880680377646177
absolute error = 4e-32
relative error = 9.0086439999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.12
y[1] (closed_form) = 0.44357700496806245564229950319375
y[1] (numeric) = 0.44357700496806245564229950319372
absolute error = 3e-32
relative error = 6.7632000000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
memory used=88.5MB, alloc=44.3MB, time=1.35
x[1] = -1.121
y[1] (closed_form) = 0.4431365024388017411719453825398
y[1] (numeric) = 0.44313650243880174117194538253977
absolute error = 3e-32
relative error = 6.7699230000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.122
y[1] (closed_form) = 0.44269648197959700453852433325483
y[1] (numeric) = 0.4426964819795970045385243332548
absolute error = 3e-32
relative error = 6.7766520000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.123
y[1] (closed_form) = 0.44225694332344594227043216021731
y[1] (numeric) = 0.44225694332344594227043216021728
absolute error = 3e-32
relative error = 6.7833870000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.124
y[1] (closed_form) = 0.44181788620185068676172231215671
y[1] (numeric) = 0.44181788620185068676172231215668
absolute error = 3e-32
relative error = 6.7901280000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.125
y[1] (closed_form) = 0.44137931034482758620689655172414
y[1] (numeric) = 0.44137931034482758620689655172411
absolute error = 3e-32
relative error = 6.7968750000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.126
y[1] (closed_form) = 0.4409412154809169460764168764077
y[1] (numeric) = 0.44094121548091694607641687640768
absolute error = 2e-32
relative error = 4.5357520000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.127
y[1] (closed_form) = 0.44050360133719273221918225792455
y[1] (numeric) = 0.44050360133719273221918225792452
absolute error = 3e-32
relative error = 6.8103870000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.128
y[1] (closed_form) = 0.44006646763927223567847687714752
y[1] (numeric) = 0.44006646763927223567847687714749
absolute error = 3e-32
relative error = 6.8171520000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.129
y[1] (closed_form) = 0.43962981411132569930815456153301
y[1] (numeric) = 0.43962981411132569930815456153297
absolute error = 4e-32
relative error = 9.0985639999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.13
y[1] (closed_form) = 0.43919364047608590627607712240327
y[1] (numeric) = 0.43919364047608590627607712240323
absolute error = 4e-32
relative error = 9.1076000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.131
y[1] (closed_form) = 0.43875794645485773054207228010658
y[1] (numeric) = 0.43875794645485773054207228010655
absolute error = 3e-32
relative error = 6.8374830000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.132
y[1] (closed_form) = 0.43832273176752764939791989564412
y[1] (numeric) = 0.43832273176752764939791989564409
absolute error = 3e-32
relative error = 6.8442720000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.133
y[1] (closed_form) = 0.43788799613257321815711333723638
y[1] (numeric) = 0.43788799613257321815711333723634
absolute error = 4e-32
relative error = 9.1347559999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.134
y[1] (closed_form) = 0.4374537392670725070823760387339
y[1] (numeric) = 0.43745373926707250708237603873387
absolute error = 3e-32
relative error = 6.8578680000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.135
y[1] (closed_form) = 0.43701996088671350063914169279682
y[1] (numeric) = 0.43701996088671350063914169279678
absolute error = 4e-32
relative error = 9.1529000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.136
y[1] (closed_form) = 0.43658666070580345916343010422197
y[1] (numeric) = 0.43658666070580345916343010422193
absolute error = 4e-32
relative error = 9.1619840000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.137
y[1] (closed_form) = 0.43615383843727824303276954634331
y[1] (numeric) = 0.43615383843727824303276954634327
absolute error = 4e-32
relative error = 9.1710760000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.138
y[1] (closed_form) = 0.43572149379271159942903055453403
y[1] (numeric) = 0.43572149379271159942903055453399
absolute error = 4e-32
relative error = 9.1801760000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.139
y[1] (closed_form) = 0.43528962648232441178224549377296
y[1] (numeric) = 0.43528962648232441178224549377292
absolute error = 4e-32
relative error = 9.1892840000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.14
y[1] (closed_form) = 0.43485823621499391198469299008523
y[1] (numeric) = 0.43485823621499391198469299008519
absolute error = 4e-32
relative error = 9.1984000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.141
y[1] (closed_form) = 0.43442732269826285546472645631985
y[1] (numeric) = 0.43442732269826285546472645631981
absolute error = 4e-32
relative error = 9.2075240000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.142
y[1] (closed_form) = 0.43399688563834865921002150888565
y[1] (numeric) = 0.43399688563834865921002150888561
absolute error = 4e-32
relative error = 9.2166560000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.143
y[1] (closed_form) = 0.43356692474015250283010810124135
y[1] (numeric) = 0.4335669247401525028301081012413
absolute error = 5e-32
relative error = 1.1532245000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.144
y[1] (closed_form) = 0.43313743970726839274823972944503
y[1] (numeric) = 0.43313743970726839274823972944498
absolute error = 5e-32
relative error = 1.1543680000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.145
y[1] (closed_form) = 0.43270843024199218961283413204098
y[1] (numeric) = 0.43270843024199218961283413204093
absolute error = 5e-32
relative error = 1.1555125000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.146
y[1] (closed_form) = 0.43227989604533059901889754793552
y[1] (numeric) = 0.43227989604533059901889754793547
absolute error = 5e-32
relative error = 1.1566580000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.147
y[1] (closed_form) = 0.43185183681701012563001784843642
y[1] (numeric) = 0.43185183681701012563001784843637
absolute error = 5e-32
relative error = 1.1578045000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.148
y[1] (closed_form) = 0.43142425225548599079168075985891
y[1] (numeric) = 0.43142425225548599079168075985886
absolute error = 5e-32
relative error = 1.1589520000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.149
y[1] (closed_form) = 0.43099714205795101372682797740368
y[1] (numeric) = 0.43099714205795101372682797740363
absolute error = 5e-32
relative error = 1.1601005000000000000000000000000e-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) = 0.43057050592034445640473627556512
y[1] (numeric) = 0.43057050592034445640473627556507
absolute error = 5e-32
relative error = 1.1612500000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.151
y[1] (closed_form) = 0.43014434353736083217445278111976
y[1] (numeric) = 0.43014434353736083217445278111971
absolute error = 5e-32
relative error = 1.1624005000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.152
y[1] (closed_form) = 0.4297186546024586782541734275735
y[1] (numeric) = 0.42971865460245867825417342757345
absolute error = 5e-32
relative error = 1.1635520000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.153
y[1] (closed_form) = 0.42929343880786929216809929042087
y[1] (numeric) = 0.42929343880786929216809929042083
absolute error = 4e-32
relative error = 9.3176360000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.154
y[1] (closed_form) = 0.42886869584460543222244904611025
y[1] (numeric) = 0.4288686958446054322224490461102
absolute error = 5e-32
relative error = 1.1658580000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.155
y[1] (closed_form) = 0.42844442540246998211244523944688
y[1] (numeric) = 0.42844442540246998211244523944683
absolute error = 5e-32
relative error = 1.1670125000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.156
y[1] (closed_form) = 0.42802062717006457975222741934379
y[1] (numeric) = 0.42802062717006457975222741934374
absolute error = 5e-32
relative error = 1.1681680000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.157
y[1] (closed_form) = 0.42759730083479821041977654620253
y[1] (numeric) = 0.42759730083479821041977654620248
absolute error = 5e-32
relative error = 1.1693245000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.158
y[1] (closed_form) = 0.42717444608289576430906242043876
y[1] (numeric) = 0.42717444608289576430906242043871
absolute error = 5e-32
relative error = 1.1704820000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.159
y[1] (closed_form) = 0.42675206259940655858174926523964
y[1] (numeric) = 0.42675206259940655858174926523959
absolute error = 5e-32
relative error = 1.1716405000000000000000000000000e-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) = 0.42633015006821282401091405184175
y[1] (numeric) = 0.4263301500682128240109140518417
absolute error = 5e-32
relative error = 1.1728000000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.161
y[1] (closed_form) = 0.42590870817203815630934771655435
y[1] (numeric) = 0.4259087081720381563093477165543
absolute error = 5e-32
relative error = 1.1739605000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.162
y[1] (closed_form) = 0.4254877365924559322351211193391
y[1] (numeric) = 0.42548773659245593223512111933905
absolute error = 5e-32
relative error = 1.1751220000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.163
y[1] (closed_form) = 0.42506723500989769056720546772486
y[1] (numeric) = 0.42506723500989769056720546772481
absolute error = 5e-32
relative error = 1.1762845000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.164
y[1] (closed_form) = 0.42464720310366147804404101072829
y[1] (numeric) = 0.42464720310366147804404101072824
absolute error = 5e-32
relative error = 1.1774480000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.165
y[1] (closed_form) = 0.42422764055192016035804812862582
y[1] (numeric) = 0.42422764055192016035804812862577
absolute error = 5e-32
relative error = 1.1786125000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.166
y[1] (closed_form) = 0.42380854703172969829917153905226
y[1] (numeric) = 0.42380854703172969829917153905221
absolute error = 5e-32
relative error = 1.1797780000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.167
y[1] (closed_form) = 0.4233899222190373891406412409728
y[1] (numeric) = 0.42338992221903738914064124097275
absolute error = 5e-32
relative error = 1.1809445000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.168
y[1] (closed_form) = 0.42297176578869007336022305839041
y[1] (numeric) = 0.42297176578869007336022305839036
absolute error = 5e-32
relative error = 1.1821120000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.169
y[1] (closed_form) = 0.42255407741444230679031725782686
y[1] (numeric) = 0.42255407741444230679031725782682
absolute error = 4e-32
relative error = 9.4662440000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.17
y[1] (closed_form) = 0.42213685676896449829034573008569
y[1] (numeric) = 0.42213685676896449829034573008565
absolute error = 4e-32
relative error = 9.4756000000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.171
y[1] (closed_form) = 0.42172010352385101303494667981871
y[1] (numeric) = 0.42172010352385101303494667981867
absolute error = 4e-32
relative error = 9.4849640000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.172
y[1] (closed_form) = 0.42130381734962824151157068803969
y[1] (numeric) = 0.42130381734962824151157068803965
absolute error = 4e-32
relative error = 9.4943360000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.173
y[1] (closed_form) = 0.4208879979157626343211434348417
y[1] (numeric) = 0.42088799791576263432114343484166
absolute error = 4e-32
relative error = 9.5037159999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.174
y[1] (closed_form) = 0.42047264489066870287552832387831
y[1] (numeric) = 0.42047264489066870287552832387827
absolute error = 4e-32
relative error = 9.5131039999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.175
y[1] (closed_form) = 0.42005775794171698608558676818062
y[1] (numeric) = 0.42005775794171698608558676818059
absolute error = 3e-32
relative error = 7.1418750000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.176
y[1] (closed_form) = 0.41964333673524198313369500993715
y[1] (numeric) = 0.41964333673524198313369500993712
absolute error = 3e-32
relative error = 7.1489280000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.177
y[1] (closed_form) = 0.41922938093655005242463408611558
y[1] (numeric) = 0.41922938093655005242463408611555
absolute error = 3e-32
relative error = 7.1559870000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.178
y[1] (closed_form) = 0.41881589020992727680882394822765
y[1] (numeric) = 0.41881589020992727680882394822762
absolute error = 3e-32
relative error = 7.1630520000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.179
y[1] (closed_form) = 0.41840286421864729517192382892176
y[1] (numeric) = 0.41840286421864729517192382892173
absolute error = 3e-32
relative error = 7.1701230000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.18
y[1] (closed_form) = 0.41799030262497910048486875104498
y[1] (numeric) = 0.41799030262497910048486875104494
absolute error = 4e-32
relative error = 9.5695999999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.181
y[1] (closed_form) = 0.4175782050901948044084566267782
y[1] (numeric) = 0.41757820509019480440845662677817
absolute error = 3e-32
relative error = 7.1842830000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.182
y[1] (closed_form) = 0.41716657127457736854664172566793
y[1] (numeric) = 0.41716657127457736854664172566789
absolute error = 4e-32
relative error = 9.5884959999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.183
y[1] (closed_form) = 0.41675540083742830244272843092842
y[1] (numeric) = 0.41675540083742830244272843092838
absolute error = 4e-32
relative error = 9.5979560000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.184
y[1] (closed_form) = 0.41634469343707532841269418316502
y[1] (numeric) = 0.41634469343707532841269418316498
absolute error = 4e-32
relative error = 9.6074240000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.185
y[1] (closed_form) = 0.41593444873088001330990235938816
y[1] (numeric) = 0.41593444873088001330990235938812
absolute error = 4e-32
relative error = 9.6169000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.186
y[1] (closed_form) = 0.4155246663752453673154945823894
y[1] (numeric) = 0.41552466637524536731549458238936
absolute error = 4e-32
relative error = 9.6263840000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
memory used=135.0MB, alloc=44.3MB, time=2.03
x[1] = -1.187
y[1] (closed_form) = 0.41511534602562340984877763059633
y[1] (numeric) = 0.41511534602562340984877763059629
absolute error = 4e-32
relative error = 9.6358759999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.188
y[1] (closed_form) = 0.41470648733652270269194275059884
y[1] (numeric) = 0.4147064873365227026919427505988
absolute error = 4e-32
relative error = 9.6453759999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.189
y[1] (closed_form) = 0.41429808996151585042347479265416
y[1] (numeric) = 0.41429808996151585042347479265413
absolute error = 3e-32
relative error = 7.2411630000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.19
y[1] (closed_form) = 0.41389015355324696825462522246596
y[1] (numeric) = 0.41389015355324696825462522246592
absolute error = 4e-32
relative error = 9.6643999999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.191
y[1] (closed_form) = 0.41348267776343911736333673905232
y[1] (numeric) = 0.41348267776343911736333673905228
absolute error = 4e-32
relative error = 9.6739240000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.192
y[1] (closed_form) = 0.41307566224290170782001797705282
y[1] (numeric) = 0.41307566224290170782001797705278
absolute error = 4e-32
relative error = 9.6834560000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.193
y[1] (closed_form) = 0.41266910664153786919957462068487
y[1] (numeric) = 0.41266910664153786919957462068483
absolute error = 4e-32
relative error = 9.6929960000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.194
y[1] (closed_form) = 0.41226301060835178897410823388175
y[1] (numeric) = 0.41226301060835178897410823388171
absolute error = 4e-32
relative error = 9.7025440000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.195
y[1] (closed_form) = 0.41185737379145601878069624489039
y[1] (numeric) = 0.41185737379145601878069624489035
absolute error = 4e-32
relative error = 9.7121000000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.196
y[1] (closed_form) = 0.41145219583807874865866584156786
y[1] (numeric) = 0.41145219583807874865866584156782
absolute error = 4e-32
relative error = 9.7216640000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.197
y[1] (closed_form) = 0.41104747639457104935077106340859
y[1] (numeric) = 0.41104747639457104935077106340855
absolute error = 4e-32
relative error = 9.7312360000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.198
y[1] (closed_form) = 0.41064321510641408276267614540712
y[1] (numeric) = 0.41064321510641408276267614540708
absolute error = 4e-32
relative error = 9.7408160000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.199
y[1] (closed_form) = 0.41023941161822628067513920448835
y[1] (numeric) = 0.41023941161822628067513920448831
absolute error = 4e-32
relative error = 9.7504039999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.2
y[1] (closed_form) = 0.40983606557377049180327868852459
y[1] (numeric) = 0.40983606557377049180327868852455
absolute error = 4e-32
relative error = 9.7600000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.201
y[1] (closed_form) = 0.40943317661596109729729065784038
y[1] (numeric) = 0.40943317661596109729729065784034
absolute error = 4e-32
relative error = 9.7696040000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.202
y[1] (closed_form) = 0.40903074438687109477896796634822
y[1] (numeric) = 0.40903074438687109477896796634818
absolute error = 4e-32
relative error = 9.7792160000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.203
y[1] (closed_form) = 0.40862876852773915100835278065748
y[1] (numeric) = 0.40862876852773915100835278065743
absolute error = 5e-32
relative error = 1.2236045000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.204
y[1] (closed_form) = 0.40822724867897662327483164708264
y[1] (numeric) = 0.4082272486789766232748316470826
absolute error = 4e-32
relative error = 9.7984640000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.205
y[1] (closed_form) = 0.40782618448017454960695751470723
y[1] (numeric) = 0.40782618448017454960695751470719
absolute error = 4e-32
relative error = 9.8081000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.206
y[1] (closed_form) = 0.40742557557011060789525577362783
y[1] (numeric) = 0.40742557557011060789525577362779
absolute error = 4e-32
relative error = 9.8177440000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.207
y[1] (closed_form) = 0.40702542158675604402224149713719
y[1] (numeric) = 0.40702542158675604402224149713715
absolute error = 4e-32
relative error = 9.8273959999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.208
y[1] (closed_form) = 0.40662572216728256909384271066465
y[1] (numeric) = 0.40662572216728256909384271066462
absolute error = 3e-32
relative error = 7.3777920000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.209
y[1] (closed_form) = 0.40622647694806922586638967437292
y[1] (numeric) = 0.40622647694806922586638967437288
absolute error = 4e-32
relative error = 9.8467240000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.21
y[1] (closed_form) = 0.40582768556470922446329288584067
y[1] (numeric) = 0.40582768556470922446329288584063
absolute error = 4e-32
relative error = 9.8564000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.211
y[1] (closed_form) = 0.4054293476520167474754928095078
y[1] (numeric) = 0.40542934765201674747549280950776
absolute error = 4e-32
relative error = 9.8660840000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.212
y[1] (closed_form) = 0.40503146284403372453972224562404
y[1] (numeric) = 0.405031462844033724539722245624
absolute error = 4e-32
relative error = 9.8757760000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.213
y[1] (closed_form) = 0.4046340307740365764885777882623
y[1] (numeric) = 0.40463403077403657648857778826226
absolute error = 4e-32
relative error = 9.8854759999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.214
y[1] (closed_form) = 0.40423705107454292916635001430999
y[1] (numeric) = 0.40423705107454292916635001430996
absolute error = 3e-32
relative error = 7.4213880000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.215
y[1] (closed_form) = 0.40384052337731829700451291784874
y[1] (numeric) = 0.40384052337731829700451291784871
absolute error = 3e-32
relative error = 7.4286750000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.216
y[1] (closed_form) = 0.40344444731338273645072168142735
y[1] (numeric) = 0.40344444731338273645072168142732
absolute error = 3e-32
relative error = 7.4359680000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.217
y[1] (closed_form) = 0.40304882251301746934511418171617
y[1] (numeric) = 0.40304882251301746934511418171614
absolute error = 3e-32
relative error = 7.4432670000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.218
y[1] (closed_form) = 0.40265364860577147633765568603323
y[1] (numeric) = 0.4026536486057714763376556860332
absolute error = 3e-32
relative error = 7.4505720000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.219
y[1] (closed_form) = 0.40225892522046806044020803222577
y[1] (numeric) = 0.40225892522046806044020803222573
absolute error = 4e-32
relative error = 9.9438439999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.22
y[1] (closed_form) = 0.4018646519852113808069442211863
y[1] (numeric) = 0.40186465198521138080694422118627
absolute error = 3e-32
relative error = 7.4652000000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.221
y[1] (closed_form) = 0.4014708285273929568366668125344
y[1] (numeric) = 0.40147082852739295683666681253437
absolute error = 3e-32
relative error = 7.4725230000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.222
y[1] (closed_form) = 0.40107745447369814269052382319864
y[1] (numeric) = 0.40107745447369814269052382319861
absolute error = 3e-32
relative error = 7.4798520000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.223
y[1] (closed_form) = 0.40068452945011257231854900912719
y[1] (numeric) = 0.40068452945011257231854900912716
absolute error = 3e-32
relative error = 7.4871870000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.224
y[1] (closed_form) = 0.40029205308192857508838448532049
y[1] (numeric) = 0.40029205308192857508838448532046
absolute error = 3e-32
relative error = 7.4945280000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.225
y[1] (closed_form) = 0.39990002499375156210947263184204
y[1] (numeric) = 0.39990002499375156210947263184201
absolute error = 3e-32
relative error = 7.5018750000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.226
y[1] (closed_form) = 0.39950844480950638334593116629299
y[1] (numeric) = 0.39950844480950638334593116629296
absolute error = 3e-32
relative error = 7.5092280000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.227
y[1] (closed_form) = 0.39911731215244365561125015914803
y[1] (numeric) = 0.399117312152443655611250159148
absolute error = 3e-32
relative error = 7.5165870000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.228
