|\^/| 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.
| Type ? for help.
#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> 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(arctan(c(x)));
> end;
exact_soln_y := proc(x) return arctan(c(x)) end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]);
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if (rad_given < glob_least_given_sing) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])*
(array_x[1] - array_given_rad_poles[1, 1])
+ array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if rad_given < glob_least_given_sing then
glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if array_rad_test_poles[1, 1] < glob_least_ratio_sing then
glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_float(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if array_rad_test_poles[1, 2] < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if array_rad_test_poles[1, 3] < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 3
> if (iter >= 0) then # if number 4
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> closed_form_val_y := evalf(exact_soln_y(ind_var));
> omniout_float(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := float_abs(numeric_val - closed_form_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 5
> relerr := abserr*glob__100/float_abs(closed_form_val_y);
> if (c(relerr) > c(glob_prec)) then # if number 6
> glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 6;
> else
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 5;
> if (glob_good_digits < glob_min_good_digits) then # if number 5
> glob_min_good_digits := glob_good_digits;
> fi;# end if 5;
> if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 5
> glob_min_apfp_est_good_digits := glob_apfp_est_good_digits;
> fi;# end if 5;
> if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 5
> est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*22*ATS_MAX_TERMS/float_abs(numeric_val));
> if (evalf(est_rel_err) > glob_prec) then # if number 6
> glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
> else
> glob_est_digits := Digits;
> fi;# end if 6;
> else
> relerr := glob__m1 ;
> glob_est_digits := -16;
> fi;# end if 5;
> array_est_digits[1] := glob_est_digits;
> if (glob_iter = 1) then # if number 5
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 5;
> array_est_rel_error[1] := est_rel_err;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," ");
> omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," ");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 4;
> #BOTTOM DISPLAY ALOT
> fi;# end if 3;
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_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_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
closed_form_val_y := evalf(exact_soln_y(ind_var));
omniout_float(ALWAYS, "y[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := float_abs(numeric_val - closed_form_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if c(glob_prec) < c(float_abs(closed_form_val_y)) then
relerr := abserr*glob__100/float_abs(closed_form_val_y);
if c(glob_prec) < c(relerr) then
glob_good_digits := -int_trunc(log10(c(relerr))) + 3
else glob_good_digits := Digits
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits
then glob_min_apfp_est_good_digits := glob_apfp_est_good_digits
end if;
if glob_prec < evalf(float_abs(numeric_val)) then
est_rel_err := evalf(array_max_est_error[1]*100.0*
sqrt(glob_iter)*22*ATS_MAX_TERMS/float_abs(numeric_val))
;
if glob_prec < evalf(est_rel_err) then
glob_est_digits := -int_trunc(log10(est_rel_err)) + 3
else glob_est_digits := Digits
end if
else relerr := glob__m1; glob_est_digits := -16
end if;
array_est_digits[1] := glob_est_digits;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
array_est_rel_error[1] := est_rel_err;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Desired digits ", 32,
glob_desired_digits_correct, 4, " ");
omniout_int(INFO, "Estimated correct digits ", 32,
glob_est_digits, 4, " ");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> 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_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_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_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_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_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_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_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_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_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_x[1] * array_x[1];
> #emit pre add FULL - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_1D0[1];
> #emit pre div CONST FULL $eq_no = 1 i = 1
> array_tmp3[1] := array_const_1D0[1] / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_x[1] * array_x[2] + array_x[2] * array_x[1];
> #emit pre add FULL CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre div CONST FULL $eq_no = 1 i = 2
> array_tmp3[2] := neg(ats(2,array_tmp2,array_tmp3,2)) / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 3
> array_tmp1[3] := array_x[2] * array_x[2];