y[1] (closed_form) = 0.39872662664514606153787264990526
y[1] (numeric) = 0.39872662664514606153787264990523
absolute error = 3e-32
relative error = 7.5239520000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.229
y[1] (closed_form) = 0.39833638790953461961464141160856
y[1] (numeric) = 0.39833638790953461961464141160853
absolute error = 3e-32
relative error = 7.5313230000000000000000000000000e-30 %
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) = 0.39794659556687492538501333121095
y[1] (numeric) = 0.39794659556687492538501333121092
absolute error = 3e-32
relative error = 7.5387000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.231
y[1] (closed_form) = 0.39755724923778336389885984556491
y[1] (numeric) = 0.39755724923778336389885984556488
absolute error = 3e-32
relative error = 7.5460830000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.232
y[1] (closed_form) = 0.39716834854223329351058691949874
y[1] (numeric) = 0.39716834854223329351058691949871
absolute error = 3e-32
relative error = 7.5534720000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.233
y[1] (closed_form) = 0.39677989309956120111622119526769
y[1] (numeric) = 0.39677989309956120111622119526765
absolute error = 4e-32
relative error = 1.0081156000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.234
y[1] (closed_form) = 0.39639188252847282892202020330147
y[1] (numeric) = 0.39639188252847282892202020330143
absolute error = 4e-32
relative error = 1.0091024000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.235
y[1] (closed_form) = 0.39600431644704927283707392410577
y[1] (numeric) = 0.39600431644704927283707392410573
absolute error = 4e-32
relative error = 1.0100900000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.236
y[1] (closed_form) = 0.39561719447275305258227255176255
y[1] (numeric) = 0.39561719447275305258227255176251
absolute error = 4e-32
relative error = 1.0110784000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.237
y[1] (closed_form) = 0.39523051622243415360792105191392
y[1] (numeric) = 0.39523051622243415360792105191388
absolute error = 4e-32
relative error = 1.0120676000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.238
y[1] (closed_form) = 0.39484428131233604091218505245901
y[1] (numeric) = 0.39484428131233604091218505245897
absolute error = 4e-32
relative error = 1.0130576000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.239
y[1] (closed_form) = 0.39445848935810164485245477434805
y[1] (numeric) = 0.39445848935810164485245477434801
absolute error = 4e-32
relative error = 1.0140484000000000000000000000000e-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) = 0.39407313997477931904161412358134
y[1] (numeric) = 0.3940731399747793190416141235813
absolute error = 4e-32
relative error = 1.0150400000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.241
y[1] (closed_form) = 0.39368823277682877042110074442508
y[1] (numeric) = 0.39368823277682877042110074442504
absolute error = 4e-32
relative error = 1.0160324000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.242
y[1] (closed_form) = 0.39330376737812696160253979840822
y[1] (numeric) = 0.39330376737812696160253979840818
absolute error = 4e-32
relative error = 1.0170256000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.243
y[1] (closed_form) = 0.39291974339197398556962950418636
y[1] (numeric) = 0.39291974339197398556962950418632
absolute error = 4e-32
relative error = 1.0180196000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.244
y[1] (closed_form) = 0.39253616043109891283185007002845
y[1] (numeric) = 0.39253616043109891283185007002841
absolute error = 4e-32
relative error = 1.0190144000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.245
y[1] (closed_form) = 0.3921530181076656111214595935334
y[1] (numeric) = 0.39215301810766561112145959353336
absolute error = 4e-32
relative error = 1.0200100000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.246
y[1] (closed_form) = 0.39177031603327853772513081210852
y[1] (numeric) = 0.39177031603327853772513081210849
absolute error = 3e-32
relative error = 7.6575480000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.247
y[1] (closed_form) = 0.39138805381898850454147128248863
y[1] (numeric) = 0.3913880538189885045414712824886
absolute error = 3e-32
relative error = 7.6650270000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.248
y[1] (closed_form) = 0.39100623107529841595555666775106
y[1] (numeric) = 0.39100623107529841595555666775102
absolute error = 4e-32
relative error = 1.0230016000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.249
y[1] (closed_form) = 0.39062484741216897962149233535456
y[1] (numeric) = 0.39062484741216897962149233535452
absolute error = 4e-32
relative error = 1.0240004000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.25
y[1] (closed_form) = 0.39024390243902439024390243902439
y[1] (numeric) = 0.39024390243902439024390243902435
absolute error = 4e-32
relative error = 1.0250000000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.251
y[1] (closed_form) = 0.38986339576475798644912809000854
y[1] (numeric) = 0.3898633957647579864491280900085
absolute error = 4e-32
relative error = 1.0260004000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.252
y[1] (closed_form) = 0.3894833269977378808367971383881
y[1] (numeric) = 0.38948332699773788083679713838806
absolute error = 4e-32
relative error = 1.0270016000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
memory used=181.5MB, alloc=44.3MB, time=2.72
x[1] = -1.253
y[1] (closed_form) = 0.38910369574581256330230750164688
y[1] (numeric) = 0.38910369574581256330230750164684
absolute error = 4e-32
relative error = 1.0280036000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.254
y[1] (closed_form) = 0.38872450161631647772064391436244
y[1] (numeric) = 0.3887245016163164777206439143624
absolute error = 4e-32
relative error = 1.0290064000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.255
y[1] (closed_form) = 0.38834574421607557208182444830633
y[1] (numeric) = 0.38834574421607557208182444830629
absolute error = 4e-32
relative error = 1.0300100000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.256
y[1] (closed_form) = 0.38796742315141282216814818493321
y[1] (numeric) = 0.38796742315141282216814818493317
absolute error = 4e-32
relative error = 1.0310144000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.257
y[1] (closed_form) = 0.38758953802815372886328903055717
y[1] (numeric) = 0.38758953802815372886328903055713
absolute error = 4e-32
relative error = 1.0320196000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.258
y[1] (closed_form) = 0.38721208845163178918315286668598
y[1] (numeric) = 0.38721208845163178918315286668593
absolute error = 5e-32
relative error = 1.2912820000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.259
y[1] (closed_form) = 0.38683507402669394111828604210081
y[1] (numeric) = 0.38683507402669394111828604210076
absolute error = 5e-32
relative error = 1.2925405000000000000000000000000e-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) = 0.38645849435770598237749265728861
y[1] (numeric) = 0.38645849435770598237749265728856
absolute error = 5e-32
relative error = 1.2938000000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.261
y[1] (closed_form) = 0.38608234904855796312218618357984
y[1] (numeric) = 0.38608234904855796312218618357979
absolute error = 5e-32
relative error = 1.2950605000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.262
y[1] (closed_form) = 0.38570663770266955278086771650871
y[1] (numeric) = 0.38570663770266955278086771650866
absolute error = 5e-32
relative error = 1.2963220000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.263
y[1] (closed_form) = 0.38533135992299538103298860305437
y[1] (numeric) = 0.38533135992299538103298860305432
absolute error = 5e-32
relative error = 1.2975845000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.264
y[1] (closed_form) = 0.38495651531203035305131932296928
y[1] (numeric) = 0.38495651531203035305131932296923
absolute error = 5e-32
relative error = 1.2988480000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.265
y[1] (closed_form) = 0.38458210347181493909180936265131
y[1] (numeric) = 0.38458210347181493909180936265126
absolute error = 5e-32
relative error = 1.3001125000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.266
y[1] (closed_form) = 0.38420812400394043851978441313746
y[1] (numeric) = 0.38420812400394043851978441313741
absolute error = 5e-32
relative error = 1.3013780000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.267
y[1] (closed_form) = 0.38383457650955421836118756882634
y[1] (numeric) = 0.38383457650955421836118756882629
absolute error = 5e-32
relative error = 1.3026445000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.268
y[1] (closed_form) = 0.38346146058936492646743031738338
y[1] (numeric) = 0.38346146058936492646743031738333
absolute error = 5e-32
relative error = 1.3039120000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.269
y[1] (closed_form) = 0.38308877584364767938227701072763
y[1] (numeric) = 0.38308877584364767938227701072758
absolute error = 5e-32
relative error = 1.3051805000000000000000000000000e-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) = 0.38271652187224922499904320869532
y[1] (numeric) = 0.38271652187224922499904320869526
absolute error = 6e-32
relative error = 1.5677400000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.271
y[1] (closed_form) = 0.38234469827459308009624380744968
y[1] (numeric) = 0.38234469827459308009624380744962
absolute error = 6e-32
relative error = 1.5692646000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.272
y[1] (closed_form) = 0.38197330464968464283968122035887
y[1] (numeric) = 0.38197330464968464283968122035881
absolute error = 6e-32
relative error = 1.5707904000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.273
y[1] (closed_form) = 0.38160234059611628033881708616848
y[1] (numeric) = 0.38160234059611628033881708616842
absolute error = 6e-32
relative error = 1.5723174000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.274
y[1] (closed_form) = 0.38123180571207239134512305400225
y[1] (numeric) = 0.38123180571207239134512305400219
absolute error = 6e-32
relative error = 1.5738456000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.275
y[1] (closed_form) = 0.3808616995953344441799571530588
y[1] (numeric) = 0.38086169959533444417995715305874
absolute error = 6e-32
relative error = 1.5753750000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.276
y[1] (closed_form) = 0.38049202184328598997936211273522
y[1] (numeric) = 0.38049202184328598997936211273516
absolute error = 6e-32
relative error = 1.5769056000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.277
y[1] (closed_form) = 0.38012277205291765134303077207877
y[1] (numeric) = 0.38012277205291765134303077207871
absolute error = 6e-32
relative error = 1.5784374000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.278
y[1] (closed_form) = 0.37975394982083208647453142160132
y[1] (numeric) = 0.37975394982083208647453142160126
absolute error = 6e-32
relative error = 1.5799704000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.279
y[1] (closed_form) = 0.37938555474324892889973257112246
y[1] (numeric) = 0.37938555474324892889973257112241
absolute error = 5e-32
relative error = 1.3179205000000000000000000000000e-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) = 0.37901758641600970285021224984839
y[1] (numeric) = 0.37901758641600970285021224984834
absolute error = 5e-32
relative error = 1.3192000000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.281
y[1] (closed_form) = 0.37865004443458271439828153463834
y[1] (numeric) = 0.37865004443458271439828153463829
absolute error = 5e-32
relative error = 1.3204805000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.282
y[1] (closed_form) = 0.37828292839406791843009558453035
y[1] (numeric) = 0.3782829283940679184300955845303
absolute error = 5e-32
relative error = 1.3217620000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.283
y[1] (closed_form) = 0.37791623788920176154316804914725
y[1] (numeric) = 0.3779162378892017615431680491472
absolute error = 5e-32
relative error = 1.3230445000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.284
y[1] (closed_form) = 0.37754997251436200095444633051631
y[1] (numeric) = 0.37754997251436200095444633051626
absolute error = 5e-32
relative error = 1.3243280000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.285
y[1] (closed_form) = 0.37718413186357249950494582692906
y[1] (numeric) = 0.37718413186357249950494582692901
absolute error = 5e-32
relative error = 1.3256125000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.286
y[1] (closed_form) = 0.37681871553050799684678098844071
y[1] (numeric) = 0.37681871553050799684678098844066
absolute error = 5e-32
relative error = 1.3268980000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.287
y[1] (closed_form) = 0.37645372310849885689826978104322
y[1] (numeric) = 0.37645372310849885689826978104317
absolute error = 5e-32
relative error = 1.3281845000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.288
y[1] (closed_form) = 0.37608915419053579165262600491022
y[1] (numeric) = 0.37608915419053579165262600491017
absolute error = 5e-32
relative error = 1.3294720000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.289
y[1] (closed_form) = 0.37572500836927456142559085575504
y[1] (numeric) = 0.37572500836927456142559085575499
absolute error = 5e-32
relative error = 1.3307605000000000000000000000000e-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) = 0.37536128523704065162719117150257
y[1] (numeric) = 0.37536128523704065162719117150252
absolute error = 5e-32
relative error = 1.3320500000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.291
y[1] (closed_form) = 0.37499798438583392614264698327246
y[1] (numeric) = 0.37499798438583392614264698327241
absolute error = 5e-32
relative error = 1.3333405000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.292
y[1] (closed_form) = 0.37463510540733325740728530411379
y[1] (numeric) = 0.37463510540733325740728530411374
absolute error = 5e-32
relative error = 1.3346320000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.293
y[1] (closed_form) = 0.37427264789290113326015055491534
y[1] (numeric) = 0.37427264789290113326015055491529
absolute error = 5e-32
relative error = 1.3359245000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.294
y[1] (closed_form) = 0.37391061143358824066083465822327
y[1] (numeric) = 0.37391061143358824066083465822322
absolute error = 5e-32
relative error = 1.3372180000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.295
y[1] (closed_form) = 0.37354899562013802635388164100074
y[1] (numeric) = 0.37354899562013802635388164100069
absolute error = 5e-32
relative error = 1.3385125000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.296
y[1] (closed_form) = 0.37318780004299123456495259022188
y[1] (numeric) = 0.37318780004299123456495259022183
absolute error = 5e-32
relative error = 1.3398080000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.297
y[1] (closed_form) = 0.37282702429229042181276701405446
y[1] (numeric) = 0.37282702429229042181276701405441
absolute error = 5e-32
relative error = 1.3411045000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.298
y[1] (closed_form) = 0.37246666795788444892066608959164
y[1] (numeric) = 0.37246666795788444892066608959159
absolute error = 5e-32
relative error = 1.3424020000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.299
y[1] (closed_form) = 0.37210673062933295031147193887328
y[1] (numeric) = 0.37210673062933295031147193887323
absolute error = 5e-32
relative error = 1.3437005000000000000000000000000e-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) = 0.37174721189591078066914498141264
y[1] (numeric) = 0.37174721189591078066914498141259
absolute error = 5e-32
relative error = 1.3450000000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.301
y[1] (closed_form) = 0.37138811134661243905056857662907
y[1] (numeric) = 0.37138811134661243905056857662902
absolute error = 5e-32
relative error = 1.3463005000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.302
y[1] (closed_form) = 0.37102942857015647053061660638675
y[1] (numeric) = 0.37102942857015647053061660638671
absolute error = 4e-32
relative error = 1.0780816000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.303
y[1] (closed_form) = 0.37067116315498984546348536905318
y[1] (numeric) = 0.37067116315498984546348536905314
absolute error = 4e-32
relative error = 1.0791236000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.304
y[1] (closed_form) = 0.37031331468929231644309617481158
y[1] (numeric) = 0.37031331468929231644309617481154
absolute error = 4e-32
relative error = 1.0801664000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.305
y[1] (closed_form) = 0.36995588276098075304519935997632
y[1] (numeric) = 0.36995588276098075304519935997628
absolute error = 4e-32
relative error = 1.0812100000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.306
y[1] (closed_form) = 0.36959886695771345443363408825134
y[1] (numeric) = 0.3695988669577134544336340882513
absolute error = 4e-32
relative error = 1.0822544000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.307
y[1] (closed_form) = 0.36924226686689443991302129161683
y[1] (numeric) = 0.3692422668668944399130212916168
absolute error = 3e-32
relative error = 8.1247470000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.308
y[1] (closed_form) = 0.36888608207567771750998943510261
y[1] (numeric) = 0.36888608207567771750998943510258
absolute error = 3e-32
relative error = 8.1325920000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.309
y[1] (closed_form) = 0.36853031217097153066485448027828
y[1] (numeric) = 0.36853031217097153066485448027826
absolute error = 2e-32
relative error = 5.4269620000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.31
y[1] (closed_form) = 0.36817495673944258311549648392916
y[1] (numeric) = 0.36817495673944258311549648392914
absolute error = 2e-32
relative error = 5.4322000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.311
y[1] (closed_form) = 0.36782001536752024205499571305772
y[1] (numeric) = 0.3678200153675202420549957130577
absolute error = 2e-32
relative error = 5.4374420000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.312
y[1] (closed_form) = 0.36746548764140071964441099691917
y[1] (numeric) = 0.36746548764140071964441099691915
absolute error = 2e-32
relative error = 5.4426880000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.313
y[1] (closed_form) = 0.36711137314705123296190228302892
y[1] (numeric) = 0.3671113731470512329619022830289
absolute error = 2e-32
relative error = 5.4479380000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.314
y[1] (closed_form) = 0.3667576714702141424692180286335
y[1] (numeric) = 0.36675767147021414246921802863349
absolute error = 1e-32
relative error = 2.7265960000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.315
y[1] (closed_form) = 0.3664043821964110690763861535784
y[1] (numeric) = 0.36640438219641106907638615357838
absolute error = 2e-32
relative error = 5.4584500000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.316
y[1] (closed_form) = 0.36605150491094698988526481630071
y[1] (numeric) = 0.3660515049109469898852648163007
absolute error = 1e-32
relative error = 2.7318560000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.317
y[1] (closed_form) = 0.36569903919891431269242626318848
y[1] (numeric) = 0.36569903919891431269242626318847
absolute error = 1e-32
relative error = 2.7344890000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.318
y[1] (closed_form) = 0.36534698464519692933166345404885
y[1] (numeric) = 0.36534698464519692933166345404884
absolute error = 1e-32
relative error = 2.7371240000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
memory used=228.0MB, alloc=44.3MB, time=3.38
x[1] = -1.319
y[1] (closed_form) = 0.36499534083447424793622509408667
y[1] (numeric) = 0.36499534083447424793622509408667
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.32
y[1] (closed_form) = 0.36464410735122520420070011668611
y[1] (numeric) = 0.36464410735122520420070011668611
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.321
y[1] (closed_form) = 0.36429328377973225172228757238963
y[1] (numeric) = 0.36429328377973225172228757238962
absolute error = 1e-32
relative error = 2.7450410000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.322
y[1] (closed_form) = 0.36394286970408533150100229866316
y[1] (numeric) = 0.36394286970408533150100229866316
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.323
y[1] (closed_form) = 0.363592864708185820678180683111
y[1] (numeric) = 0.363592864708185820678180683111
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.324
y[1] (closed_form) = 0.36324326837575046059246430045158
y[1] (numeric) = 0.36324326837575046059246430045158
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.325
y[1] (closed_form) = 0.3628940802903152642322522113858
y[1] (numeric) = 0.3628940802903152642322522113858
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.326
y[1] (closed_form) = 0.36254530003523940316342526998748
y[1] (numeric) = 0.36254530003523940316342526998748
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.327
y[1] (closed_form) = 0.36219692719370907401095790583532
y[1] (numeric) = 0.36219692719370907401095790583531
absolute error = 1e-32
relative error = 2.7609290000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.328
y[1] (closed_form) = 0.36184896134874134457284453810704
y[1] (numeric) = 0.36184896134874134457284453810703
absolute error = 1e-32
relative error = 2.7635840000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.329
y[1] (closed_form) = 0.36150140208318797964457905149985
y[1] (numeric) = 0.36150140208318797964457905149984
absolute error = 1e-32
relative error = 2.7662410000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.33
y[1] (closed_form) = 0.36115424897973924663223662826393
y[1] (numeric) = 0.36115424897973924663223662826392
absolute error = 1e-32
relative error = 2.7689000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.331
y[1] (closed_form) = 0.36080750162092770103201769688634
y[1] (numeric) = 0.36080750162092770103201769688633
absolute error = 1e-32
relative error = 2.7715610000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.332
y[1] (closed_form) = 0.36046115958913195185392383599882
y[1] (numeric) = 0.36046115958913195185392383599881
absolute error = 1e-32
relative error = 2.7742240000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.333
y[1] (closed_form) = 0.36011522246658040706704517177316
y[1] (numeric) = 0.36011522246658040706704517177315
absolute error = 1e-32
relative error = 2.7768890000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.334
y[1] (closed_form) = 0.35976968983535499914374813819186
y[1] (numeric) = 0.35976968983535499914374813819184
absolute error = 2e-32
relative error = 5.5591119999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.335
y[1] (closed_form) = 0.35942456127739489077986144183163
y[1] (numeric) = 0.35942456127739489077986144183161
absolute error = 2e-32
relative error = 5.5644500000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.336
y[1] (closed_form) = 0.35907983637450016086776669577607
y[1] (numeric) = 0.35907983637450016086776669577605
absolute error = 2e-32
relative error = 5.5697920000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.337
y[1] (closed_form) = 0.35873551470833547079910847049885
y[1] (numeric) = 0.35873551470833547079910847049882
absolute error = 3e-32
relative error = 8.3627069999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.338
y[1] (closed_form) = 0.35839159586043371117364646245991