> #emit pre add FULL CONST $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre div CONST FULL $eq_no = 1 i = 3
> array_tmp3[3] := neg(ats(3,array_tmp2,array_tmp3,2)) / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp3[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre add FULL CONST $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre div CONST FULL $eq_no = 1 i = 4
> array_tmp3[4] := neg(ats(4,array_tmp2,array_tmp3,2)) / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp3[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre add FULL CONST $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre div CONST FULL $eq_no = 1 i = 5
> array_tmp3[5] := neg(ats(5,array_tmp2,array_tmp3,2)) / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp3[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit mult LINEAR - LINEAR $eq_no = 1 i = 1
> #emit FULL - NOT FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit div CONST FULL $eq_no = 1 i = 1
> array_tmp3[kkk] := neg(ats(kkk,array_tmp2,array_tmp3,2)) / array_tmp2[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp4[kkk] := array_tmp3[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp4[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_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_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
array_tmp1[1] := array_x[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_1D0[1];
array_tmp3[1] := array_const_1D0[1]/array_tmp2[1];
array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_x[1]*array_x[2] + array_x[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := neg(ats(2, array_tmp2, array_tmp3, 2))/array_tmp2[1];
array_tmp4[2] := array_tmp3[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp1[3] := array_x[2]*array_x[2];
array_tmp2[3] := array_tmp1[3];
array_tmp3[3] := neg(ats(3, array_tmp2, array_tmp3, 2))/array_tmp2[1];
array_tmp4[3] := array_tmp3[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp2[4] := array_tmp1[4];
array_tmp3[4] := neg(ats(4, array_tmp2, array_tmp3, 2))/array_tmp2[1];
array_tmp4[4] := array_tmp3[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp2[5] := array_tmp1[5];
array_tmp3[5] := neg(ats(5, array_tmp2, array_tmp3, 2))/array_tmp2[1];
array_tmp4[5] := array_tmp3[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp2[kkk] := array_tmp1[kkk];
array_tmp3[kkk] :=
neg(ats(kkk, array_tmp2, array_tmp3, 2))/array_tmp2[1];
array_tmp4[kkk] := array_tmp3[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y_set_initial[1, kkk + order_d] then
temporary := c(array_tmp4[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_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_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 := 20;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=20;
> #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..(20),[]);
> array_norms:= Array(0..(20),[]);
> array_fact_1:= Array(0..(20),[]);
> 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..(20),[]);
> array_x:= Array(0..(20),[]);
> array_tmp0:= Array(0..(20),[]);
> array_tmp1:= Array(0..(20),[]);
> array_tmp2:= Array(0..(20),[]);
> array_tmp3:= Array(0..(20),[]);
> array_tmp4:= Array(0..(20),[]);
> array_m1:= Array(0..(20),[]);
> array_y_higher := Array(0..(2) ,(0..20+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..20+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..20+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..20+ 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..(20) ,(0..20+ 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 <= 20) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) 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 <= 20) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) 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 <= 20) 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 <= 20) 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 <= 20) 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 <= 20) 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 <=20) do # do number 1
> term := 1;
> while (term <= 20) 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_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_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;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 20;
> 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/sing2_backpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = 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:=20;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := c(-1.5);");
> 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,"");
> 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,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=100000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=false;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(arctan(c(x)));");
> 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(-1.5);
> x_end := c(-2.0);
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> 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 ) = 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,"2016-08-26T17:08:40-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sing2_back")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = 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,"sing2_back diffeq.mxt")
> ;
> logitem_str(html_log_file,"sing2_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_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_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 := 20;
Digits := 32;
max_terms := 20;
glob_html_log := true;
array_y_init := Array(0 .. 20, []);
array_norms := Array(0 .. 20, []);
array_fact_1 := Array(0 .. 20, []);
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 .. 20, []);
array_x := Array(0 .. 20, []);
array_tmp0 := Array(0 .. 20, []);
array_tmp1 := Array(0 .. 20, []);
array_tmp2 := Array(0 .. 20, []);
array_tmp3 := Array(0 .. 20, []);
array_tmp4 := Array(0 .. 20, []);
array_m1 := Array(0 .. 20, []);
array_y_higher := Array(0 .. 2, 0 .. 21, []);
array_y_higher_work := Array(0 .. 2, 0 .. 21, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 21, []);
array_y_set_initial := Array(0 .. 2, 0 .. 21, []);
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 .. 20, 0 .. 21, []);
term := 1;
while term <= 20 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 20 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 20 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 <= 20 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 20 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 <= 20 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 <= 20 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 <= 20 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 <= 20 do
term := 1;
while term <= 20 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_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_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;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 20;
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/sing2_backpostode.ode#################");
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = 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:=20;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := c(-1.5);");
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, "");
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, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=100000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=false;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(arctan(c(x)));");
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(-1.5);
x_end := c(-2.0);
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
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 ) = 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, "2016-08-26T17:08:40-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sing2_back");
logitem_str(html_log_file, "diff ( y , x , 1 ) = 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, "sing2_back diffeq.mxt");
logitem_str(html_log_file, "sing2_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/sing2_backpostode.ode#################
diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=20;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(-1.5);
x_end := c(-2.0);
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
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(arctan(c(x)));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
x[1] = -1.501
y[1] (closed_form) = -0.98310127359900396476034773737684
y[1] (numeric) = -0.98310127359900396476034773737684
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 14
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.502
y[1] (closed_form) = -0.98340854026177727563391104913087
y[1] (numeric) = -0.98340854026177727563391104913087
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 14
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.503
y[1] (closed_form) = -0.9837155235700465720273252455123
y[1] (numeric) = -0.9837155235700465720273252455123
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 14
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.504
y[1] (closed_form) = -0.98402222385780658567937768037798
y[1] (numeric) = -0.98402222385780658567937768037798
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 14
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.505
y[1] (closed_form) = -0.98432864145864946425894653704764
y[1] (numeric) = -0.98432864145864946425894653704764
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] = -1.506
memory used=4.4MB, alloc=40.3MB, time=0.09
y[1] (closed_form) = -0.9846347767057650282660065385424
y[1] (numeric) = -0.98463477670576502826600653854241
absolute error = 1e-32
relative error = 1.0156049975663479005392035556027e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.507
y[1] (closed_form) = -0.98494062993194102921194323609649
y[1] (numeric) = -0.9849406299319410292119432360965
absolute error = 1e-32
relative error = 1.0152896221461587656659697438830e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.508
y[1] (closed_form) = -0.98524620146956340906975142451197
y[1] (numeric) = -0.98524620146956340906975142451198
absolute error = 1e-32
relative error = 1.0149747327200351259048605356962e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.509
y[1] (closed_form) = -0.98555149165061656098473757267363