y[1] (numeric) = 0.35839159586043371117364646245989
absolute error = 2e-32
relative error = 5.5804880000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.339
y[1] (closed_form) = 0.35804807941219962899058011307874
y[1] (numeric) = 0.35804807941219962899058011307872
absolute error = 2e-32
relative error = 5.5858420000000000000000000000001e-30 %
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) = 0.35770496494491343539848333094863
y[1] (numeric) = 0.35770496494491343539848333094861
absolute error = 2e-32
relative error = 5.5912000000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.341
y[1] (closed_form) = 0.35736225203973439407979398780894
y[1] (numeric) = 0.35736225203973439407979398780892
absolute error = 2e-32
relative error = 5.5965620000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.342
y[1] (closed_form) = 0.35701994027770439034560958298643
y[1] (numeric) = 0.3570199402777043903456095829864
absolute error = 3e-32
relative error = 8.4028920000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.343
y[1] (closed_form) = 0.35667802923975148101634691075809
y[1] (numeric) = 0.35667802923975148101634691075806
absolute error = 3e-32
relative error = 8.4109469999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.344
y[1] (closed_form) = 0.35633651850669342516362972929827
y[1] (numeric) = 0.35633651850669342516362972929825
absolute error = 2e-32
relative error = 5.6126720000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.345
y[1] (closed_form) = 0.35599540765924119578857432739118
y[1] (numeric) = 0.35599540765924119578857432739115
absolute error = 3e-32
relative error = 8.4270749999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.346
y[1] (closed_form) = 0.35565469627800247251144852467319
y[1] (numeric) = 0.35565469627800247251144852467316
absolute error = 3e-32
relative error = 8.4351480000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.347
y[1] (closed_form) = 0.35531438394348511534748503149329
y[1] (numeric) = 0.35531438394348511534748503149326
absolute error = 3e-32
relative error = 8.4432270000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.348
y[1] (closed_form) = 0.35497447023610061964343524413724
y[1] (numeric) = 0.35497447023610061964343524413721
absolute error = 3e-32
relative error = 8.4513120000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.349
y[1] (closed_form) = 0.35463495473616755224925446866641
y[1] (numeric) = 0.35463495473616755224925446866637
absolute error = 4e-32
relative error = 1.1279204000000000000000000000000e-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) = 0.35429583702391496899911426040744
y[1] (numeric) = 0.3542958370239149689991142604074
absolute error = 4e-32
relative error = 1.1290000000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.351
y[1] (closed_form) = 0.35395711667948581357574204454833
y[1] (numeric) = 0.35395711667948581357574204454829
absolute error = 4e-32
relative error = 1.1300804000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.352
y[1] (closed_form) = 0.35361879328294029783189245462364
y[1] (numeric) = 0.35361879328294029783189245462359
absolute error = 5e-32
relative error = 1.4139520000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.353
y[1] (closed_form) = 0.35328086641425926364255889810285
y[1] (numeric) = 0.3532808664142592636425588981028
absolute error = 5e-32
relative error = 1.4153045000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.354
y[1] (closed_form) = 0.35294333565334752636133773994853
y[1] (numeric) = 0.35294333565334752636133773994848
absolute error = 5e-32
relative error = 1.4166580000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.355
y[1] (closed_form) = 0.3526062005800371999541611939246
y[1] (numeric) = 0.35260620058003719995416119392455
absolute error = 5e-32
relative error = 1.4180125000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.356
y[1] (closed_form) = 0.35226946077409100388341853557358
y[1] (numeric) = 0.35226946077409100388341853557353
absolute error = 5e-32
relative error = 1.4193680000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.357
y[1] (closed_form) = 0.35193311581520555181528860803062
y[1] (numeric) = 0.35193311581520555181528860803057
absolute error = 5e-32
relative error = 1.4207245000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.358
y[1] (closed_form) = 0.35159716528301462222290979001211
y[1] (numeric) = 0.35159716528301462222290979001206
absolute error = 5e-32
relative error = 1.4220820000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.359
y[1] (closed_form) = 0.35126160875709241095781664214275
y[1] (numeric) = 0.3512616087570924109578166421427
absolute error = 5e-32
relative error = 1.4234405000000000000000000000000e-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) = 0.35092644581695676586187535092645
y[1] (numeric) = 0.35092644581695676586187535092639
absolute error = 6e-32
relative error = 1.7097600000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.361
y[1] (closed_form) = 0.35059167604207240349175285670862
y[1] (numeric) = 0.35059167604207240349175285670857
absolute error = 5e-32
relative error = 1.4261605000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.362
y[1] (closed_form) = 0.35025729901185410802775719043209
y[1] (numeric) = 0.35025729901185410802775719043204
absolute error = 5e-32
relative error = 1.4275220000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.363
y[1] (closed_form) = 0.34992331430566991243868906129222
y[1] (numeric) = 0.34992331430566991243868906129217
absolute error = 5e-32
relative error = 1.4288845000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.364
y[1] (closed_form) = 0.34958972150284426197414714091542
y[1] (numeric) = 0.34958972150284426197414714091537
absolute error = 5e-32
relative error = 1.4302480000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.365
y[1] (closed_form) = 0.34925652018266116005553178670904
y[1] (numeric) = 0.34925652018266116005553178670899
absolute error = 5e-32
relative error = 1.4316125000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.366
y[1] (closed_form) = 0.34892370992436729663679414478101
y[1] (numeric) = 0.34892370992436729663679414478096
absolute error = 5e-32
relative error = 1.4329780000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.367
y[1] (closed_form) = 0.34859129030717515910577967845242
y[1] (numeric) = 0.34859129030717515910577967845237
absolute error = 5e-32
relative error = 1.4343445000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.368
y[1] (closed_form) = 0.34825926091026612579681718896269
y[1] (numeric) = 0.34825926091026612579681718896264
absolute error = 5e-32
relative error = 1.4357120000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.369
y[1] (closed_form) = 0.34792762131279354218500633750162
y[1] (numeric) = 0.34792762131279354218500633750157
absolute error = 5e-32
relative error = 1.4370805000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.37
y[1] (closed_form) = 0.34759637109388577983245854913275
y[1] (numeric) = 0.34759637109388577983245854913269
absolute error = 6e-32
relative error = 1.7261400000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.371
y[1] (closed_form) = 0.34726550983264927815654798636358
y[1] (numeric) = 0.34726550983264927815654798636352
absolute error = 6e-32
relative error = 1.7277846000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.372
y[1] (closed_form) = 0.34693503710817156909003102986972
y[1] (numeric) = 0.34693503710817156909003102986966
absolute error = 6e-32
relative error = 1.7294304000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.373
y[1] (closed_form) = 0.34660495249952428470269440291925
y[1] (numeric) = 0.34660495249952428470269440291919
absolute error = 6e-32
relative error = 1.7310774000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.374
y[1] (closed_form) = 0.34627525558576614785399373103277
y[1] (numeric) = 0.34627525558576614785399373103272
absolute error = 5e-32
relative error = 1.4439380000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.375
y[1] (closed_form) = 0.34594594594594594594594594594595
y[1] (numeric) = 0.34594594594594594594594594594589
absolute error = 6e-32
relative error = 1.7343750000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.376
y[1] (closed_form) = 0.34561702315910548784534052954058
y[1] (numeric) = 0.34561702315910548784534052954052
absolute error = 6e-32
relative error = 1.7360256000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.377
y[1] (closed_form) = 0.34528848680428254404413615553727
y[1] (numeric) = 0.34528848680428254404413615553721
absolute error = 6e-32
relative error = 1.7376774000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.378
y[1] (closed_form) = 0.34496033646051377012671083078868
y[1] (numeric) = 0.34496033646051377012671083078862
absolute error = 6e-32
relative error = 1.7393304000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.379
y[1] (closed_form) = 0.34463257170683761361243517030535
y[1] (numeric) = 0.3446325717068376136124351703053
absolute error = 5e-32
relative error = 1.4508205000000000000000000000000e-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) = 0.3443051921222972042418399669467
y[1] (numeric) = 0.34430519212229720424183996694665
absolute error = 5e-32
relative error = 1.4522000000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.381
y[1] (closed_form) = 0.34397819728594322777445074421403
y[1] (numeric) = 0.34397819728594322777445074421398
absolute error = 5e-32
relative error = 1.4535805000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.382
y[1] (closed_form) = 0.34365158677683678336616351492341
y[1] (numeric) = 0.34365158677683678336616351492337
absolute error = 4e-32
relative error = 1.1639696000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.383
y[1] (closed_form) = 0.34332536017405222459383751578009
y[1] (numeric) = 0.34332536017405222459383751578005
absolute error = 4e-32
relative error = 1.1650756000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.384
y[1] (closed_form) = 0.34299951705667998419458225402819
y[1] (numeric) = 0.34299951705667998419458225402814
absolute error = 5e-32
relative error = 1.4577280000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
memory used=274.5MB, alloc=44.3MB, time=4.07
x[1] = -1.385
y[1] (closed_form) = 0.34267405700382938258701779335041
y[1] (numeric) = 0.34267405700382938258701779335036
absolute error = 5e-32
relative error = 1.4591125000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.386
y[1] (closed_form) = 0.34234897959463142024158882792034
y[1] (numeric) = 0.34234897959463142024158882792029
absolute error = 5e-32
relative error = 1.4604980000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.387
y[1] (closed_form) = 0.34202428440824155396681475178101
y[1] (numeric) = 0.34202428440824155396681475178096
absolute error = 5e-32
relative error = 1.4618845000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.388
y[1] (closed_form) = 0.34169997102384245717815963129206
y[1] (numeric) = 0.34169997102384245717815963129202
absolute error = 4e-32
relative error = 1.1706176000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.389
y[1] (closed_form) = 0.34137603902064676421600773694655
y[1] (numeric) = 0.34137603902064676421600773694651
absolute error = 4e-32
relative error = 1.1717284000000000000000000000000e-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) = 0.34105248797789979877903209303912
y[1] (numeric) = 0.34105248797789979877903209303908
absolute error = 4e-32
relative error = 1.1728400000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.391
y[1] (closed_form) = 0.34072931747488228653904536504206
y[1] (numeric) = 0.34072931747488228653904536504202
absolute error = 4e-32
relative error = 1.1739524000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.392
y[1] (closed_form) = 0.34040652709091305200322433062461
y[1] (numeric) = 0.34040652709091305200322433062457
absolute error = 4e-32
relative error = 1.1750656000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.393
y[1] (closed_form) = 0.34008411640535169968940117648699
y[1] (numeric) = 0.34008411640535169968940117648696
absolute error = 3e-32
relative error = 8.8213470000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.394
y[1] (closed_form) = 0.33976208499760127967991693496546
y[1] (numeric) = 0.33976208499760127967991693496543
absolute error = 3e-32
relative error = 8.8297080000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.395
y[1] (closed_form) = 0.33944043244711093761933452703219
y[1] (numeric) = 0.33944043244711093761933452703216
absolute error = 3e-32
relative error = 8.8380749999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.396
y[1] (closed_form) = 0.3391191583333785492211111171399
y[1] (numeric) = 0.33911915833337854922111111713987
absolute error = 3e-32
relative error = 8.8464479999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.397
y[1] (closed_form) = 0.33879826223595333934813181556229
y[1] (numeric) = 0.33879826223595333934813181556227
absolute error = 2e-32
relative error = 5.9032180000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.398
y[1] (closed_form) = 0.33847774373443848573180919061848
y[1] (numeric) = 0.33847774373443848573180919061846
absolute error = 2e-32
relative error = 5.9088080000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.399
y[1] (closed_form) = 0.33815760240849370739425558154485
y[1] (numeric) = 0.33815760240849370739425558154483
absolute error = 2e-32
relative error = 5.9144019999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.4
y[1] (closed_form) = 0.33783783783783783783783783783784
y[1] (numeric) = 0.33783783783783783783783783783782
absolute error = 2e-32
relative error = 5.9200000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.401
y[1] (closed_form) = 0.3375184496022513830662268576256
y[1] (numeric) = 0.33751844960225138306622685762559
absolute error = 1e-32
relative error = 2.9628010000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.402
y[1] (closed_form) = 0.33719943728157906450085716096957
y[1] (numeric) = 0.33719943728157906450085716096955
absolute error = 2e-32
relative error = 5.9312080000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.403
y[1] (closed_form) = 0.33688080045573234685651471882749
y[1] (numeric) = 0.33688080045573234685651471882747
absolute error = 2e-32
relative error = 5.9368180000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.404
y[1] (closed_form) = 0.33656253870469195103957436955105
y[1] (numeric) = 0.33656253870469195103957436955103
absolute error = 2e-32
relative error = 5.9424320000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.405
y[1] (closed_form) = 0.33624465160851035213221139701247
y[1] (numeric) = 0.33624465160851035213221139701244
absolute error = 3e-32
relative error = 8.9220749999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.406
y[1] (closed_form) = 0.33592713874731426252571522247111
y[1] (numeric) = 0.33592713874731426252571522247108
absolute error = 3e-32
relative error = 8.9305079999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.407
y[1] (closed_form) = 0.33560999970130710026583668076341
y[1] (numeric) = 0.33560999970130710026583668076338
absolute error = 3e-32
relative error = 8.9389469999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.408
y[1] (closed_form) = 0.3352932340507714426729040149353
y[1] (numeric) = 0.33529323405077144267290401493528
absolute error = 2e-32
relative error = 5.9649280000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.409
y[1] (closed_form) = 0.33497684137607146529924653659069
y[1] (numeric) = 0.33497684137607146529924653659067
absolute error = 2e-32
relative error = 5.9705620000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.41
y[1] (closed_form) = 0.3346608212576553662862688665038
y[1] (numeric) = 0.33466082125765536628626886650378
absolute error = 2e-32
relative error = 5.9762000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.411
y[1] (closed_form) = 0.33434517327605777618332279588796
y[1] (numeric) = 0.33434517327605777618332279588794
absolute error = 2e-32
relative error = 5.9818419999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.412
y[1] (closed_form) = 0.33402989701190215329032809752604
y[1] (numeric) = 0.33402989701190215329032809752603
absolute error = 1e-32
relative error = 2.9937440000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.413
y[1] (closed_form) = 0.33371499204590316458589807209512
y[1] (numeric) = 0.33371499204590316458589807209511
absolute error = 1e-32
relative error = 2.9965690000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.414
y[1] (closed_form) = 0.33340045795886905230253024275554
y[1] (numeric) = 0.33340045795886905230253024275553
absolute error = 1e-32
relative error = 2.9993960000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.415
y[1] (closed_form) = 0.33308629433170398621022741466745
y[1] (numeric) = 0.33308629433170398621022741466744
absolute error = 1e-32
relative error = 3.0022250000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.416
y[1] (closed_form) = 0.33277250074541040166971929974017
y[1] (numeric) = 0.33277250074541040166971929974016
absolute error = 1e-32
relative error = 3.0050560000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.417
y[1] (closed_form) = 0.33245907678109132351626007475675
y[1] (numeric) = 0.33245907678109132351626007475674
absolute error = 1e-32
relative error = 3.0078890000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.418
y[1] (closed_form) = 0.33214602201995267583478259714275
y[1] (numeric) = 0.33214602201995267583478259714274
absolute error = 1e-32
relative error = 3.0107240000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.419
y[1] (closed_form) = 0.33183333604330557768699555111046
y[1] (numeric) = 0.33183333604330557768699555111046
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.42
y[1] (closed_form) = 0.33152101843256862485081554170534
y[1] (numeric) = 0.33152101843256862485081554170534
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.421
y[1] (closed_form) = 0.33120906876927015763233209935875
y[1] (numeric) = 0.33120906876927015763233209935874
absolute error = 1e-32
relative error = 3.0192410000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.422
y[1] (closed_form) = 0.33089748663505051481030970681159
y[1] (numeric) = 0.33089748663505051481030970681158
absolute error = 1e-32
relative error = 3.0220840000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.423
y[1] (closed_form) = 0.3305862716116642737730373175701
y[1] (numeric) = 0.33058627161166427377303731757009
absolute error = 1e-32
relative error = 3.0249290000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.424
y[1] (closed_form) = 0.33027542328098247690714240419371
y[1] (numeric) = 0.3302754232809824769071424041937
absolute error = 1e-32
relative error = 3.0277760000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.425
y[1] (closed_form) = 0.32996494122499484429779335945556
y[1] (numeric) = 0.32996494122499484429779335945555
absolute error = 1e-32
relative error = 3.0306250000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.426
y[1] (closed_form) = 0.3296548250258119727995210774702
y[1] (numeric) = 0.32965482502581197279952107747019
absolute error = 1e-32
relative error = 3.0334760000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.427
y[1] (closed_form) = 0.32934507426566752153669776891766
y[1] (numeric) = 0.32934507426566752153669776891765
absolute error = 1e-32
relative error = 3.0363290000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.428
y[1] (closed_form) = 0.32903568852692038389251851812855
y[1] (numeric) = 0.32903568852692038389251851812854
absolute error = 1e-32
relative error = 3.0391840000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.429
y[1] (closed_form) = 0.32872666739205684604513877360627
y[1] (numeric) = 0.32872666739205684604513877360626
absolute error = 1e-32
relative error = 3.0420410000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.43
y[1] (closed_form) = 0.32841801044369273210942888107984
y[1] (numeric) = 0.32841801044369273210942888107983
absolute error = 1e-32
relative error = 3.0449000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.431
y[1] (closed_form) = 0.32810971726457553594261492288929
y[1] (numeric) = 0.32810971726457553594261492288929
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.432
y[1] (closed_form) = 0.32780178743758653967188352284647
y[1] (numeric) = 0.32780178743758653967188352284647
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.433
y[1] (closed_form) = 0.32749422054574291900183691508304
y[1] (numeric) = 0.32749422054574291900183691508304
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.434
y[1] (closed_form) = 0.32718701617219983535949346214904
y[1] (numeric) = 0.32718701617219983535949346214904
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.435
y[1] (closed_form) = 0.32688017390025251493433794506779
y[1] (numeric) = 0.32688017390025251493433794506778
absolute error = 1e-32
relative error = 3.0592250000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.436
y[1] (closed_form) = 0.32657369331333831467073533945376
y[1] (numeric) = 0.32657369331333831467073533945375
absolute error = 1e-32
relative error = 3.0620960000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.437
y[1] (closed_form) = 0.32626757399503877526983144038325
y[1] (numeric) = 0.32626757399503877526983144038324
absolute error = 1e-32
relative error = 3.0649690000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.438
y[1] (closed_form) = 0.3259618155290816612578736076541
y[1] (numeric) = 0.3259618155290816612578736076541
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.439
y[1] (closed_form) = 0.32565641749934298817769507552135
y[1] (numeric) = 0.32565641749934298817769507552135
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.44
y[1] (closed_form) = 0.32535137948984903695991671004685
y[1] (numeric) = 0.32535137948984903695991671004685
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.441
y[1] (closed_form) = 0.32504670108477835553023080591104
y[1] (numeric) = 0.32504670108477835553023080591104
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.442
y[1] (closed_form) = 0.32474238186846374770894249591799
y[1] (numeric) = 0.32474238186846374770894249591799
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.443
y[1] (closed_form) = 0.32443842142539424945875560345709
y[1] (numeric) = 0.32443842142539424945875560345709
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.444
y[1] (closed_form) = 0.3241348193402170925366013037999
y[1] (numeric) = 0.3241348193402170925366013037999
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.445
y[1] (closed_form) = 0.32383157519773965560511977720388
y[1] (numeric) = 0.32383157519773965560511977720388
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.446
y[1] (closed_form) = 0.32352868858293140285921713822051
y[1] (numeric) = 0.32352868858293140285921713822052
absolute error = 1e-32
relative error = 3.0909160000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.447
y[1] (closed_form) = 0.32322615908092581022293231417971
y[1] (numeric) = 0.32322615908092581022293231417971
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.448
y[1] (closed_form) = 0.32292398627702227917166122432108
y[1] (numeric) = 0.32292398627702227917166122432109
absolute error = 1e-32
relative error = 3.0967040000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.449
y[1] (closed_form) = 0.32262216975668803823459858220461
y[1] (numeric) = 0.32262216975668803823459858220462
absolute error = 1e-32
relative error = 3.0996010000000000000000000000000e-30 %
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) = 0.322320709105560032232070910556
y[1] (numeric) = 0.32232070910556003223207091055601
absolute error = 1e-32
relative error = 3.1025000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
memory used=321.1MB, alloc=44.3MB, time=4.74
x[1] = -1.451
y[1] (closed_form) = 0.32201960390944679930224792224901
y[1] (numeric) = 0.32201960390944679930224792224902
absolute error = 1e-32
relative error = 3.1054010000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.452
y[1] (closed_form) = 0.32171885375433033577153328631948
y[1] (numeric) = 0.32171885375433033577153328631949
absolute error = 1e-32
relative error = 3.1083040000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.453
y[1] (closed_form) = 0.32141845822636794892274996633142
y[1] (numeric) = 0.32141845822636794892274996633142
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.454
y[1] (closed_form) = 0.32111841691189409771504979262173
y[1] (numeric) = 0.32111841691189409771504979262173
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.455
y[1] (closed_form) = 0.32081872939742222150929171245017
y[1] (numeric) = 0.32081872939742222150929171245018
absolute error = 1e-32
relative error = 3.1170250000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.456
y[1] (closed_form) = 0.32051939526964655685244825534883
y[1] (numeric) = 0.32051939526964655685244825534883
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.457
y[1] (closed_form) = 0.32022041411544394237441515744117
y[1] (numeric) = 0.32022041411544394237441515744117
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.458
y[1] (closed_form) = 0.31992178552187561185041481058711
y[1] (numeric) = 0.31992178552187561185041481058711
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.459
y[1] (closed_form) = 0.31962350907618897548200024227462
y[1] (numeric) = 0.31962350907618897548200024227462
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.46
y[1] (closed_form) = 0.31932558436581938944948269255333
y[1] (numeric) = 0.31932558436581938944948269255333
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.461
y[1] (closed_form) = 0.3190280109783919137884225372872
y[1] (numeric) = 0.3190280109783919137884225372872
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.462
y[1] (closed_form) = 0.31873078850172305864264031485502
y[1] (numeric) = 0.31873078850172305864264031485503
absolute error = 1e-32
relative error = 3.1374440000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.463
y[1] (closed_form) = 0.31843391652382251894602194837613
y[1] (numeric) = 0.31843391652382251894602194837614
absolute error = 1e-32
relative error = 3.1403690000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.464
y[1] (closed_form) = 0.31813739463289489758520991977847
y[1] (numeric) = 0.31813739463289489758520991977848
absolute error = 1e-32
relative error = 3.1432960000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.465
y[1] (closed_form) = 0.31784122241734141709509014771671
y[1] (numeric) = 0.31784122241734141709509014771671
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.466
y[1] (closed_form) = 0.31754539946576161993880265061496
y[1] (numeric) = 0.31754539946576161993880265061496
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.467
y[1] (closed_form) = 0.3172499253669550574238227410457
y[1] (numeric) = 0.3172499253669550574238227410457
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.468
y[1] (closed_form) = 0.31695479970992296730547850032203
y[1] (numeric) = 0.31695479970992296730547850032203
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.469
y[1] (closed_form) = 0.31666002208386994012908962460271
y[1] (numeric) = 0.31666002208386994012908962460271
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.47
y[1] (closed_form) = 0.31636559207820557436173241798222
y[1] (numeric) = 0.31636559207820557436173241798222
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.471
y[1] (closed_form) = 0.31607150928254612036445573592352
y[1] (numeric) = 0.31607150928254612036445573592352
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.472
y[1] (closed_form) = 0.31577777328671611325559305592045
y[1] (numeric) = 0.31577777328671611325559305592046
absolute error = 1e-32
relative error = 3.1667840000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.473
y[1] (closed_form) = 0.31548438368074999471563657334744
y[1] (numeric) = 0.31548438368074999471563657334744
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.474
y[1] (closed_form) = 0.31519134005489372378396029093421
y[1] (numeric) = 0.31519134005489372378396029093422
absolute error = 1e-32
relative error = 3.1726760000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.475
y[1] (closed_form) = 0.31489864199960637669750049202913
y[1] (numeric) = 0.31489864199960637669750049202913
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.476
y[1] (closed_form) = 0.31460628910556173582132376259054
y[1] (numeric) = 0.31460628910556173582132376259055
absolute error = 1e-32
relative error = 3.1785760000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.477
y[1] (closed_form) = 0.31431428096364986772083485644795
y[1] (numeric) = 0.31431428096364986772083485644796
absolute error = 1e-32
relative error = 3.1815290000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.478
y[1] (closed_form) = 0.31402261716497869042519918454607
y[1] (numeric) = 0.31402261716497869042519918454607
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.479
y[1] (closed_form) = 0.31373129730087552993137755334138
y[1] (numeric) = 0.31373129730087552993137755334138
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.48
y[1] (closed_form) = 0.31344032096288866599799398194584
y[1] (numeric) = 0.31344032096288866599799398194584
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.481
y[1] (closed_form) = 0.31314968774278886727808099366154
y[1] (numeric) = 0.31314968774278886727808099366154
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.482
y[1] (closed_form) = 0.31285939723257091583957070684949
y[1] (numeric) = 0.3128593972325709158395707068495
absolute error = 1e-32
relative error = 3.1963240000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.483
y[1] (closed_form) = 0.31256944902445512112222434422148
y[1] (numeric) = 0.31256944902445512112222434422149
absolute error = 1e-32
relative error = 3.1992890000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.484
y[1] (closed_form) = 0.31227984271088882337951744020466
y[1] (numeric) = 0.31227984271088882337951744020466
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.485
y[1] (closed_form) = 0.31199057788454788665382305454375
y[1] (numeric) = 0.31199057788454788665382305454376
absolute error = 1e-32
relative error = 3.2052250000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.486
y[1] (closed_form) = 0.31170165413833818133306069828651
y[1] (numeric) = 0.31170165413833818133306069828652
absolute error = 1e-32
relative error = 3.2081960000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.487
y[1] (closed_form) = 0.31141307106539705633680444722779
y[1] (numeric) = 0.31141307106539705633680444722779
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.488
y[1] (closed_form) = 0.31112482825909480097966985922224
y[1] (numeric) = 0.31112482825909480097966985922224
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.489
y[1] (closed_form) = 0.31083692531303609655962582694279
y[1] (numeric) = 0.31083692531303609655962582694279
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.49
y[1] (closed_form) = 0.31054936182106145771870438806248
y[1] (numeric) = 0.31054936182106145771870438806249
absolute error = 1e-32
relative error = 3.2201000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.491
y[1] (closed_form) = 0.31026213737724866362340878184569
y[1] (numeric) = 0.3102621373772486636234087818457
absolute error = 1e-32
relative error = 3.2230810000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.492
y[1] (closed_form) = 0.30997525157591417901194768609674
y[1] (numeric) = 0.30997525157591417901194768609675
absolute error = 1e-32
relative error = 3.2260640000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.493
y[1] (closed_form) = 0.30968870401161456515525159265158
y[1] (numeric) = 0.30968870401161456515525159265159
absolute error = 1e-32
relative error = 3.2290490000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.494
y[1] (closed_form) = 0.30940249427914788077855568440451
y[1] (numeric) = 0.30940249427914788077855568440451
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.495
y[1] (closed_form) = 0.30911662197355507299016236350569
y[1] (numeric) = 0.3091166219735550729901623635057
absolute error = 1e-32
relative error = 3.2350250000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.496
y[1] (closed_form) = 0.30883108669012135826382575008894
y[1] (numeric) = 0.30883108669012135826382575008895
absolute error = 1e-32
relative error = 3.2380160000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.497
y[1] (closed_form) = 0.30854588802437759352103002490891
y[1] (numeric) = 0.30854588802437759352103002490892
absolute error = 1e-32
relative error = 3.2410090000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.498
y[1] (closed_form) = 0.30826102557210163735926342877506
y[1] (numeric) = 0.30826102557210163735926342877507
absolute error = 1e-32
relative error = 3.2440040000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.499
y[1] (closed_form) = 0.30797649892931970147222005783183
y[1] (numeric) = 0.30797649892931970147222005783184
absolute error = 1e-32
relative error = 3.2470010000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.5
y[1] (closed_form) = 0.30769230769230769230769230769231
y[1] (numeric) = 0.30769230769230769230769230769232
absolute error = 1e-32
relative error = 3.2500000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.501
y[1] (closed_form) = 0.30740845145759254300874792230313
y[1] (numeric) = 0.30740845145759254300874792230314
absolute error = 1e-32
relative error = 3.2530010000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.502
y[1] (closed_form) = 0.30712492982195353568361709629349
y[1] (numeric) = 0.3071249298219535356836170962935
absolute error = 1e-32
relative error = 3.2560040000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.503
y[1] (closed_form) = 0.30684174238242361404954696350946
y[1] (numeric) = 0.30684174238242361404954696350947
absolute error = 1e-32
relative error = 3.2590090000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.504
y[1] (closed_form) = 0.30655888873629068649571308049991
y[1] (numeric) = 0.30655888873629068649571308049992
absolute error = 1e-32
relative error = 3.2620160000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.505
y[1] (closed_form) = 0.30627636848109891961011018292356
y[1] (numeric) = 0.30627636848109891961011018292357
absolute error = 1e-32
relative error = 3.2650250000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.506
y[1] (closed_form) = 0.30599418121465002221517755618359
y[1] (numeric) = 0.3059941812146500222151775561836
absolute error = 1e-32
relative error = 3.2680360000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.507
y[1] (closed_form) = 0.30571232653500451995674782004183
y[1] (numeric) = 0.30571232653500451995674782004184
absolute error = 1e-32
relative error = 3.2710490000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.508
y[1] (closed_form) = 0.30543080404048302049074178146792
y[1] (numeric) = 0.30543080404048302049074178146794
absolute error = 2e-32
relative error = 6.5481280000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.509
y[1] (closed_form) = 0.30514961332966746931186626146867
y[1] (numeric) = 0.30514961332966746931186626146868
absolute error = 1e-32
relative error = 3.2770810000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.51
y[1] (closed_form) = 0.30486875400140239626840645102283
y[1] (numeric) = 0.30486875400140239626840645102285
absolute error = 2e-32
relative error = 6.5602000000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.511
y[1] (closed_form) = 0.30458822565479615280703939940075
y[1] (numeric) = 0.30458822565479615280703939940077
absolute error = 2e-32
relative error = 6.5662420000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.512
y[1] (closed_form) = 0.30430802788922213999143068593464
y[1] (numeric) = 0.30430802788922213999143068593466
absolute error = 2e-32
relative error = 6.5722880000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.513
y[1] (closed_form) = 0.30402816030432002733821217456446
y[1] (numeric) = 0.30402816030432002733821217456448
absolute error = 2e-32
relative error = 6.5783379999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.514
y[1] (closed_form) = 0.30374862249999696251377500003037
y[1] (numeric) = 0.3037486224999969625137750000304
absolute error = 3e-32
relative error = 9.8765880000000000000000000000002e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.515
y[1] (closed_form) = 0.30346941407642877193514858621187
y[1] (numeric) = 0.30346941407642877193514858621189
absolute error = 2e-32
relative error = 6.5904499999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.516
y[1] (closed_form) = 0.30319053463406115231807355159818
y[1] (numeric) = 0.3031905346340611523180735515982
absolute error = 2e-32
relative error = 6.5965120000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
memory used=367.7MB, alloc=44.3MB, time=5.42
x[1] = -1.517
y[1] (closed_form) = 0.30291198377361085321521381496743
y[1] (numeric) = 0.30291198377361085321521381496745
absolute error = 2e-32
relative error = 6.6025779999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.518
y[1] (closed_form) = 0.30263376109606685058729107678303
y[1] (numeric) = 0.30263376109606685058729107678305
absolute error = 2e-32
relative error = 6.6086479999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.519
y[1] (closed_form) = 0.30235586620269151144976311929662
y[1] (numeric) = 0.30235586620269151144976311929665
absolute error = 3e-32
relative error = 9.9220830000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.52
y[1] (closed_form) = 0.30207829869502174963750604156597
y[1] (numeric) = 0.302078298695021749637506041566
absolute error = 3e-32
relative error = 9.9312000000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.521
y[1] (closed_form) = 0.30180105817487017272979962522345
y[1] (numeric) = 0.30180105817487017272979962522347
absolute error = 2e-32
relative error = 6.6268819999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.522
y[1] (closed_form) = 0.30152414424432622017775451351492
y[1] (numeric) = 0.30152414424432622017775451351494
absolute error = 2e-32
relative error = 6.6329679999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.523
y[1] (closed_form) = 0.30124755650575729267615978049898
y[1] (numeric) = 0.30124755650575729267615978049901
absolute error = 3e-32
relative error = 9.9585870000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.524
y[1] (closed_form) = 0.30097129456180987282156976996162
y[1] (numeric) = 0.30097129456180987282156976996165
absolute error = 3e-32
relative error = 9.9677280000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.525
y[1] (closed_form) = 0.30069535801541063709828979515129
y[1] (numeric) = 0.30069535801541063709828979515132
absolute error = 3e-32
relative error = 9.9768749999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.526
y[1] (closed_form) = 0.30041974646976755923376141144407
y[1] (numeric) = 0.3004197464697675592337614114441
absolute error = 3e-32
relative error = 9.9860280000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.527
y[1] (closed_form) = 0.30014445952837100496468950505878
y[1] (numeric) = 0.30014445952837100496468950505882
absolute error = 4e-32
relative error = 1.3326916000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.528
y[1] (closed_form) = 0.29986949679499481825509538248954
y[1] (numeric) = 0.29986949679499481825509538248958
absolute error = 4e-32
relative error = 1.3339136000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.529
y[1] (closed_form) = 0.29959485787369739900732239792129
y[1] (numeric) = 0.29959485787369739900732239792133
absolute error = 4e-32
relative error = 1.3351364000000000000000000000000e-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) = 0.29932054236882277230686342003652
y[1] (numeric) = 0.29932054236882277230686342003656
absolute error = 4e-32
relative error = 1.3363600000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.531
y[1] (closed_form) = 0.2990465498850016492417226157841
y[1] (numeric) = 0.29904654988500164924172261578414
absolute error = 4e-32
relative error = 1.3375844000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.532
y[1] (closed_form) = 0.29877288002715247933686761732213
y[1] (numeric) = 0.29877288002715247933686761732218
absolute error = 5e-32
relative error = 1.6735120000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.533
y[1] (closed_form) = 0.29849953240048249464417213990434
y[1] (numeric) = 0.29849953240048249464417213990439
absolute error = 5e-32
relative error = 1.6750445000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.534
y[1] (closed_form) = 0.29822650661048874552809353337572
y[1] (numeric) = 0.29822650661048874552809353337577
absolute error = 5e-32
relative error = 1.6765780000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.535
y[1] (closed_form) = 0.29795380226295912818717457858159
y[1] (numeric) = 0.29795380226295912818717457858164
absolute error = 5e-32
relative error = 1.6781125000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.536
y[1] (closed_form) = 0.2976814189639734039513040827602
y[1] (numeric) = 0.29768141896397340395130408276025
absolute error = 5e-32
relative error = 1.6796480000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.537
y[1] (closed_form) = 0.29740935631990421039451648525192
y[1] (numeric) = 0.29740935631990421039451648525197
absolute error = 5e-32
relative error = 1.6811845000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.538
y[1] (closed_form) = 0.29713761393741806430295675696877
y[1] (numeric) = 0.29713761393741806430295675696882
absolute error = 5e-32
relative error = 1.6827220000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.539
y[1] (closed_form) = 0.2968661914234763565374833643608
y[1] (numeric) = 0.29686619142347635653748336436085
absolute error = 5e-32
relative error = 1.6842605000000000000000000000000e-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) = 0.29659508838533633883022897140823
y[1] (numeric) = 0.29659508838533633883022897140829
absolute error = 6e-32
relative error = 2.0229600000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.541
y[1] (closed_form) = 0.29632430443055210255428587176092
y[1] (numeric) = 0.29632430443055210255428587176097
absolute error = 5e-32
relative error = 1.6873405000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.542
y[1] (closed_form) = 0.29605383916697554950553087782332
y[1] (numeric) = 0.29605383916697554950553087782337
absolute error = 5e-32
relative error = 1.6888820000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.543
y[1] (closed_form) = 0.29578369220275735473545254461231
y[1] (numeric) = 0.29578369220275735473545254461237
absolute error = 6e-32
relative error = 2.0285094000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.544
y[1] (closed_form) = 0.29551386314634792147369217384726
y[1] (numeric) = 0.29551386314634792147369217384731
absolute error = 5e-32
relative error = 1.6919680000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.545
y[1] (closed_form) = 0.29524435160649832817885902820322
y[1] (numeric) = 0.29524435160649832817885902820327
absolute error = 5e-32
relative error = 1.6935125000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.546
y[1] (closed_form) = 0.29497515719226126775602958718817
y[1] (numeric) = 0.29497515719226126775602958718822
absolute error = 5e-32
relative error = 1.6950580000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.547
y[1] (closed_form) = 0.29470627951299197897919049489731
y[1] (numeric) = 0.29470627951299197897919049489736
absolute error = 5e-32
relative error = 1.6966045000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.548
y[1] (closed_form) = 0.2944377181783491701567350861407
y[1] (numeric) = 0.29443771817834917015673508614075
absolute error = 5e-32
relative error = 1.6981520000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.549
y[1] (closed_form) = 0.29416947279829593507797403130728
y[1] (numeric) = 0.29416947279829593507797403130733
absolute error = 5e-32
relative error = 1.6997005000000000000000000000000e-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) = 0.29390154298310066127847171197649
y[1] (numeric) = 0.29390154298310066127847171197654
absolute error = 5e-32
relative error = 1.7012500000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.551
y[1] (closed_form) = 0.29363392834333793066187142886087
y[1] (numeric) = 0.29363392834333793066187142886092
absolute error = 5e-32
relative error = 1.7028005000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.552
y[1] (closed_form) = 0.29336662848988941251572445128706
y[1] (numeric) = 0.29336662848988941251572445128711
absolute error = 5e-32
relative error = 1.7043520000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.553
y[1] (closed_form) = 0.29309964303394474895869024321115
y[1] (numeric) = 0.2930996430339447489586902432112
absolute error = 5e-32
relative error = 1.7059045000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.554
y[1] (closed_form) = 0.29283297158700243285632794481621
y[1] (numeric) = 0.29283297158700243285632794481626
absolute error = 5e-32
relative error = 1.7074580000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.555
y[1] (closed_form) = 0.29256661376087067824255235113845
y[1] (numeric) = 0.2925666137608706782425523511385
absolute error = 5e-32
relative error = 1.7090125000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.556
y[1] (closed_form) = 0.29230056916766828328368120998405
y[1] (numeric) = 0.2923005691676682832836812099841
absolute error = 5e-32
relative error = 1.7105680000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.557
y[1] (closed_form) = 0.29203483741982548582185466068618
y[1] (numeric) = 0.29203483741982548582185466068623
absolute error = 5e-32
relative error = 1.7121245000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.558
y[1] (closed_form) = 0.29176941813008481153446205305302
y[1] (numeric) = 0.29176941813008481153446205305306
absolute error = 4e-32
relative error = 1.3709456000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.559
y[1] (closed_form) = 0.29150431091150191474606622220033
y[1] (numeric) = 0.29150431091150191474606622220037
absolute error = 4e-32
relative error = 1.3721924000000000000000000000000e-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) = 0.2912395153774464119291705498602
y[1] (numeric) = 0.29123951537744641192917054986025
absolute error = 5e-32
relative error = 1.7168000000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.561
y[1] (closed_form) = 0.29097503114160270793002981621144
y[1] (numeric) = 0.29097503114160270793002981621149
absolute error = 5e-32
relative error = 1.7183605000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.562
y[1] (closed_form) = 0.29071085781797081495556193827394
y[1] (numeric) = 0.29071085781797081495556193827399
absolute error = 5e-32
relative error = 1.7199220000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.563
y[1] (closed_form) = 0.29044699502086716435727420142325
y[1] (numeric) = 0.29044699502086716435727420142329
absolute error = 4e-32
relative error = 1.3771876000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.564
y[1] (closed_form) = 0.29018344236492541124797451957229
y[1] (numeric) = 0.29018344236492541124797451957233
absolute error = 4e-32
relative error = 1.3784384000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.565
y[1] (closed_form) = 0.28992019946509723198689560698418