y[1] (numeric) = -0.98555149165061656098473757267364
absolute error = 1e-32
relative error = 1.0146603282241345487276712183737e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.51
y[1] (closed_form) = -0.98585650080668359123639033173802
y[1] (numeric) = -0.98585650080668359123639033173803
absolute error = 1e-32
relative error = 1.0143464075976000535183737410635e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.511
y[1] (closed_form) = -0.98616122926894658244212719255684
y[1] (numeric) = -0.98616122926894658244212719255685
absolute error = 1e-32
relative error = 1.0140329697825499265225548265063e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.512
y[1] (closed_form) = -0.98646567736818685799366920818855
y[1] (numeric) = -0.98646567736818685799366920818855
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] = -1.513
y[1] (closed_form) = -0.98676984543478524771683937729389
y[1] (numeric) = -0.98676984543478524771683937729389
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] = -1.514
y[1] (closed_form) = -0.98707373379872235474562380020178
y[1] (numeric) = -0.98707373379872235474562380020179
absolute error = 1e-32
relative error = 1.0130955426719048784320153085668e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.515
y[1] (closed_form) = -0.98737734278957882360137807187295
y[1] (numeric) = -0.98737734278957882360137807187296
absolute error = 1e-32
relative error = 1.0127840255831262335345418482739e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.516
y[1] (closed_form) = -0.98768067273653560946810456528295
y[1] (numeric) = -0.98768067273653560946810456528296
absolute error = 1e-32
relative error = 1.0124729860606987681761494415628e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.517
y[1] (closed_form) = -0.98798372396837424865476928529662
y[1] (numeric) = -0.98798372396837424865476928529663
absolute error = 1e-32
relative error = 1.0121624230643807621195390458299e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.518
y[1] (closed_form) = -0.9882864968134771302356698373165
y[1] (numeric) = -0.9882864968134771302356698373165
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] = -1.519
y[1] (closed_form) = -0.98858899159982776885990875726318
y[1] (numeric) = -0.98858899159982776885990875726318
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] = -1.52
y[1] (closed_form) = -0.9888912086550110787210689901915
y[1] (numeric) = -0.98889120865501107872106899019151
absolute error = 1e-32
relative error = 1.0112335828731837608199914232457e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.521
y[1] (closed_form) = -0.98919314830621364867823068446841
y[1] (numeric) = -0.98919314830621364867823068446842
absolute error = 1e-32
relative error = 1.0109249156368408175054508491175e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.522
y[1] (closed_form) = -0.98949481088022401851951068734359
y[1] (numeric) = -0.9894948108802240185195106873436
absolute error = 1e-32
relative error = 1.0106167197687786656931726859718e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.523
y[1] (closed_form) = -0.98979619670343295635934818633987
y[1] (numeric) = -0.98979619670343295635934818633987
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] = -1.524
y[1] (closed_form) = -0.99009730610183373716080183958421
y[1] (numeric) = -0.99009730610183373716080183958421
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] = -1.525
y[1] (closed_form) = -0.99039813940102242237416547740178
y[1] (numeric) = -0.99039813940102242237416547740177
absolute error = 1e-32
relative error = 1.0096949501589175393516249432437e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.526
y[1] (closed_form) = -0.99069869692619814068325103761255
y[1] (numeric) = -0.99069869692619814068325103761254
absolute error = 1e-32
relative error = 1.0093886295628132411230180264630e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.527
y[1] (closed_form) = -0.99099897900216336985072881841382
y[1] (numeric) = -0.99099897900216336985072881841381
absolute error = 1e-32
relative error = 1.0090827752485676180975535439494e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.528
y[1] (closed_form) = -0.9912989859533242196539563959113
y[1] (numeric) = -0.99129898595332421965395639591129
absolute error = 1e-32
relative error = 1.0087773862073591102177024628328e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.529
y[1] (closed_form) = -0.99159871810369071590276865868826
y[1] (numeric) = -0.99159871810369071590276865868826
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] = -1.53
y[1] (closed_form) = -0.99189817577687708553074235968741
y[1] (numeric) = -0.9918981757768770855307423596874
absolute error = 1e-32
relative error = 1.0081679999227515289002876770172e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.531
y[1] (closed_form) = -0.99219735929610204275148937653489
y[1] (numeric) = -0.99219735929610204275148937653488
absolute error = 1e-32
relative error = 1.0078640006756653850196823697524e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.532
y[1] (closed_form) = -0.99249626898418907627157350567385
y[1] (numeric) = -0.99249626898418907627157350567384
absolute error = 1e-32
relative error = 1.0075604626942234496474832341855e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.533