y[1] (numeric) = 0.28992019946509723198689560698421
absolute error = 3e-32
relative error = 1.0347675000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.566
y[1] (closed_form) = 0.28965726593665311456871771045628
y[1] (numeric) = 0.28965726593665311456871771045631
absolute error = 3e-32
relative error = 1.0357068000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.567
y[1] (closed_form) = 0.28939464139518314195183373467547
y[1] (numeric) = 0.2893946413951831419518337346755
absolute error = 3e-32
relative error = 1.0366467000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.568
y[1] (closed_form) = 0.28913232545659776836105919579578
y[1] (numeric) = 0.28913232545659776836105919579582
absolute error = 4e-32
relative error = 1.3834496000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.569
y[1] (closed_form) = 0.28887031773712858859984845863132
y[1] (numeric) = 0.28887031773712858859984845863135
absolute error = 3e-32
relative error = 1.0385283000000000000000000000000e-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) = 0.28860861785332910040693815117319
y[1] (numeric) = 0.28860861785332910040693815117323
absolute error = 4e-32
relative error = 1.3859600000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.571
y[1] (closed_form) = 0.2883472254220754598921985063037
y[1] (numeric) = 0.28834722542207545989219850630374
absolute error = 4e-32
relative error = 1.3872164000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.572
y[1] (closed_form) = 0.28808614006056723008633365445335
y[1] (numeric) = 0.28808614006056723008633365445339
absolute error = 4e-32
relative error = 1.3884736000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.573
y[1] (closed_form) = 0.28782536138632812263893258237778
y[1] (numeric) = 0.28782536138632812263893258237782
absolute error = 4e-32
relative error = 1.3897316000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.574
y[1] (closed_form) = 0.28756488901720673269923358205779
y[1] (numeric) = 0.28756488901720673269923358205783
absolute error = 4e-32
relative error = 1.3909904000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.575
y[1] (closed_form) = 0.28730472257137726701382653977375
y[1] (numeric) = 0.28730472257137726701382653977379
absolute error = 4e-32
relative error = 1.3922500000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.576
y[1] (closed_form) = 0.28704486166734026527537935848918
y[1] (numeric) = 0.28704486166734026527537935848922
absolute error = 4e-32
relative error = 1.3935104000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.577
y[1] (closed_form) = 0.28678530592392331475633716660133
y[1] (numeric) = 0.28678530592392331475633716660137
absolute error = 4e-32
relative error = 1.3947716000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.578
y[1] (closed_form) = 0.2865260549602817582614057426698
y[1] (numeric) = 0.28652605496028175826140574266985
absolute error = 5e-32
relative error = 1.7450420000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.579
y[1] (closed_form) = 0.28626710839589939543249377870007
y[1] (numeric) = 0.28626710839589939543249377870011
absolute error = 4e-32
relative error = 1.3972964000000000000000000000000e-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) = 0.28600846585058917743965221370553
y[1] (numeric) = 0.28600846585058917743965221370557
absolute error = 4e-32
relative error = 1.3985600000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.581
y[1] (closed_form) = 0.28575012694449389509141289436018
y[1] (numeric) = 0.28575012694449389509141289436022
absolute error = 4e-32
relative error = 1.3998244000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.582
y[1] (closed_form) = 0.2854920912980868603977932603311
y[1] (numeric) = 0.28549209129808686039779326033114
absolute error = 4e-32
relative error = 1.4010896000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
memory used=414.2MB, alloc=44.3MB, time=6.10
x[1] = -1.583
y[1] (closed_form) = 0.28523435853217258161909860808485
y[1] (numeric) = 0.28523435853217258161909860808489
absolute error = 4e-32
relative error = 1.4023556000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.584
y[1] (closed_form) = 0.28497692826788743183351875832133
y[1] (numeric) = 0.28497692826788743183351875832136
absolute error = 3e-32
relative error = 1.0527168000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.585
y[1] (closed_form) = 0.28471980012670031105638163842009
y[1] (numeric) = 0.28471980012670031105638163842012
absolute error = 3e-32
relative error = 1.0536675000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.586
y[1] (closed_form) = 0.28446297373041330194379239209466
y[1] (numeric) = 0.28446297373041330194379239209469
absolute error = 3e-32
relative error = 1.0546188000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.587
y[1] (closed_form) = 0.28420644870116231911325314353648
y[1] (numeric) = 0.28420644870116231911325314353651
absolute error = 3e-32
relative error = 1.0555707000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.588
y[1] (closed_form) = 0.28395022466141775211372547237959
y[1] (numeric) = 0.28395022466141775211372547237963
absolute error = 4e-32
relative error = 1.4086976000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.589
y[1] (closed_form) = 0.28369430123398510207746499850635
y[1] (numeric) = 0.28369430123398510207746499850639
absolute error = 4e-32
relative error = 1.4099684000000000000000000000000e-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) = 0.28343867804200561208582523171112
y[1] (numeric) = 0.28343867804200561208582523171116
absolute error = 4e-32
relative error = 1.4112400000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.591
y[1] (closed_form) = 0.2831833547089568912810960102014
y[1] (numeric) = 0.28318335470895689128109601020144
absolute error = 4e-32
relative error = 1.4125124000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.592
y[1] (closed_form) = 0.28292833085865353275631043349147
y[1] (numeric) = 0.28292833085865353275631043349151
absolute error = 4e-32
relative error = 1.4137856000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.593
y[1] (closed_form) = 0.28267360611524772525482318907274
y[1] (numeric) = 0.28267360611524772525482318907278
absolute error = 4e-32
relative error = 1.4150596000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.594
y[1] (closed_form) = 0.28241918010322985871133257795617
y[1] (numeric) = 0.2824191801032298587113325779562
absolute error = 3e-32
relative error = 1.0622508000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.595
y[1] (closed_form) = 0.282165052447429123665888361397
y[1] (numeric) = 0.28216505244742912366588836139703
absolute error = 3e-32
relative error = 1.0632075000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.596
y[1] (closed_form) = 0.28191122277301410458229777944168
y[1] (numeric) = 0.28191122277301410458229777944171
absolute error = 3e-32
relative error = 1.0641648000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.597
y[1] (closed_form) = 0.28165769070549336710221273098395
y[1] (numeric) = 0.28165769070549336710221273098398
absolute error = 3e-32
relative error = 1.0651227000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.598
y[1] (closed_form) = 0.28140445587071603926605215437623
y[1] (numeric) = 0.28140445587071603926605215437626
absolute error = 3e-32
relative error = 1.0660812000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.599
y[1] (closed_form) = 0.28115151789487238673178510689802
y[1] (numeric) = 0.28115151789487238673178510689805
absolute error = 3e-32
relative error = 1.0670403000000000000000000000000e-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) = 0.28089887640449438202247191011236
y[1] (numeric) = 0.28089887640449438202247191011239
absolute error = 3e-32
relative error = 1.0680000000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.601
y[1] (closed_form) = 0.28064653102645626783333300591238
y[1] (numeric) = 0.28064653102645626783333300591241
absolute error = 3e-32
relative error = 1.0689603000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.602
y[1] (closed_form) = 0.28039448138797511442898785443264
y[1] (numeric) = 0.28039448138797511442898785443267
absolute error = 3e-32
relative error = 1.0699212000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.603
y[1] (closed_form) = 0.28014272711661137116137929952552
y[1] (numeric) = 0.28014272711661137116137929952555
absolute error = 3e-32
relative error = 1.0708827000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.604
y[1] (closed_form) = 0.27989126784026941213877232972535
y[1] (numeric) = 0.27989126784026941213877232972538
absolute error = 3e-32
relative error = 1.0718448000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.605
y[1] (closed_form) = 0.27964010318719807607609007207724
y[1] (numeric) = 0.27964010318719807607609007207727
absolute error = 3e-32
relative error = 1.0728075000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.606
y[1] (closed_form) = 0.27938923278599120035672417242115
y[1] (numeric) = 0.27938923278599120035672417242119
absolute error = 4e-32
relative error = 1.4316944000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.607
y[1] (closed_form) = 0.27913865626558814933583143821447
y[1] (numeric) = 0.27913865626558814933583143821451
absolute error = 4e-32
relative error = 1.4329796000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.608
y[1] (closed_form) = 0.27888837325527433691500374825974
y[1] (numeric) = 0.27888837325527433691500374825977
absolute error = 3e-32
relative error = 1.0756992000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.609
y[1] (closed_form) = 0.27863838338468174341807376728289
y[1] (numeric) = 0.27863838338468174341807376728293
absolute error = 4e-32
relative error = 1.4355524000000000000000000000000e-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) = 0.27838868628378942679769494167757
y[1] (numeric) = 0.27838868628378942679769494167761
absolute error = 4e-32
relative error = 1.4368400000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.611
y[1] (closed_form) = 0.27813928158292402820221059538216
y[1] (numeric) = 0.2781392815829240282022105953822
absolute error = 4e-32
relative error = 1.4381284000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.612
y[1] (closed_form) = 0.27789016891276027193220369127069
y[1] (numeric) = 0.27789016891276027193220369127073
absolute error = 4e-32
relative error = 1.4394176000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.613
y[1] (closed_form) = 0.27764134790432145981599597308989
y[1] (numeric) = 0.27764134790432145981599597308993
absolute error = 4e-32
relative error = 1.4407076000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.614
y[1] (closed_form) = 0.27739281818897996003324275533177
y[1] (numeric) = 0.27739281818897996003324275533181
absolute error = 4e-32
relative error = 1.4419984000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.615
y[1] (closed_form) = 0.27714457939845769041564758295284
y[1] (numeric) = 0.27714457939845769041564758295288
absolute error = 4e-32
relative error = 1.4432900000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.616
y[1] (closed_form) = 0.27689663116482659625369933899236
y[1] (numeric) = 0.27689663116482659625369933899241
absolute error = 5e-32
relative error = 1.8057280000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.617
y[1] (closed_form) = 0.27664897312050912263821313534857
y[1] (numeric) = 0.27664897312050912263821313534862
absolute error = 5e-32
relative error = 1.8073445000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.618
y[1] (closed_form) = 0.27640160489827868136533547968393
y[1] (numeric) = 0.27640160489827868136533547968398
absolute error = 5e-32
relative error = 1.8089620000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.619
y[1] (closed_form) = 0.27615452613126011243355376908124
y[1] (numeric) = 0.27615452613126011243355376908129
absolute error = 5e-32
relative error = 1.8105805000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.62
y[1] (closed_form) = 0.27590773645293014016113011808851
y[1] (numeric) = 0.27590773645293014016113011808856
absolute error = 5e-32
relative error = 1.8122000000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.621
y[1] (closed_form) = 0.27566123549711782395225988459167
y[1] (numeric) = 0.27566123549711782395225988459172
absolute error = 5e-32
relative error = 1.8138205000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.622
y[1] (closed_form) = 0.27541502289800500374013601095491
y[1] (numeric) = 0.27541502289800500374013601095496
absolute error = 5e-32
relative error = 1.8154420000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.623
y[1] (closed_form) = 0.27516909829012674013498144947524
y[1] (numeric) = 0.27516909829012674013498144947529
absolute error = 5e-32
relative error = 1.8170645000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.624
y[1] (closed_form) = 0.27492346130837174930499348981244
y[1] (numeric) = 0.27492346130837174930499348981249
absolute error = 5e-32
relative error = 1.8186880000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.625
y[1] (closed_form) = 0.27467811158798283261802575107296
y[1] (numeric) = 0.27467811158798283261802575107302
absolute error = 6e-32
relative error = 2.1843750000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.626
y[1] (closed_form) = 0.27443304876455730107171594203535
y[1] (numeric) = 0.27443304876455730107171594203541
absolute error = 6e-32
relative error = 2.1863256000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.627
y[1] (closed_form) = 0.27418827247404739453965022898834
y[1] (numeric) = 0.2741882724740473945396502289884
absolute error = 6e-32
relative error = 2.1882774000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.628
y[1] (closed_form) = 0.27394378235276069586103818118861
y[1] (numeric) = 0.27394378235276069586103818118867
absolute error = 6e-32
relative error = 2.1902304000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.629
y[1] (closed_form) = 0.27369957803736053980125578840395
y[1] (numeric) = 0.27369957803736053980125578840401
absolute error = 6e-32
relative error = 2.1921846000000000000000000000000e-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) = 0.27345565916486641691049796275534
y[1] (numeric) = 0.2734556591648664169104979627554
absolute error = 6e-32
relative error = 2.1941400000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.631
y[1] (closed_form) = 0.27321202537265437230766624746835
y[1] (numeric) = 0.27321202537265437230766624746841
absolute error = 6e-32
relative error = 2.1960966000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.632
y[1] (closed_form) = 0.27296867629845739941650215754442
y[1] (numeric) = 0.27296867629845739941650215754448
absolute error = 6e-32
relative error = 2.1980544000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.633
y[1] (closed_form) = 0.27272561158036582868086167111528
y[1] (numeric) = 0.27272561158036582868086167111534
absolute error = 6e-32
relative error = 2.2000134000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.634
y[1] (closed_form) = 0.27248283085682771128591187469278
y[1] (numeric) = 0.27248283085682771128591187469284
absolute error = 6e-32
relative error = 2.2019736000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.635
y[1] (closed_form) = 0.2722403337666491979119166400098
y[1] (numeric) = 0.27224033376664919791191664000987
absolute error = 7e-32
relative error = 2.5712575000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.636
y[1] (closed_form) = 0.27199811994899491254716447399916
y[1] (numeric) = 0.27199811994899491254716447399923
absolute error = 7e-32
relative error = 2.5735472000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.637
y[1] (closed_form) = 0.27175618904338832138647833600424
y[1] (numeric) = 0.27175618904338832138647833600432
absolute error = 8e-32
relative error = 2.9438152000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.638
y[1] (closed_form) = 0.27151454068971209684163425688099
y[1] (numeric) = 0.27151454068971209684163425688107
absolute error = 8e-32
relative error = 2.9464352000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.639
y[1] (closed_form) = 0.27127317452820847668990302255284
y[1] (numeric) = 0.27127317452820847668990302255291
absolute error = 7e-32
relative error = 2.5804247000000000000000000000000e-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) = 0.2710320901994796183868169991327
y[1] (numeric) = 0.27103209019947961838681699913277
absolute error = 7e-32
relative error = 2.5827200000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.641
y[1] (closed_form) = 0.27079128734448794856915237723609
y[1] (numeric) = 0.27079128734448794856915237723617
absolute error = 8e-32
relative error = 2.9543048000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.642
y[1] (closed_form) = 0.27055076560455650777400569888133
y[1] (numeric) = 0.2705507656045565077740056988814
absolute error = 7e-32
relative error = 2.5873148000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.643
y[1] (closed_form) = 0.27031052462136929039973250070483
y[1] (numeric) = 0.27031052462136929039973250070491
absolute error = 8e-32
relative error = 2.9595592000000000000000000000001e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.644
y[1] (closed_form) = 0.2700705640369715799344052614067
y[1] (numeric) = 0.27007056403697157993440526140678
absolute error = 8e-32
relative error = 2.9621888000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.645
y[1] (closed_form) = 0.26983088349377027947733757867257
y[1] (numeric) = 0.26983088349377027947733757867265
absolute error = 8e-32
relative error = 2.9648200000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.646
y[1] (closed_form) = 0.2695914826345342375791116205791
y[1] (numeric) = 0.26959148263453423757911162057919
absolute error = 9e-32
relative error = 3.3383844000000000000000000000001e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.647
y[1] (closed_form) = 0.26935236110239456942543639796165
y[1] (numeric) = 0.26935236110239456942543639796174
absolute error = 9e-32
relative error = 3.3413481000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.648
y[1] (closed_form) = 0.26911351854084497339005528668125
y[1] (numeric) = 0.26911351854084497339005528668134
absolute error = 9e-32
relative error = 3.3443136000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
memory used=460.8MB, alloc=44.3MB, time=6.77
x[1] = -1.649
y[1] (closed_form) = 0.26887495459374204298181249144642
y[1] (numeric) = 0.26887495459374204298181249144651
absolute error = 9e-32
relative error = 3.3472808999999999999999999999999e-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) = 0.26863666890530557421087978509066
y[1] (numeric) = 0.26863666890530557421087978509076
absolute error = 1.0e-31
relative error = 3.7225000000000000000000000000001e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.651
y[1] (closed_form) = 0.26839866112011886839903687824444
y[1] (numeric) = 0.26839866112011886839903687824453
absolute error = 9e-32
relative error = 3.3532209000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.652
y[1] (closed_form) = 0.26816093088312903045879117342933
y[1] (numeric) = 0.26816093088312903045879117342942
absolute error = 9e-32
relative error = 3.3561936000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.653
y[1] (closed_form) = 0.26792347783964726266601543399986
y[1] (numeric) = 0.26792347783964726266601543399996
absolute error = 1.0e-31
relative error = 3.7324090000000000000000000000001e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.654
y[1] (closed_form) = 0.26768630163534915395067505131546
y[1] (numeric) = 0.26768630163534915395067505131556
absolute error = 1.0e-31
relative error = 3.7357160000000000000000000000001e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.655
y[1] (closed_form) = 0.26744940191627496473011012229124
y[1] (numeric) = 0.26744940191627496473011012229134
absolute error = 1.0e-31
relative error = 3.7390250000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.656
y[1] (closed_form) = 0.26721277832882990730923145329548
y[1] (numeric) = 0.26721277832882990730923145329558
absolute error = 1.0e-31
relative error = 3.7423360000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.657
y[1] (closed_form) = 0.26697643051978442187188388447503
y[1] (numeric) = 0.26697643051978442187188388447513
absolute error = 1.0e-31
relative error = 3.7456490000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.658
y[1] (closed_form) = 0.26674035813627444808752498023454
y[1] (numeric) = 0.26674035813627444808752498023464
absolute error = 1.0e-31
relative error = 3.7489640000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.659
y[1] (closed_form) = 0.26650456082580169235726215600591
y[1] (numeric) = 0.26650456082580169235726215600601
absolute error = 1.0e-31
relative error = 3.7522810000000000000000000000000e-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) = 0.26626903823623389072318670784961
y[1] (numeric) = 0.26626903823623389072318670784971
absolute error = 1.0e-31
relative error = 3.7556000000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.661
y[1] (closed_form) = 0.26603379001580506746483897905809
y[1] (numeric) = 0.26603379001580506746483897905818
absolute error = 9e-32
relative error = 3.3830289000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.662
y[1] (closed_form) = 0.26579881581311578940653503600511
y[1] (numeric) = 0.2657988158131157894065350360052
absolute error = 9e-32
relative error = 3.3860196000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.663
y[1] (closed_form) = 0.26556411527713341595918173322544
y[1] (numeric) = 0.26556411527713341595918173322554
absolute error = 1.0e-31
relative error = 3.7655690000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.664
y[1] (closed_form) = 0.26532968805719234492010392433222
y[1] (numeric) = 0.26532968805719234492010392433231
absolute error = 9e-32
relative error = 3.3920064000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.665
y[1] (closed_form) = 0.26509553380299425405430482009954
y[1] (numeric) = 0.26509553380299425405430482009964
absolute error = 1.0e-31
relative error = 3.7722250000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.666
y[1] (closed_form) = 0.26486165216460833848047810706556
y[1] (numeric) = 0.26486165216460833848047810706565
absolute error = 9e-32
relative error = 3.3980003999999999999999999999999e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.667
y[1] (closed_form) = 0.26462804279247154388498841855371
y[1] (numeric) = 0.2646280427924715438849884185538
absolute error = 9e-32
relative error = 3.4010001000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.668
y[1] (closed_form) = 0.26439470533738879558693509427258
y[1] (numeric) = 0.26439470533738879558693509427267
absolute error = 9e-32
relative error = 3.4040016000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.669
y[1] (closed_form) = 0.26416163945053322347731287383825
y[1] (numeric) = 0.26416163945053322347731287383834
absolute error = 9e-32
relative error = 3.4070049000000000000000000000000e-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) = 0.26392884478344638285518224286732
y[1] (numeric) = 0.26392884478344638285518224286741
absolute error = 9e-32
relative error = 3.4100100000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.671
y[1] (closed_form) = 0.26369632098803847118366158690864
y[1] (numeric) = 0.26369632098803847118366158690872
absolute error = 8e-32
relative error = 3.0337928000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.672
y[1] (closed_form) = 0.26346406771658854078845310761137
y[1] (numeric) = 0.26346406771658854078845310761145
absolute error = 8e-32
relative error = 3.0364672000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.673