y[1] (closed_form) = -0.99279490516356673755168609370703
y[1] (numeric) = -0.99279490516356673755168609370702
absolute error = 1e-32
relative error = 1.0072573849835039148024289807873e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.534
y[1] (closed_form) = -0.99309326815626893010775613158899
y[1] (numeric) = -0.99309326815626893010775613158898
absolute error = 1e-32
relative error = 1.0069547665513369042031581283280e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.535
y[1] (closed_form) = -0.99339135828393519984371060417091
y[1] (numeric) = -0.9933913582839351998437106041709
absolute error = 1e-32
relative error = 1.0066526064082952199653306655054e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.536
y[1] (closed_form) = -0.99368917586781102640764089949904
y[1] (numeric) = -0.99368917586781102640764089949903
absolute error = 1e-32
relative error = 1.0063509035676851259335398545291e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.537
y[1] (closed_form) = -0.99398672122874811556317093961612
y[1] (numeric) = -0.99398672122874811556317093961611
absolute error = 1e-32
relative error = 1.0060496570455371674807906947054e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.538
y[1] (closed_form) = -0.99428399468720469256786239782779
y[1] (numeric) = -0.99428399468720469256786239782777
absolute error = 2e-32
relative error = 2.0114977317211940552183768576798e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.539
y[1] (closed_form) = -0.99458099656324579655053191688854
y[1] (numeric) = -0.99458099656324579655053191688852
absolute error = 2e-32
relative error = 2.0108970580686328383726845935783e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.54
y[1] (closed_form) = -0.99487772717654357587939463874932
y[1] (numeric) = -0.9948777271765435758793946387493
absolute error = 2e-32
relative error = 2.0102972911816880263056931026699e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.541
y[1] (closed_form) = -0.9951741868463775845129875998069
y[1] (numeric) = -0.99517418684637758451298759980688
absolute error = 2e-32
relative error = 2.0096984291140328050741051682160e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.542
y[1] (closed_form) = -0.99547037589163507932586563642001
y[1] (numeric) = -0.99547037589163507932586563641999
absolute error = 2e-32
relative error = 2.0091004699246982042283857913480e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.543
y[1] (closed_form) = -0.99576629463081131840110138422489
y[1] (numeric) = -0.99576629463081131840110138422487
absolute error = 2e-32
relative error = 2.0085034116780551670955192320692e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.544
y[1] (closed_form) = -0.99606194338200986028165974190967
y[1] (numeric) = -0.99606194338200986028165974190965
absolute error = 2e-32
relative error = 2.0079072524437966917037547427228e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.545
y[1] (closed_form) = -0.9963573224629428641727558060101
y[1] (numeric) = -0.99635732246294286417275580601008
absolute error = 2e-32
relative error = 2.0073119902969200420284850624773e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.546
y[1] (closed_form) = -0.99665243219093139108734376838494
y[1] (numeric) = -0.99665243219093139108734376838492
absolute error = 2e-32
relative error = 2.0067176233177090292400565785294e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.547
y[1] (closed_form) = -0.99694727288290570592692260273558
y[1] (numeric) = -0.99694727288290570592692260273555
absolute error = 3e-32
relative error = 3.0091862243875745439539329787192e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.548
y[1] (closed_form) = -0.99724184485540558048988255126777
y[1] (numeric) = -0.99724184485540558048988255126775
absolute error = 2e-32
relative error = 2.0055315672097460699414486869408e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.549
y[1] (closed_form) = -0.99753614842458059739965445777235
y[1] (numeric) = -0.99753614842458059739965445777233
absolute error = 2e-32
relative error = 2.0049398742678359866643891290517e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.55
y[1] (closed_form) = -0.9978301839061904549449618794427
y[1] (numeric) = -0.99783018390619045494496187944269
absolute error = 1e-32
relative error = 1.0021745344336201570957514174432e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.551
y[1] (closed_form) = -0.99812395161560527282451364706925
y[1] (numeric) = -0.99812395161560527282451364706923
absolute error = 2e-32
relative error = 2.0037591491144122463150941120963e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.552
y[1] (closed_form) = -0.99841745186780589878851213227124
y[1] (numeric) = -0.99841745186780589878851213227122
absolute error = 2e-32
relative error = 2.0031701131209866638806943773121e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.553
y[1] (closed_form) = -0.99871068497738421616938992156386
y[1] (numeric) = -0.99871068497738421616938992156384
absolute error = 2e-32
relative error = 2.0025819590037628972477737693479e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.554
y[1] (closed_form) = -0.99900365125854345229422489073047
y[1] (numeric) = -0.99900365125854345229422489073045