y[1] (closed_form) = 0.26323208462174470752151461635635
y[1] (numeric) = 0.26323208462174470752151461635643
absolute error = 8e-32
relative error = 3.0391432000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.674
y[1] (closed_form) = 0.26300037135652435541238984229446
y[1] (numeric) = 0.26300037135652435541238984229454
absolute error = 8e-32
relative error = 3.0418208000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.675
y[1] (closed_form) = 0.26276892757431433732961077352603
y[1] (numeric) = 0.26276892757431433732961077352611
absolute error = 8e-32
relative error = 3.0445000000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.676
y[1] (closed_form) = 0.26253775292887117167448679120057
y[1] (numeric) = 0.26253775292887117167448679120065
absolute error = 8e-32
relative error = 3.0471808000000000000000000000001e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.677
y[1] (closed_form) = 0.26230684707432123512949695579789
y[1] (numeric) = 0.26230684707432123512949695579796
absolute error = 7e-32
relative error = 2.6686303000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.678
y[1] (closed_form) = 0.26207620966516095148340376194674
y[1] (numeric) = 0.26207620966516095148340376194682
absolute error = 8e-32
relative error = 3.0525472000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.679
y[1] (closed_form) = 0.26184584035625697655510899202182
y[1] (numeric) = 0.2618458403562569765551089920219
absolute error = 8e-32
relative error = 3.0552328000000000000000000000000e-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) = 0.26161573880284637923817496860611
y[1] (numeric) = 0.26161573880284637923817496860619
absolute error = 8e-32
relative error = 3.0579200000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.681
y[1] (closed_form) = 0.26138590466053681868783753088601
y[1] (numeric) = 0.26138590466053681868783753088609
absolute error = 8e-32
relative error = 3.0606088000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.682
y[1] (closed_form) = 0.26115633758530671767224043932764
y[1] (numeric) = 0.26115633758530671767224043932772
absolute error = 8e-32
relative error = 3.0632992000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.683
y[1] (closed_form) = 0.26092703723350543210952464573284
y[1] (numeric) = 0.26092703723350543210952464573292
absolute error = 8e-32
relative error = 3.0659912000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.684
y[1] (closed_form) = 0.26069800326185341681230995115562
y[1] (numeric) = 0.2606980032618534168123099511557
absolute error = 8e-32
relative error = 3.0686848000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.685
y[1] (closed_form) = 0.26046923532744238746101101133692
y[1] (numeric) = 0.260469235327442387461011011337
absolute error = 8e-32
relative error = 3.0713800000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.686
y[1] (closed_form) = 0.26024073308773547882733443744802
y[1] (numeric) = 0.26024073308773547882733443744809
absolute error = 7e-32
relative error = 2.6898172000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.687
y[1] (closed_form) = 0.26001249620056739926920887817869
y[1] (numeric) = 0.26001249620056739926920887817876
absolute error = 7e-32
relative error = 2.6921783000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.688
y[1] (closed_form) = 0.25978452432414458151830545672198
y[1] (numeric) = 0.25978452432414458151830545672205
absolute error = 7e-32
relative error = 2.6945408000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.689
y[1] (closed_form) = 0.25955681711704532978121177214753
y[1] (numeric) = 0.2595568171170453297812117721476
absolute error = 7e-32
relative error = 2.6969047000000000000000000000000e-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) = 0.25932937423821996317522885817277
y[1] (numeric) = 0.25932937423821996317522885817284
absolute error = 7e-32
relative error = 2.6992700000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.691
y[1] (closed_form) = 0.25910219534699095551966702258672
y[1] (numeric) = 0.25910219534699095551966702258679
absolute error = 7e-32
relative error = 2.7016367000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.692
y[1] (closed_form) = 0.25887528010305307150342336670408
y[1] (numeric) = 0.25887528010305307150342336670416
absolute error = 8e-32
relative error = 3.0902912000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.693
y[1] (closed_form) = 0.25864862816647349924953100537498
y[1] (numeric) = 0.25864862816647349924953100537505
absolute error = 7e-32
relative error = 2.7063743000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.694
y[1] (closed_form) = 0.2584222391976919792972775733945
y[1] (numeric) = 0.25842223919769197929727757339457
absolute error = 7e-32
relative error = 2.7087452000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.695
y[1] (closed_form) = 0.25819611285752093002239851279039
y[1] (numeric) = 0.25819611285752093002239851279046
absolute error = 7e-32
relative error = 2.7111175000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.696
y[1] (closed_form) = 0.25797024880714556951575888655913
y[1] (numeric) = 0.2579702488071455695157588865592
absolute error = 7e-32
relative error = 2.7134912000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.697
y[1] (closed_form) = 0.25774464670812403394084605711261
y[1] (numeric) = 0.25774464670812403394084605711267
absolute error = 6e-32
relative error = 2.3278854000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.698
y[1] (closed_form) = 0.25751930622238749239030450112845
y[1] (numeric) = 0.25751930622238749239030450112851
absolute error = 6e-32
relative error = 2.3299224000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.699
y[1] (closed_form) = 0.25729422701224025826165330580628
y[1] (numeric) = 0.25729422701224025826165330580634
absolute error = 6e-32
relative error = 2.3319606000000000000000000000000e-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) = 0.25706940874035989717223650385604
y[1] (numeric) = 0.2570694087403598971722365038561
absolute error = 6e-32
relative error = 2.3340000000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.701
y[1] (closed_form) = 0.25684485106979733143336635501969
y[1] (numeric) = 0.25684485106979733143336635501974
absolute error = 5e-32
relative error = 1.9467005000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.702
y[1] (closed_form) = 0.25662055366397694110352996968798
y[1] (numeric) = 0.25662055366397694110352996968803
absolute error = 5e-32
relative error = 1.9484020000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.703
y[1] (closed_form) = 0.25639651618669666164044029435346
y[1] (numeric) = 0.25639651618669666164044029435351
absolute error = 5e-32
relative error = 1.9501045000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.704
y[1] (closed_form) = 0.25617273830212807817162343837099
y[1] (numeric) = 0.25617273830212807817162343837104
absolute error = 5e-32
relative error = 1.9518080000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.705
y[1] (closed_form) = 0.2559492196748165164031456159098
y[1] (numeric) = 0.25594921967481651640314561590986
absolute error = 6e-32
relative error = 2.3442150000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.706
y[1] (closed_form) = 0.25572595996968113018599460520515
y[1] (numeric) = 0.2557259599696811301859946052052
absolute error = 5e-32
relative error = 1.9552180000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.707
y[1] (closed_form) = 0.25550295885201498575954258838294
y[1] (numeric) = 0.255502958852014985759542588383
absolute error = 6e-32
relative error = 2.3483094000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.708
y[1] (closed_form) = 0.2552802159874851426914295283647
y[1] (numeric) = 0.25528021598748514269142952836475
absolute error = 5e-32
relative error = 1.9586320000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.709
y[1] (closed_form) = 0.25505773104213273153311886378922
y[1] (numeric) = 0.25505773104213273153311886378928
absolute error = 6e-32
relative error = 2.3524086000000000000000000000000e-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) = 0.25483550368237302821029025763869
y[1] (numeric) = 0.25483550368237302821029025763875
absolute error = 6e-32
relative error = 2.3544600000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.711
y[1] (closed_form) = 0.25461353357499552516714741945365
y[1] (numeric) = 0.2546135335749955251671474194537
absolute error = 5e-32
relative error = 1.9637605000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.712
y[1] (closed_form) = 0.25439182038716399928363263378975
y[1] (numeric) = 0.2543918203871639992836326337898
absolute error = 5e-32
relative error = 1.9654720000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.713
y[1] (closed_form) = 0.25417036378641657658445356803086
y[1] (numeric) = 0.25417036378641657658445356803091
absolute error = 5e-32
relative error = 1.9671845000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.714
y[1] (closed_form) = 0.25394916344066579375874219995144
y[1] (numeric) = 0.2539491634406657937587421999515
absolute error = 6e-32
relative error = 2.3626776000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
memory used=507.5MB, alloc=44.3MB, time=7.44
x[1] = -1.715
y[1] (closed_form) = 0.25372821901819865650908029863811
y[1] (numeric) = 0.25372821901819865650908029863817
absolute error = 6e-32
relative error = 2.3647350000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.716
y[1] (closed_form) = 0.25350753018767669474854081065624
y[1] (numeric) = 0.2535075301876766947485408106563
absolute error = 6e-32
relative error = 2.3667936000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.717
y[1] (closed_form) = 0.2532870966181360146643097458036
y[1] (numeric) = 0.25328709661813601466430974580366
absolute error = 6e-32
relative error = 2.3688534000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.718
y[1] (closed_form) = 0.25306691797898734766636872254857
y[1] (numeric) = 0.25306691797898734766636872254862
absolute error = 5e-32
relative error = 1.9757620000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.719
y[1] (closed_form) = 0.25284699394001609623963422142469
y[1] (numeric) = 0.25284699394001609623963422142474
absolute error = 5e-32
relative error = 1.9774805000000000000000000000000e-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) = 0.2526273241713823767178658043654
y[1] (numeric) = 0.25262732417138237671786580436545
absolute error = 5e-32
relative error = 1.9792000000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.721
y[1] (closed_form) = 0.25240790834362105899757208832964
y[1] (numeric) = 0.25240790834362105899757208832969
absolute error = 5e-32
relative error = 1.9809205000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.722
y[1] (closed_form) = 0.25218874612764180321006011170953
y[1] (numeric) = 0.25218874612764180321006011170957
absolute error = 4e-32
relative error = 1.5861136000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.723
y[1] (closed_form) = 0.25196983719472909336969090104162
y[1] (numeric) = 0.25196983719472909336969090104166
absolute error = 4e-32
relative error = 1.5874916000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.724
y[1] (closed_form) = 0.25175118121654226801632153258063
y[1] (numeric) = 0.25175118121654226801632153258067
absolute error = 4e-32
relative error = 1.5888704000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.725
y[1] (closed_form) = 0.2515327778651155478698317874548
y[1] (numeric) = 0.25153277786511554786983178745484
absolute error = 4e-32
relative error = 1.5902500000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.726
y[1] (closed_form) = 0.25131462681285806051455161952172
y[1] (numeric) = 0.25131462681285806051455161952176
absolute error = 4e-32
relative error = 1.5916304000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.727
y[1] (closed_form) = 0.25109672773255386213132409079758
y[1] (numeric) = 0.25109672773255386213132409079762
absolute error = 4e-32
relative error = 1.5930116000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.728
y[1] (closed_form) = 0.25087908029736195629485717955717
y[1] (numeric) = 0.25087908029736195629485717955721
absolute error = 4e-32
relative error = 1.5943936000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.729
y[1] (closed_form) = 0.250661684180816309853936930011
y[1] (numeric) = 0.25066168418081630985393693001104
absolute error = 4e-32
relative error = 1.5957764000000000000000000000000e-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) = 0.25044453905682586591199378897543
y[1] (numeric) = 0.25044453905682586591199378897547
absolute error = 4e-32
relative error = 1.5971600000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.731
y[1] (closed_form) = 0.25022764459967455392543366327516
y[1] (numeric) = 0.2502276445996745539254336632752
absolute error = 4e-32
relative error = 1.5985444000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.732
y[1] (closed_form) = 0.25001100048402129693706523087016
y[1] (numeric) = 0.25001100048402129693706523087019
absolute error = 3e-32
relative error = 1.1999472000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.733
y[1] (closed_form) = 0.24979460638490001596187534799511
y[1] (numeric) = 0.24979460638490001596187534799514
absolute error = 3e-32
relative error = 1.2009867000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.734
y[1] (closed_form) = 0.24957846197771963154232501305295
y[1] (numeric) = 0.24957846197771963154232501305298
absolute error = 3e-32
relative error = 1.2020268000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.735
y[1] (closed_form) = 0.24936256693826406249025927472897
y[1] (numeric) = 0.249362566938264062490259274729
absolute error = 3e-32
relative error = 1.2030675000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.736
y[1] (closed_form) = 0.24914692094269222183244570590299
y[1] (numeric) = 0.24914692094269222183244570590301
absolute error = 2e-32
relative error = 8.0273919999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.737
y[1] (closed_form) = 0.24893152366753800997667760554759
y[1] (numeric) = 0.24893152366753800997667760554761
absolute error = 2e-32
relative error = 8.0343379999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.738
y[1] (closed_form) = 0.24871637478971030511529993702501
y[1] (numeric) = 0.24871637478971030511529993702504
absolute error = 3e-32
relative error = 1.2061932000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.739
y[1] (closed_form) = 0.24850147398649295088293816214771
y[1] (numeric) = 0.24850147398649295088293816214773
absolute error = 2e-32
relative error = 8.0482420000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.74
y[1] (closed_form) = 0.24828682093554474128513258516238
y[1] (numeric) = 0.2482868209355447412851325851624
absolute error = 2e-32
relative error = 8.0552000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.741
y[1] (closed_form) = 0.24807241531489940291450357856863
y[1] (numeric) = 0.24807241531489940291450357856865
absolute error = 2e-32
relative error = 8.0621619999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.742
y[1] (closed_form) = 0.24785825680296557447099612250543
y[1] (numeric) = 0.24785825680296557447099612250545
absolute error = 2e-32
relative error = 8.0691280000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.743
y[1] (closed_form) = 0.24764434507852678360267545044649
y[1] (numeric) = 0.24764434507852678360267545044651
absolute error = 2e-32
relative error = 8.0760980000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.744
y[1] (closed_form) = 0.24743067982074142108346925525345
y[1] (numeric) = 0.24743067982074142108346925525347
absolute error = 2e-32
relative error = 8.0830719999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.745
y[1] (closed_form) = 0.24721726070914271234417587035927
y[1] (numeric) = 0.24721726070914271234417587035929
absolute error = 2e-32
relative error = 8.0900500000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.746
y[1] (closed_form) = 0.24700408742363868637298210010779
y[1] (numeric) = 0.24700408742363868637298210010781
absolute error = 2e-32
relative error = 8.0970320000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.747
y[1] (closed_form) = 0.24679115964451214200165893017513
y[1] (numeric) = 0.24679115964451214200165893017515
absolute error = 2e-32
relative error = 8.1040180000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.748
y[1] (closed_form) = 0.24657847705242061159352820265989
y[1] (numeric) = 0.24657847705242061159352820265991
absolute error = 2e-32
relative error = 8.1110080000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.749
y[1] (closed_form) = 0.24636603932839632214921848996834
y[1] (numeric) = 0.24636603932839632214921848996836
absolute error = 2e-32
relative error = 8.1180020000000000000000000000001e-30 %
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) = 0.24615384615384615384615384615385
y[1] (numeric) = 0.24615384615384615384615384615386
absolute error = 1e-32
relative error = 4.0624999999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.751
y[1] (closed_form) = 0.24594189721055159602764485301405
y[1] (numeric) = 0.24594189721055159602764485301407
absolute error = 2e-32
relative error = 8.1320020000000000000000000000002e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.752
y[1] (closed_form) = 0.24573019218066870065737741012172
y[1] (numeric) = 0.24573019218066870065737741012174
absolute error = 2e-32
relative error = 8.1390080000000000000000000000002e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.753
y[1] (closed_form) = 0.24551873074672803325502104218282
y[1] (numeric) = 0.24551873074672803325502104218283
absolute error = 1e-32
relative error = 4.0730090000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.754
y[1] (closed_form) = 0.2453075125916346213286051127973
y[1] (numeric) = 0.24530751259163462132860511279731
absolute error = 1e-32
relative error = 4.0765160000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.755
y[1] (closed_form) = 0.24509653739866790031923823996176
y[1] (numeric) = 0.24509653739866790031923823996177
absolute error = 1e-32
relative error = 4.0800250000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.756
y[1] (closed_form) = 0.24488580485148165707367340461796
y[1] (numeric) = 0.24488580485148165707367340461796
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.757
y[1] (closed_form) = 0.24467531463410397086014872833675
y[1] (numeric) = 0.24467531463410397086014872833675
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.758
y[1] (closed_form) = 0.24446506643093715194286166895323
y[1] (numeric) = 0.24446506643093715194286166895323
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.759
y[1] (closed_form) = 0.24425505992675767773036244275577
y[1] (numeric) = 0.24425505992675767773036244275577
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.76
y[1] (closed_form) = 0.24404529480671612651308082780164
y[1] (numeric) = 0.24404529480671612651308082780164
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.761
y[1] (closed_form) = 0.24383577075633710880512913420501
y[1] (numeric) = 0.24383577075633710880512913420501
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.762
y[1] (closed_form) = 0.24362648746151919630545304294355
y[1] (numeric) = 0.24362648746151919630545304294355
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.763
y[1] (closed_form) = 0.24341744460853484849333121397878
y[1] (numeric) = 0.24341744460853484849333121397878
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.764
y[1] (closed_form) = 0.2432086418840303368731540464081
y[1] (numeric) = 0.2432086418840303368731540464081
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.765
y[1] (closed_form) = 0.24300007897502566688334173708606
y[1] (numeric) = 0.24300007897502566688334173708606
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.766
y[1] (closed_form) = 0.24279175556891449748419182879491
y[1] (numeric) = 0.2427917555689144974841918287949
absolute error = 1e-32
relative error = 4.1187560000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.767
y[1] (closed_form) = 0.24258367135346405843937676373491
y[1] (numeric) = 0.2425836713534640584393767637349
absolute error = 1e-32
relative error = 4.1222889999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.768
y[1] (closed_form) = 0.24237582601681506530574256197065
y[1] (numeric) = 0.24237582601681506530574256197065
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.769
y[1] (closed_form) = 0.24216821924748163214599062663691
y[1] (numeric) = 0.2421682192474816321459906266369
absolute error = 1e-32
relative error = 4.1293609999999999999999999999999e-30 %
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) = 0.24196085073435118197875583730552
y[1] (numeric) = 0.24196085073435118197875583730552
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.771
y[1] (closed_form) = 0.24175372016668435498052552907197
y[1] (numeric) = 0.24175372016668435498052552907197
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.772
y[1] (closed_form) = 0.24154682723411491445377566676586
y[1] (numeric) = 0.24154682723411491445377566676586
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.773
y[1] (closed_form) = 0.2413401716266496505756325103553
y[1] (numeric) = 0.2413401716266496505756325103553
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.774
y[1] (closed_form) = 0.24113375303466828194130032823126
y[1] (numeric) = 0.24113375303466828194130032823126
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.775
y[1] (closed_form) = 0.24092757114892335491642824875772
y[1] (numeric) = 0.24092757114892335491642824875771
absolute error = 1e-32
relative error = 4.1506250000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.776
y[1] (closed_form) = 0.24072162566054014081252214638956
y[1] (numeric) = 0.24072162566054014081252214638955
absolute error = 1e-32
relative error = 4.1541760000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.777
y[1] (closed_form) = 0.24051591626101653089944053592719
y[1] (numeric) = 0.24051591626101653089944053592717
absolute error = 2e-32
relative error = 8.3154579999999999999999999999998e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.778
y[1] (closed_form) = 0.24031044264222292926894679622924
y[1] (numeric) = 0.24031044264222292926894679622923
absolute error = 1e-32
relative error = 4.1612840000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.779
y[1] (closed_form) = 0.24010520449640214356322366207978
y[1] (numeric) = 0.24010520449640214356322366207977
absolute error = 1e-32
relative error = 4.1648409999999999999999999999999e-30 %
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) = 0.23990020151616927358218980903944
y[1] (numeric) = 0.23990020151616927358218980903943
absolute error = 1e-32
relative error = 4.1684000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
memory used=554.0MB, alloc=44.3MB, time=8.13
x[1] = -1.781
y[1] (closed_form) = 0.23969543339451159778339251014091
y[1] (numeric) = 0.2396954333945115977833925101409
absolute error = 1e-32
relative error = 4.1719610000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.782
y[1] (closed_form) = 0.23949089982478845768818476435532
y[1] (numeric) = 0.23949089982478845768818476435531
absolute error = 1e-32
relative error = 4.1755240000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.783
y[1] (closed_form) = 0.2392866005007311402078299839989
y[1] (numeric) = 0.23928660050073114020782998399889
absolute error = 1e-32
relative error = 4.1790890000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.784
y[1] (closed_form) = 0.23908253511644275790311228080913
y[1] (numeric) = 0.23908253511644275790311228080912
absolute error = 1e-32
relative error = 4.1826560000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.785
y[1] (closed_form) = 0.23887870336639812719096560743868
y[1] (numeric) = 0.23887870336639812719096560743867
absolute error = 1e-32
relative error = 4.1862250000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.786
y[1] (closed_form) = 0.23867510494544364451157049173755
y[1] (numeric) = 0.23867510494544364451157049173753
absolute error = 2e-32
relative error = 8.3795919999999999999999999999998e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.787
y[1] (closed_form) = 0.23847173954879716046930284456245
y[1] (numeric) = 0.23847173954879716046930284456244
absolute error = 1e-32
relative error = 4.1933690000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.788
y[1] (closed_form) = 0.2382686068720478519608553271142
y[1] (numeric) = 0.23826860687204785196085532711419
absolute error = 1e-32
relative error = 4.1969440000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.789
y[1] (closed_form) = 0.23806570661115609230378803010388
y[1] (numeric) = 0.23806570661115609230378803010387
absolute error = 1e-32
relative error = 4.2005210000000000000000000000001e-30 %
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) = 0.23786303846245331937870174353607
y[1] (numeric) = 0.23786303846245331937870174353606
absolute error = 1e-32
relative error = 4.2041000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.791
y[1] (closed_form) = 0.23766060212264190179816388172012
y[1] (numeric) = 0.23766060212264190179816388172011
absolute error = 1e-32
relative error = 4.2076810000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.792
y[1] (closed_form) = 0.23745839728879500311545417242899
y[1] (numeric) = 0.23745839728879500311545417242898
absolute error = 1e-32
relative error = 4.2112640000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.793
y[1] (closed_form) = 0.23725642365835644408613452107062
y[1] (numeric) = 0.23725642365835644408613452107061
absolute error = 1e-32
relative error = 4.2148490000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.794
y[1] (closed_form) = 0.23705468092914056299538501947167
y[1] (numeric) = 0.23705468092914056299538501947166
absolute error = 1e-32
relative error = 4.2184360000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.795
y[1] (closed_form) = 0.23685316879933207406398588355114
y[1] (numeric) = 0.23685316879933207406398588355113
absolute error = 1e-32
relative error = 4.2220250000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.796
y[1] (closed_form) = 0.23665188696748592394576317393724
y[1] (numeric) = 0.23665188696748592394576317393723
absolute error = 1e-32
relative error = 4.2256160000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.797
y[1] (closed_form) = 0.23645083513252714632925447761035
y[1] (numeric) = 0.23645083513252714632925447761034
absolute error = 1e-32
relative error = 4.2292090000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.798
y[1] (closed_form) = 0.23625001299375071465628930609591
y[1] (numeric) = 0.2362500129937507146562893060959
absolute error = 1e-32
relative error = 4.2328040000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.799
y[1] (closed_form) = 0.23604942025082139297011779574219
y[1] (numeric) = 0.23604942025082139297011779574218
absolute error = 1e-32
relative error = 4.2364010000000000000000000000000e-30 %
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) = 0.23584905660377358490566037735849
y[1] (numeric) = 0.23584905660377358490566037735848
absolute error = 1e-32
relative error = 4.2400000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.801
y[1] (closed_form) = 0.2356489217530111808343904151215
y[1] (numeric) = 0.23564892175301118083439041512149
absolute error = 1e-32
relative error = 4.2436009999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.802
y[1] (closed_form) = 0.23544901539930740317630139734282
y[1] (numeric) = 0.23544901539930740317630139734281
absolute error = 1e-32
relative error = 4.2472039999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.803
y[1] (closed_form) = 0.23524933724380464989135009359395
y[1] (numeric) = 0.23524933724380464989135009359394
absolute error = 1e-32
relative error = 4.2508090000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.804
y[1] (closed_form) = 0.23504988698801433616270717297039
y[1] (numeric) = 0.23504988698801433616270717297038
absolute error = 1e-32
relative error = 4.2544160000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.805
y[1] (closed_form) = 0.2348506643338167342840871061114
y[1] (numeric) = 0.23485066433381673428408710611139
absolute error = 1e-32
relative error = 4.2580250000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.806
y[1] (closed_form) = 0.23465166898346081176336974814367
y[1] (numeric) = 0.23465166898346081176336974814366
absolute error = 1e-32
relative error = 4.2616360000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.807
y[1] (closed_form) = 0.23445290063956406765466682015517
y[1] (numeric) = 0.23445290063956406765466682015515
absolute error = 2e-32
relative error = 8.5304979999999999999999999999998e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.808
y[1] (closed_form) = 0.23425435900511236713092757230027
y[1] (numeric) = 0.23425435900511236713092757230025
absolute error = 2e-32
relative error = 8.5377279999999999999999999999998e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.809
y[1] (closed_form) = 0.23405604378345977430911922136108
y[1] (numeric) = 0.23405604378345977430911922136106
absolute error = 2e-32
relative error = 8.5449619999999999999999999999999e-30 %
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) = 0.23385795467832838333995930871589
y[1] (numeric) = 0.23385795467832838333995930871587
absolute error = 2e-32
relative error = 8.5521999999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.811
y[1] (closed_form) = 0.23366009139380814777411892036887
y[1] (numeric) = 0.23366009139380814777411892036886
absolute error = 1e-32
relative error = 4.2797210000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.812
y[1] (closed_form) = 0.23346245363435670821675774815191
y[1] (numeric) = 0.2334624536343567082167577481519
absolute error = 1e-32
relative error = 4.2833440000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.813
y[1] (closed_form) = 0.23326504110479921828219424959686
y[1] (numeric) = 0.23326504110479921828219424959685
absolute error = 1e-32
relative error = 4.2869690000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.814
y[1] (closed_form) = 0.23306785351032816886045668247488
y[1] (numeric) = 0.23306785351032816886045668247487
absolute error = 1e-32
relative error = 4.2905960000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.815
y[1] (closed_form) = 0.23287089055650321070740354778802
y[1] (numeric) = 0.23287089055650321070740354778801
absolute error = 1e-32
relative error = 4.2942250000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.816
y[1] (closed_form) = 0.23267415194925097537004497126009
y[1] (numeric) = 0.23267415194925097537004497126008
absolute error = 1e-32
relative error = 4.2978560000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.817
y[1] (closed_form) = 0.23247763739486489445863978729226
y[1] (numeric) = 0.23247763739486489445863978729225
absolute error = 1e-32
relative error = 4.3014890000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.818
y[1] (closed_form) = 0.23228134660000501727708656010837
y[1] (numeric) = 0.23228134660000501727708656010836
absolute error = 1e-32
relative error = 4.3051240000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.819
y[1] (closed_form) = 0.23208527927169782682307048360306
y[1] (numeric) = 0.23208527927169782682307048360305
absolute error = 1e-32
relative error = 4.3087610000000000000000000000000e-30 %
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) = 0.2318894351173360541693720434097
y[1] (numeric) = 0.23188943511733605416937204340969
absolute error = 1e-32
relative error = 4.3124000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.821
y[1] (closed_form) = 0.23169381384467849123768750111503
y[1] (numeric) = 0.23169381384467849123768750111501
absolute error = 2e-32
relative error = 8.6320819999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.822
y[1] (closed_form) = 0.23149841516184980197625567055368
y[1] (numeric) = 0.23149841516184980197625567055366
absolute error = 2e-32
relative error = 8.6393680000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.823
y[1] (closed_form) = 0.2313032387773403319525300989122
y[1] (numeric) = 0.23130323877734033195253009891218
absolute error = 2e-32
relative error = 8.6466580000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.824
y[1] (closed_form) = 0.23110828440000591637208064015146
y[1] (numeric) = 0.23110828440000591637208064015144
absolute error = 2e-32
relative error = 8.6539520000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.825
y[1] (closed_form) = 0.23091355173906768653485351421562
y[1] (numeric) = 0.2309135517390676865348535142156
absolute error = 2e-32
relative error = 8.6612499999999999999999999999998e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.826
y[1] (closed_form) = 0.23071904050411187473986428183161
y[1] (numeric) = 0.2307190405041118747398642818316
absolute error = 1e-32
relative error = 4.3342760000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.827
y[1] (closed_form) = 0.23052475040508961764934373061431
y[1] (numeric) = 0.2305247504050896176493437306143
absolute error = 1e-32
relative error = 4.3379290000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.828
y[1] (closed_form) = 0.23033068115231675812330246287991
y[1] (numeric) = 0.2303306811523167581233024628799
absolute error = 1e-32
relative error = 4.3415840000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.829
y[1] (closed_form) = 0.23013683245647364553542599823577
y[1] (numeric) = 0.23013683245647364553542599823576
absolute error = 1e-32
relative error = 4.3452410000000000000000000000000e-30 %
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) = 0.2299432040286049345811584538619
y[1] (numeric) = 0.22994320402860493458115845386189
absolute error = 1e-32
relative error = 4.3488999999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.831
y[1] (closed_form) = 0.22974979558011938258877934163358
y[1] (numeric) = 0.22974979558011938258877934163357
absolute error = 1e-32
relative error = 4.3525610000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.832
y[1] (closed_form) = 0.22955660682278964534422472306291
y[1] (numeric) = 0.2295566068227896453442247230629
absolute error = 1e-32
relative error = 4.3562240000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.833
y[1] (closed_form) = 0.22936363746875207144035088966715
y[1] (numeric) = 0.22936363746875207144035088966714
absolute error = 1e-32
relative error = 4.3598889999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.834
y[1] (closed_form) = 0.22917088723050649516128588701509
y[1] (numeric) = 0.22917088723050649516128588701508
absolute error = 1e-32
relative error = 4.3635559999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.835
y[1] (closed_form) = 0.22897835582091602791246157456966
y[1] (numeric) = 0.22897835582091602791246157456966
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.836
y[1] (closed_form) = 0.22878604295320684820686650974995
y[1] (numeric) = 0.22878604295320684820686650974994
absolute error = 1e-32
relative error = 4.3708959999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.837
y[1] (closed_form) = 0.2285939483409679902180077625933
y[1] (numeric) = 0.22859394834096799021800776259329
absolute error = 1e-32
relative error = 4.3745690000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.838
y[1] (closed_form) = 0.22840207169815113091001780622551
y[1] (numeric) = 0.2284020716981511309100178062255
absolute error = 1e-32
relative error = 4.3782440000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.839
y[1] (closed_form) = 0.22821041273907037575529088726155
y[1] (numeric) = 0.22821041273907037575529088726154
absolute error = 1e-32
relative error = 4.3819209999999999999999999999999e-30 %
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) = 0.22801897117840204304998175848231
y[1] (numeric) = 0.2280189711784020430499817584823
absolute error = 1e-32
relative error = 4.3855999999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.841
y[1] (closed_form) = 0.22782774673118444683764835288513
y[1] (numeric) = 0.22782774673118444683764835288513
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.842
y[1] (closed_form) = 0.22763673911281767845126889271116
y[1] (numeric) = 0.22763673911281767845126889271116
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.843
y[1] (closed_form) = 0.22744594803906338668381305853617
y[1] (numeric) = 0.22744594803906338668381305853617
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.844
y[1] (closed_form) = 0.22725537322604455659749619119994
y[1] (numeric) = 0.22725537322604455659749619119994
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.845
y[1] (closed_form) = 0.22706501439024528698179506247126
y[1] (numeric) = 0.22706501439024528698179506247126
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.846
y[1] (closed_form) = 0.22687487124851056647025352813112
y[1] (numeric) = 0.22687487124851056647025352813112
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
memory used=600.5MB, alloc=44.3MB, time=8.80
x[1] = -1.847
y[1] (closed_form) = 0.22668494351804604832605636883816
y[1] (numeric) = 0.22668494351804604832605636883816
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.848
y[1] (closed_form) = 0.2264952309164178239062998289508
y[1] (numeric) = 0.2264952309164178239062998289508
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.849
y[1] (closed_form) = 0.22630573316155219481483778065588
y[1] (numeric) = 0.22630573316155219481483778065588
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.85
y[1] (closed_form) = 0.22611644997173544375353306953081
y[1] (numeric) = 0.2261164499717354437535330695308
absolute error = 1e-32
relative error = 4.4225000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.851
y[1] (closed_form) = 0.2259273810656136040816944372838
y[1] (numeric) = 0.22592738106561360408169443728379
absolute error = 1e-32
relative error = 4.4262010000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.852
y[1] (closed_form) = 0.22573852616219222809343046711622
y[1] (numeric) = 0.22573852616219222809343046711621
absolute error = 1e-32
relative error = 4.4299039999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.853
y[1] (closed_form) = 0.22554988498083615402260325617347
y[1] (numeric) = 0.22554988498083615402260325617346
absolute error = 1e-32
relative error = 4.4336090000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.854
y[1] (closed_form) = 0.22536145724126927178501598714178
y[1] (numeric) = 0.22536145724126927178501598714177
absolute error = 1e-32
relative error = 4.4373159999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.855
y[1] (closed_form) = 0.22517324266357428746742024645211
y[1] (numeric) = 0.22517324266357428746742024645211
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.856
y[1] (closed_form) = 0.22498524096819248657288081901827
y[1] (numeric) = 0.22498524096819248657288081901827
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.857
y[1] (closed_form) = 0.22479745187592349603198777821214
y[1] (numeric) = 0.22479745187592349603198777821213
absolute error = 1e-32
relative error = 4.4484489999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.858
y[1] (closed_form) = 0.22460987510792504498935798411739
y[1] (numeric) = 0.22460987510792504498935798411738
absolute error = 1e-32
relative error = 4.4521639999999999999999999999999e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.859
y[1] (closed_form) = 0.22442251038571272437482060225576
y[1] (numeric) = 0.22442251038571272437482060225575
absolute error = 1e-32
relative error = 4.4558810000000000000000000000000e-30 %
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) = 0.22423535743115974526863395820253
y[1] (numeric) = 0.22423535743115974526863395820252
absolute error = 1e-32
relative error = 4.4596000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.861
y[1] (closed_form) = 0.22404841596649669607003395005647
y[1] (numeric) = 0.22404841596649669607003395005646
absolute error = 1e-32
relative error = 4.4633210000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.862
y[1] (closed_form) = 0.22386168571431129847836734986268
y[1] (numeric) = 0.22386168571431129847836734986267
absolute error = 1e-32
relative error = 4.4670440000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.863
y[1] (closed_form) = 0.22367516639754816229601663606418
y[1] (numeric) = 0.22367516639754816229601663606416
absolute error = 2e-32
relative error = 8.9415379999999999999999999999998e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.864
y[1] (closed_form) = 0.22348885773950853906227651114226
y[1] (numeric) = 0.22348885773950853906227651114224
absolute error = 2e-32
relative error = 8.9489920000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.865
y[1] (closed_form) = 0.22330275946385007452729597105996
y[1] (numeric) = 0.22330275946385007452729597105994
absolute error = 2e-32
relative error = 8.9564500000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.866
y[1] (closed_form) = 0.22311687129458655997515370521263
y[1] (numeric) = 0.22311687129458655997515370521261
absolute error = 2e-32
relative error = 8.9639120000000000000000000000002e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.867
y[1] (closed_form) = 0.22293119295608768240508871658289
y[1] (numeric) = 0.22293119295608768240508871658287
absolute error = 2e-32
relative error = 8.9713780000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.868
y[1] (closed_form) = 0.22274572417307877357986236096212
y[1] (numeric) = 0.2227457241730787735798623609621
absolute error = 2e-32
relative error = 8.9788480000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.869
y[1] (closed_form) = 0.22256046467064055795018251070905
y[1] (numeric) = 0.22256046467064055795018251070903
absolute error = 2e-32
relative error = 8.9863220000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.87
y[1] (closed_form) = 0.22237541417420889946407525184016
y[1] (numeric) = 0.22237541417420889946407525184013
absolute error = 3e-32
relative error = 1.3490700000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.871
y[1] (closed_form) = 0.22219057240957454727004442256114
y[1] (numeric) = 0.22219057240957454727004442256112
absolute error = 2e-32
relative error = 9.0012820000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.872
y[1] (closed_form) = 0.22200593910288288032281439593072
y[1] (numeric) = 0.2220059391028828803228143959307
absolute error = 2e-32
relative error = 9.0087680000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.873
y[1] (closed_form) = 0.22182151398063365090040679847449
y[1] (numeric) = 0.22182151398063365090040679847447
absolute error = 2e-32
relative error = 9.0162580000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.874
y[1] (closed_form) = 0.22163729676968072704125733951908
y[1] (numeric) = 0.22163729676968072704125733951906
absolute error = 2e-32
relative error = 9.0237520000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.875
y[1] (closed_form) = 0.22145328719723183391003460207612
y[1] (numeric) = 0.2214532871972318339100346020761
absolute error = 2e-32
relative error = 9.0312500000000000000000000000002e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.876
y[1] (closed_form) = 0.22126948499084829410077851455599
y[1] (numeric) = 0.22126948499084829410077851455597
absolute error = 2e-32
relative error = 9.0387520000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.877
y[1] (closed_form) = 0.22108588987844476688593228271845
y[1] (numeric) = 0.22108588987844476688593228271842
absolute error = 3e-32
relative error = 1.3569387000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.878
y[1] (closed_form) = 0.22090250158828898641979781235835
y[1] (numeric) = 0.22090250158828898641979781235832
absolute error = 3e-32
relative error = 1.3580652000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.879
y[1] (closed_form) = 0.22071931984900149890490109456918
y[1] (numeric) = 0.22071931984900149890490109456915
absolute error = 3e-32
relative error = 1.3591923000000000000000000000000e-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) = 0.22053634438955539872971065631616
y[1] (numeric) = 0.22053634438955539872971065631613
absolute error = 3e-32
relative error = 1.3603200000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.881
y[1] (closed_form) = 0.22035357493927606358610899877726
y[1] (numeric) = 0.22035357493927606358610899877723
absolute error = 3e-32
relative error = 1.3614483000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.882
y[1] (closed_form) = 0.22017101122784088857497395376937
y[1] (numeric) = 0.22017101122784088857497395376934
absolute error = 3e-32
relative error = 1.3625772000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.883
y[1] (closed_form) = 0.21998865298527901930818408386495
y[1] (numeric) = 0.21998865298527901930818408386492
absolute error = 3e-32
relative error = 1.3637067000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.884
y[1] (closed_form) = 0.21980649994197108401531963381996
y[1] (numeric) = 0.21980649994197108401531963381992
absolute error = 4e-32
relative error = 1.8197824000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.885
y[1] (closed_form) = 0.2196245518286489246632881089777
y[1] (numeric) = 0.21962455182864892466328810897767
absolute error = 3e-32
relative error = 1.3659675000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.886
y[1] (closed_form) = 0.21944280837639532709706130968735
y[1] (numeric) = 0.21944280837639532709706130968731
absolute error = 4e-32
relative error = 1.8227984000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.887
y[1] (closed_form) = 0.21926126931664375020966858878404
y[1] (numeric) = 0.219261269316643750209668588784
absolute error = 4e-32
relative error = 1.8243076000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.888
y[1] (closed_form) = 0.21907993438117805414954922112702
y[1] (numeric) = 0.21907993438117805414954922112698
absolute error = 4e-32
relative error = 1.8258176000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.889
y[1] (closed_form) = 0.21889880330213222757332507938912
y[1] (numeric) = 0.21889880330213222757332507938909
absolute error = 3e-32
relative error = 1.3704963000000000000000000000000e-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) = 0.21871787581199011395201329804685
y[1] (numeric) = 0.21871787581199011395201329804682
absolute error = 3e-32
relative error = 1.3716300000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.891
y[1] (closed_form) = 0.2185371516435851369386572771451
y[1] (numeric) = 0.21853715164358513693865727714507
absolute error = 3e-32
relative error = 1.3727643000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.892
y[1] (closed_form) = 0.21835663053010002480531322821936
y[1] (numeric) = 0.21835663053010002480531322821933
absolute error = 3e-32
relative error = 1.3738992000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.893
y[1] (closed_form) = 0.21817631220506653395728849606486
y[1] (numeric) = 0.21817631220506653395728849606483
absolute error = 3e-32
relative error = 1.3750347000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.894
y[1] (closed_form) = 0.21799619640236517153248710116506
y[1] (numeric) = 0.21799619640236517153248710116503
absolute error = 3e-32
relative error = 1.3761708000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.895
y[1] (closed_form) = 0.21781628285622491709367733784939
y[1] (numeric) = 0.21781628285622491709367733784936