absolute error = 2e-32
relative error = 2.0019946848846875562572133080829e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.555
y[1] (closed_form) = -0.99929635102509848777132081959536
y[1] (numeric) = -0.99929635102509848777132081959534
absolute error = 2e-32
relative error = 2.0014082888908374274008063406578e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.556
y[1] (closed_form) = -0.99958878459047616664347768728934
y[1] (numeric) = -0.99958878459047616664347768728933
absolute error = 1e-32
relative error = 1.0004113845772012189448098980883e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.557
y[1] (closed_form) = -0.99988095226771560740051264188759
y[1] (numeric) = -0.99988095226771560740051264188757
absolute error = 2e-32
relative error = 2.0002381238126686863195985685500e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.558
y[1] (closed_form) = -1.0001728543694685148436293462945
y[1] (numeric) = -1.0001728543694685148436293462945
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] = -1.559
y[1] (closed_form) = -1.0004644912079994927942699648733
y[1] (numeric) = -1.0004644912079994927942699648733
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] = -1.56
y[1] (closed_form) = -1.0007558630951863576401204729864
y[1] (numeric) = -1.0007558630951863576401204729863
absolute error = 1e-31
relative error = 9.9924470780231195695041504208782e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.561
y[1] (closed_form) = -1.0010469703425204527109762447437
y[1] (numeric) = -1.0010469703425204527109762447437
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] = -1.562
y[1] (closed_form) = -1.0013378132611069634772110032747
y[1] (numeric) = -1.0013378132611069634772110032746
absolute error = 1e-31
relative error = 9.9866397409206984795123833259935e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.563
y[1] (closed_form) = -1.0016283921616652335636282031507
y[1] (numeric) = -1.0016283921616652335636282031506
absolute error = 1e-31
relative error = 9.9837425518844277414517124878672e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.564
y[1] (closed_form) = -1.001918707354529081571509756627
y[1] (numeric) = -1.0019187073545290815715097566269
absolute error = 1e-31
relative error = 9.9808496703330827548601767358754e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.565
y[1] (closed_form) = -1.0022087591496471187017127145426
y[1] (numeric) = -1.0022087591496471187017127145424
absolute error = 2e-31
relative error = 1.9955922174307851709345529703947e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.566
y[1] (closed_form) = -1.0024985478565830671717000694497
y[1] (numeric) = -1.0024985478565830671717000694495
absolute error = 2e-31
relative error = 1.9950153586517902704066465140728e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.567
y[1] (closed_form) = -1.0027880737845160794194272632517
y[1] (numeric) = -1.0027880737845160794194272632515
absolute error = 2e-31
relative error = 1.9944393559169607872432465925644e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.568
y[1] (closed_form) = -1.0030773372422410580870412547239
y[1] (numeric) = -1.0030773372422410580870412547236
absolute error = 3e-31
relative error = 2.9907963111278092180339826162946e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.569
y[1] (closed_form) = -1.0033663385381689767773841342047
y[1] (numeric) = -1.0033663385381689767773841342044
absolute error = 3e-31
relative error = 2.9899348670305000923592591927199e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.57
y[1] (closed_form) = -1.0036550779803272015763282638849
y[1] (numeric) = -1.0036550779803272015763282638847
absolute error = 2e-31
relative error = 1.9927164659243644153112744467419e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.571
y[1] (closed_form) = -1.0039435558763598133340047729067
y[1] (numeric) = -1.0039435558763598133340047729065
absolute error = 2e-31
relative error = 1.9921438693375198474508749766600e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.572
y[1] (closed_form) = -1.004231772533527930698021947339
y[1] (numeric) = -1.0042317725335279306980219473388
absolute error = 2e-31
relative error = 1.9915721198048697547926563574943e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.573
y[1] (closed_form) = -1.0045197282587100338918046264291
y[1] (numeric) = -1.0045197282587100338918046264289
absolute error = 2e-31
relative error = 1.9910012155429843464938403992728e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.574
y[1] (closed_form) = -1.0048074233584022892312201487656
y[1] (numeric) = -1.0048074233584022892312201487654
absolute error = 2e-31
relative error = 1.9904311547732514288682017670631e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.575
y[1] (closed_form) = -1.0050948581387188743726906855402
y[1] (numeric) = -1.00509485813871887437269068554
absolute error = 2e-31
relative error = 1.9898619357218605849435159616717e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.576
y[1] (closed_form) = -1.0053820329053923042860259533815
y[1] (numeric) = -1.0053820329053923042860259533813
absolute error = 2e-31
relative error = 1.9892935566197874151690296312179e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.577