absolute error = 3e-32
relative error = 1.3773075000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.896
y[1] (closed_form) = 0.21763657130122294342145583196367
y[1] (numeric) = 0.21763657130122294342145583196364
absolute error = 3e-32
relative error = 1.3784448000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.897
y[1] (closed_form) = 0.21745706147228433641564220832865
y[1] (numeric) = 0.21745706147228433641564220832862
absolute error = 3e-32
relative error = 1.3795827000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.898
y[1] (closed_form) = 0.21727775310468181411279844185778
y[1] (numeric) = 0.21727775310468181411279844185775
absolute error = 3e-32
relative error = 1.3807212000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.899
y[1] (closed_form) = 0.21709864593403544482752706623094
y[1] (numeric) = 0.21709864593403544482752706623091
absolute error = 3e-32
relative error = 1.3818603000000000000000000000000e-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) = 0.21691973969631236442516268980477
y[1] (numeric) = 0.21691973969631236442516268980475
absolute error = 2e-32
relative error = 9.2200000000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.901
y[1] (closed_form) = 0.21674103412782649273343171931342
y[1] (numeric) = 0.2167410341278264927334317193134
absolute error = 2e-32
relative error = 9.2276020000000000000000000000002e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.902
y[1] (closed_form) = 0.21656252896523824910061581720737
y[1] (numeric) = 0.21656252896523824910061581720734
absolute error = 3e-32
relative error = 1.3852812000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.903
y[1] (closed_form) = 0.21638422394555426710771541752742
y[1] (numeric) = 0.2163842239455542671077154175274
absolute error = 2e-32
relative error = 9.2428180000000000000000000000002e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.904
y[1] (closed_form) = 0.21620611880612710844207059735156
y[1] (numeric) = 0.21620611880612710844207059735154
absolute error = 2e-32
relative error = 9.2504320000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.905
y[1] (closed_form) = 0.21602821328465497593985774542155
y[1] (numeric) = 0.21602821328465497593985774542153
absolute error = 2e-32
relative error = 9.2580500000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.906
y[1] (closed_form) = 0.21585050711918142580484178589529
y[1] (numeric) = 0.21585050711918142580484178589527
absolute error = 2e-32
relative error = 9.2656720000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.907
y[1] (closed_form) = 0.21567300004809507901072520261939
y[1] (numeric) = 0.21567300004809507901072520261937
absolute error = 2e-32
relative error = 9.2732980000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.908
y[1] (closed_form) = 0.21549569181012933189439676721983
y[1] (numeric) = 0.21549569181012933189439676721981
absolute error = 2e-32
relative error = 9.2809280000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.909
y[1] (closed_form) = 0.21531858214436206594734470201092
y[1] (numeric) = 0.21531858214436206594734470201091
absolute error = 1e-32
relative error = 4.6442810000000000000000000000001e-30 %
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) = 0.21514167079021535681246100557217
y[1] (numeric) = 0.21514167079021535681246100557215
absolute error = 2e-32
relative error = 9.2962000000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.911
y[1] (closed_form) = 0.21496495748745518249342583418764
y[1] (numeric) = 0.21496495748745518249342583418762
absolute error = 2e-32
relative error = 9.3038420000000000000000000000000e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.912
y[1] (closed_form) = 0.21478844197619113078382316553487
y[1] (numeric) = 0.21478844197619113078382316553485
absolute error = 2e-32
relative error = 9.3114880000000000000000000000002e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.913
y[1] (closed_form) = 0.21461212399687610592310147140218
y[1] (numeric) = 0.21461212399687610592310147140216
absolute error = 2e-32
relative error = 9.3191380000000000000000000000001e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
memory used=647.2MB, alloc=44.3MB, time=9.47
TOP MAIN SOLVE Loop
x[1] = -1.914
y[1] (closed_form) = 0.21443600329030603448645579316018
y[1] (numeric) = 0.21443600329030603448645579316015
absolute error = 3e-32
relative error = 1.3990188000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.915
y[1] (closed_form) = 0.21426007959761957051567044657157
y[1] (numeric) = 0.21426007959761957051567044657154
absolute error = 3e-32
relative error = 1.4001675000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.916
y[1] (closed_form) = 0.21408435266029779989792458065157
y[1] (numeric) = 0.21408435266029779989792458065154
absolute error = 3e-32
relative error = 1.4013168000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.917
y[1] (closed_form) = 0.21390882222016394399952597804996
y[1] (numeric) = 0.21390882222016394399952597804993
absolute error = 3e-32
relative error = 1.4024667000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.918
y[1] (closed_form) = 0.21373348801938306256150181117758
y[1] (numeric) = 0.21373348801938306256150181117755
absolute error = 3e-32
relative error = 1.4036172000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.919
y[1] (closed_form) = 0.21355834980046175586393855840853
y[1] (numeric) = 0.2135583498004617558639385584085
absolute error = 3e-32
relative error = 1.4047683000000000000000000000000e-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) = 0.21338340730624786616592693752134
y[1] (numeric) = 0.21338340730624786616592693752131
absolute error = 3e-32
relative error = 1.4059200000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.921
y[1] (closed_form) = 0.21320866027993017842793152846517
y[1] (numeric) = 0.21320866027993017842793152846514
absolute error = 3e-32
relative error = 1.4070723000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.922
y[1] (closed_form) = 0.21303410846503812032336873392125
y[1] (numeric) = 0.21303410846503812032336873392122
absolute error = 3e-32
relative error = 1.4082252000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.923
y[1] (closed_form) = 0.21285975160544146154614086334638
y[1] (numeric) = 0.21285975160544146154614086334635
absolute error = 3e-32
relative error = 1.4093787000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.924
y[1] (closed_form) = 0.21268558944535001242083842360844
y[1] (numeric) = 0.21268558944535001242083842360841
absolute error = 3e-32
relative error = 1.4105328000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.925
y[1] (closed_form) = 0.21251162172931332182228715632886
y[1] (numeric) = 0.21251162172931332182228715632883
absolute error = 3e-32
relative error = 1.4116875000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.926
y[1] (closed_form) = 0.21233784820222037441108097801114
y[1] (numeric) = 0.21233784820222037441108097801111
absolute error = 3e-32
relative error = 1.4128428000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.927
y[1] (closed_form) = 0.21216426860929928719170675333718
y[1] (numeric) = 0.21216426860929928719170675333715
absolute error = 3e-32
relative error = 1.4139987000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.928
y[1] (closed_form) = 0.21199088269611700539983176403549
y[1] (numeric) = 0.21199088269611700539983176403546
absolute error = 3e-32
relative error = 1.4151552000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.929
y[1] (closed_form) = 0.21181769020857899772528982485007
y[1] (numeric) = 0.21181769020857899772528982485004
absolute error = 3e-32
relative error = 1.4163123000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.93
y[1] (closed_form) = 0.21164469089292895087726724375119
y[1] (numeric) = 0.21164469089292895087726724375116
absolute error = 3e-32
relative error = 1.4174700000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.931
y[1] (closed_form) = 0.2114718844957484634981552250156
y[1] (numeric) = 0.21147188449574846349815522501557
absolute error = 3e-32
relative error = 1.4186283000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.932
y[1] (closed_form) = 0.211299270763956739432500870553
y[1] (numeric) = 0.21129927076395673943250087055296
absolute error = 4e-32
relative error = 1.8930496000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.933
y[1] (closed_form) = 0.21112684944481028035745464625802
y[1] (numeric) = 0.21112684944481028035745464625798
absolute error = 4e-32
relative error = 1.8945956000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.934
y[1] (closed_form) = 0.21095462028590257778107804561514
y[1] (numeric) = 0.2109546202859025777810780456151
absolute error = 4e-32
relative error = 1.8961424000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.935
y[1] (closed_form) = 0.21078258303516380441484120167151
y[1] (numeric) = 0.21078258303516380441484120167147
absolute error = 4e-32
relative error = 1.8976900000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.936
y[1] (closed_form) = 0.21061073744086050492660637021661
y[1] (numeric) = 0.21061073744086050492660637021657
absolute error = 4e-32
relative error = 1.8992384000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.937
y[1] (closed_form) = 0.21043908325159528608035953096495
y[1] (numeric) = 0.21043908325159528608035953096491
absolute error = 4e-32
relative error = 1.9007876000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.938
y[1] (closed_form) = 0.21026762021630650626891882912896
y[1] (numeric) = 0.21026762021630650626891882912892
absolute error = 4e-32
relative error = 1.9023376000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.939
y[1] (closed_form) = 0.2100963480842679644458152063955
y[1] (numeric) = 0.21009634808426796444581520639546
absolute error = 4e-32
relative error = 1.9038884000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.94
y[1] (closed_form) = 0.20992526660508858846250734738433
y[1] (numeric) = 0.20992526660508858846250734738429
absolute error = 4e-32
relative error = 1.9054400000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.941
y[1] (closed_form) = 0.20975437552871212281705999457575
y[1] (numeric) = 0.20975437552871212281705999457571
absolute error = 4e-32
relative error = 1.9069924000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.942
y[1] (closed_form) = 0.20958367460541681582038176085497
y[1] (numeric) = 0.20958367460541681582038176085493
absolute error = 4e-32
relative error = 1.9085456000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.943
y[1] (closed_form) = 0.20941316358581510618608579364134
y[1] (numeric) = 0.2094131635858151061860857936413
absolute error = 4e-32
relative error = 1.9100996000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.944
y[1] (closed_form) = 0.20924284222085330905000401746257
y[1] (numeric) = 0.20924284222085330905000401746253
absolute error = 4e-32
relative error = 1.9116544000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.945
y[1] (closed_form) = 0.2090727102618113014253532022099
y[1] (numeric) = 0.20907271026181130142535320220986
absolute error = 4e-32
relative error = 1.9132100000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.946
y[1] (closed_form) = 0.20890276746030220709951877158488
y[1] (numeric) = 0.20890276746030220709951877158484
absolute error = 4e-32
relative error = 1.9147664000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.947
y[1] (closed_form) = 0.20873301356827208097839007983829
y[1] (numeric) = 0.20873301356827208097839007983825
absolute error = 4e-32
relative error = 1.9163236000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.948
y[1] (closed_form) = 0.20856344833799959288414884422479
y[1] (numeric) = 0.20856344833799959288414884422475
absolute error = 4e-32
relative error = 1.9178816000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.949
y[1] (closed_form) = 0.20839407152209571081238052507387
y[1] (numeric) = 0.20839407152209571081238052507383
absolute error = 4e-32
relative error = 1.9194404000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.95
y[1] (closed_form) = 0.20822488287350338365434669442998
y[1] (numeric) = 0.20822488287350338365434669442994
absolute error = 4e-32
relative error = 1.9210000000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.951
y[1] (closed_form) = 0.20805588214549722339022482726681
y[1] (numeric) = 0.20805588214549722339022482726676
absolute error = 5e-32
relative error = 2.4032004999999999999999999999999e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.952
y[1] (closed_form) = 0.20788706909168318675909048575724
y[1] (numeric) = 0.2078870690916831867590904857572
absolute error = 4e-32
relative error = 1.9241216000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.953
y[1] (closed_form) = 0.20771844346599825641138554641064
y[1] (numeric) = 0.20771844346599825641138554641059
absolute error = 5e-32
relative error = 2.4071044999999999999999999999999e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.954
y[1] (closed_form) = 0.20755000502271012154958494149996
y[1] (numeric) = 0.20755000502271012154958494149991
absolute error = 5e-32
relative error = 2.4090579999999999999999999999999e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.955
y[1] (closed_form) = 0.20738175351641685806274334952639
y[1] (numeric) = 0.20738175351641685806274334952635
absolute error = 4e-32
relative error = 1.9288100000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.956
y[1] (closed_form) = 0.20721368870204660816057237393948
y[1] (numeric) = 0.20721368870204660816057237393944
absolute error = 4e-32
relative error = 1.9303744000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.957
y[1] (closed_form) = 0.20704581033485725951266799438243
y[1] (numeric) = 0.20704581033485725951266799438239
absolute error = 4e-32
relative error = 1.9319396000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.958
y[1] (closed_form) = 0.20687811817043612389847745980151
y[1] (numeric) = 0.20687811817043612389847745980147
absolute error = 4e-32
relative error = 1.9335056000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.959
y[1] (closed_form) = 0.20671061196469961537356431728343
y[1] (numeric) = 0.20671061196469961537356431728338
absolute error = 5e-32
relative error = 2.4188404999999999999999999999999e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.96
y[1] (closed_form) = 0.20654329147389292795769993390615
y[1] (numeric) = 0.2065432914738929279576999339061
absolute error = 5e-32
relative error = 2.4208000000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.961
y[1] (closed_form) = 0.20637615645458971285027967064842
y[1] (numeric) = 0.20637615645458971285027967064837
absolute error = 5e-32
relative error = 2.4227605000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.962
y[1] (closed_form) = 0.20620920666369175517853180694529
y[1] (numeric) = 0.20620920666369175517853180694524
absolute error = 5e-32
relative error = 2.4247220000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.963
y[1] (closed_form) = 0.20604244185842865028395739124719
y[1] (numeric) = 0.20604244185842865028395739124714
absolute error = 5e-32
relative error = 2.4266845000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.964
y[1] (closed_form) = 0.20587586179635747955240940638578
y[1] (numeric) = 0.20587586179635747955240940638572
absolute error = 6e-32
relative error = 2.9143775999999999999999999999999e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.965
y[1] (closed_form) = 0.20570946623536248579318998812028
y[1] (numeric) = 0.20570946623536248579318998812022
absolute error = 6e-32
relative error = 2.9167350000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.966
y[1] (closed_form) = 0.20554325493365474817251492038488
y[1] (numeric) = 0.20554325493365474817251492038482
absolute error = 6e-32
relative error = 2.9190935999999999999999999999999e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.967
y[1] (closed_form) = 0.20537722764977185670666525093298
y[1] (numeric) = 0.20537722764977185670666525093292
absolute error = 6e-32
relative error = 2.9214534000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.968
y[1] (closed_form) = 0.20521138414257758632011662573384
y[1] (numeric) = 0.20521138414257758632011662573378
absolute error = 6e-32
relative error = 2.9238143999999999999999999999999e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.969
y[1] (closed_form) = 0.20504572417126157047390782907634
y[1] (numeric) = 0.20504572417126157047390782907629
absolute error = 5e-32
relative error = 2.4384805000000000000000000000001e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.97
y[1] (closed_form) = 0.20488024749533897436948103833309
y[1] (numeric) = 0.20488024749533897436948103833304
absolute error = 5e-32
relative error = 2.4404500000000000000000000000001e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.971
y[1] (closed_form) = 0.20471495387465016773319745719461
y[1] (numeric) = 0.20471495387465016773319745719456
absolute error = 5e-32
relative error = 2.4424205000000000000000000000001e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.972
y[1] (closed_form) = 0.20454984306936039718670327836124
y[1] (numeric) = 0.20454984306936039718670327836119
absolute error = 5e-32
relative error = 2.4443920000000000000000000000001e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.973
y[1] (closed_form) = 0.20438491483995945820829234564187
y[1] (numeric) = 0.20438491483995945820829234564181
absolute error = 6e-32
relative error = 2.9356374000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.974
y[1] (closed_form) = 0.20422016894726136669038343562041
y[1] (numeric) = 0.20422016894726136669038343562035
absolute error = 6e-32
relative error = 2.9380056000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.975
y[1] (closed_form) = 0.20405560515240403009820175997959
y[1] (numeric) = 0.20405560515240403009820175997954
absolute error = 5e-32
relative error = 2.4503125000000000000000000000001e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.976
y[1] (closed_form) = 0.20389122321684891823472610068638
y[1] (numeric) = 0.20389122321684891823472610068632
absolute error = 6e-32
relative error = 2.9427456000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.977
y[1] (closed_form) = 0.20372702290238073361693493101497
y[1] (numeric) = 0.20372702290238073361693493101491
absolute error = 6e-32
relative error = 2.9451174000000000000000000000001e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.978
y[1] (closed_form) = 0.20356300397110708146835694528471
y[1] (numeric) = 0.20356300397110708146835694528464
absolute error = 7e-32
relative error = 3.4387388000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.979
y[1] (closed_form) = 0.20339916618545813933290361869491
y[1] (numeric) = 0.20339916618545813933290361869484
absolute error = 7e-32
relative error = 3.4415086999999999999999999999999e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.98
y[1] (closed_form) = 0.20323550930818632631493374522397
y[1] (numeric) = 0.2032355093081863263149337452239
absolute error = 7e-32
relative error = 3.4442799999999999999999999999999e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.981
y[1] (closed_form) = 0.2030720331023659719504723557026
y[1] (numeric) = 0.20307203310236597195047235570253
absolute error = 7e-32
relative error = 3.4470527000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.982
y[1] (closed_form) = 0.2029087373313929847144789993515
y[1] (numeric) = 0.20290873733139298471447899935144
absolute error = 6e-32
relative error = 2.9569944000000000000000000000001e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.983
y[1] (closed_form) = 0.2027456217589845201690330797729
y[1] (numeric) = 0.20274562175898452016903307977284
absolute error = 6e-32
relative error = 2.9593734000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.984
y[1] (closed_form) = 0.20258268614917864875727677008648
y[1] (numeric) = 0.20258268614917864875727677008642
absolute error = 6e-32
relative error = 2.9617536000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.985
y[1] (closed_form) = 0.20241993026633402324792899108846
y[1] (numeric) = 0.2024199302663340232479289910884
absolute error = 6e-32
relative error = 2.9641350000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.986
y[1] (closed_form) = 0.20225735387512954583515702047411
y[1] (numeric) = 0.20225735387512954583515702047404
absolute error = 7e-32
relative error = 3.4609372000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.987
y[1] (closed_form) = 0.20209495674056403489856550978756
y[1] (numeric) = 0.20209495674056403489856550978749
absolute error = 7e-32
relative error = 3.4637183000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.988
y[1] (closed_form) = 0.20193273862795589142803601833872
y[1] (numeric) = 0.20193273862795589142803601833865
absolute error = 7e-32
relative error = 3.4665008000000000000000000000001e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.989
y[1] (closed_form) = 0.20177069930294276511812362934642
y[1] (numeric) = 0.20177069930294276511812362934634
absolute error = 8e-32
relative error = 3.9648968000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.99
y[1] (closed_form) = 0.20160883853148122013669079252434
y[1] (numeric) = 0.20160883853148122013669079252427
absolute error = 7e-32
relative error = 3.4720700000000000000000000000001e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.991
y[1] (closed_form) = 0.20144715607984640057243223871649
y[1] (numeric) = 0.20144715607984640057243223871642
absolute error = 7e-32
relative error = 3.4748567000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.992
y[1] (closed_form) = 0.20128565171463169556591863550872
y[1] (numeric) = 0.20128565171463169556591863550865
absolute error = 7e-32
relative error = 3.4776448000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.993
y[1] (closed_form) = 0.2011243252027484041287605974921
y[1] (numeric) = 0.20112432520274840412876059749203
absolute error = 7e-32
relative error = 3.4804343000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.994
y[1] (closed_form) = 0.20096317631142539965546873053169
y[1] (numeric) = 0.20096317631142539965546873053162
absolute error = 7e-32
relative error = 3.4832252000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.995
y[1] (closed_form) = 0.20080220480820879413255957550414
y[1] (numeric) = 0.20080220480820879413255957550407
absolute error = 7e-32
relative error = 3.4860175000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.996
y[1] (closed_form) = 0.20064141046096160204943162301245
y[1] (numeric) = 0.20064141046096160204943162301238
absolute error = 7e-32
relative error = 3.4888111999999999999999999999999e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.997
y[1] (closed_form) = 0.20048079303786340401550999607258
y[1] (numeric) = 0.20048079303786340401550999607252
absolute error = 6e-32
relative error = 2.9928054000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.998
y[1] (closed_form) = 0.20032035230741001008813294220117
y[1] (numeric) = 0.20032035230741001008813294220111
absolute error = 6e-32
relative error = 2.9952024000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.999
y[1] (closed_form) = 0.20016008803841312281562793922579
y[1] (numeric) = 0.20016008803841312281562793922573
absolute error = 6e-32
relative error = 2.9976006000000000000000000000000e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = -0.001
Finished!
diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ;
Iterations = 1000
Total Elapsed Time = 10 Seconds
Elapsed Time(since restart) = 10 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 10 Seconds
Time to Timeout = 2 Minutes 49 Seconds
Percent Done = 0 %
> quit
memory used=708.2MB, alloc=76.3MB, time=10.35