y[1] (closed_form) = -1.0056689479637737579452443166746
y[1] (numeric) = -1.0056689479637737579452443166745
absolute error = 1e-31
relative error = 9.9436300785138891950029597712342e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.578
y[1] (closed_form) = -1.0059556036188334057306841692848
y[1] (numeric) = -1.0059556036188334057306841692846
absolute error = 2e-31
relative error = 1.9881593112113324570924626842326e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.579
y[1] (closed_form) = -1.0062420001751607375357412285954
y[1] (numeric) = -1.0062420001751607375357412285952
absolute error = 2e-31
relative error = 1.9875934413906909738261814870047e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.58
y[1] (closed_form) = -1.0065281379369648915716009811645
y[1] (numeric) = -1.0065281379369648915716009811643
absolute error = 2e-31
relative error = 1.9870284044908166799082444859662e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.581
y[1] (closed_form) = -1.0068140172080749838633689895111
y[1] (numeric) = -1.0068140172080749838633689895109
absolute error = 2e-31
relative error = 1.9864641987663809947696875038172e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.582
y[1] (closed_form) = -1.0070996382919404384310351039872
y[1] (numeric) = -1.007099638291940438431035103987
absolute error = 2e-31
relative error = 1.9859008224767480685020214023166e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.583
y[1] (closed_form) = -1.0073850014916313181487408227815
y[1] (numeric) = -1.0073850014916313181487408227814
absolute error = 1e-31
relative error = 9.9266913694297972153265161079853e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.584
y[1] (closed_form) = -1.0076701071098386562758521072564
y[1] (numeric) = -1.0076701071098386562758521072563
absolute error = 1e-31
relative error = 9.9238827563135938625272877774428e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.585
y[1] (closed_form) = -1.0079549554488747886533728894521
y[1] (numeric) = -1.007954955448874788653372889452
absolute error = 1e-31
relative error = 9.9210782644018830095964290836528e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.586
y[1] (closed_form) = -1.0082395468106736865592673041213
y[1] (numeric) = -1.0082395468106736865592673041212
absolute error = 1e-31
relative error = 9.9182778850845760245345839649560e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.587
y[1] (closed_form) = -1.0085238814967912902162913394908
y[1] (numeric) = -1.0085238814967912902162913394907
absolute error = 1e-31
relative error = 9.9154816097746673962638010907097e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.588
y[1] (closed_form) = -1.008807959808405842945967129505
y[1] (numeric) = -1.0088079598084058429459671295049
absolute error = 1e-31
relative error = 9.9126894299081595028866301487158e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.589
y[1] (closed_form) = -1.0090917820463182259623655059993
y[1] (numeric) = -1.0090917820463182259623655059992
absolute error = 1e-31
relative error = 9.9099013369439876685178279969791e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.59
y[1] (closed_form) = -1.0093753485109522937993946924935
y[1] (numeric) = -1.0093753485109522937993946924935
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] = -1.591
y[1] (closed_form) = -1.0096586595023552103653251525016
y[1] (numeric) = -1.0096586595023552103653251525016
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] = -1.592
y[1] (closed_form) = -1.0099417153201977856183126048325
y[1] (numeric) = -1.0099417153201977856183126048324
absolute error = 1e-31
relative error = 9.9015614943972701784384100812268e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.593
y[1] (closed_form) = -1.0102245162637748128567130867272
y[1] (numeric) = -1.0102245162637748128567130867271
absolute error = 1e-31
relative error = 9.8987896640878477837764750418765e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.594
y[1] (closed_form) = -1.0105070626320054066180156832441
y[1] (numeric) = -1.010507062632005406618015683244
absolute error = 1e-31
relative error = 9.8960218783168292879219808824331e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.595
y[1] (closed_form) = -1.0107893547234333411802501484831
y[1] (numeric) = -1.0107893547234333411802501484829
absolute error = 2e-31
relative error = 1.9786516257358379769423144315890e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.596
y[1] (closed_form) = -1.0110713928362273896597581214427
y[1] (numeric) = -1.0110713928362273896597581214426
absolute error = 1e-31
relative error = 9.8904984067923210855263332625312e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.597
y[1] (closed_form) = -1.011353177268181663699247986941
y[1] (numeric) = -1.0113531772681816636992479869408
absolute error = 2e-31
relative error = 1.9775485408591916078653517785836e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.598
y[1] (closed_form) = -1.0116347083167159537400846505073
y[1] (numeric) = -1.0116347083167159537400846505071
absolute error = 2e-31
relative error = 1.9769982025704214260019990384210e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.599
y[1] (closed_form) = -1.0119159862788760698727965858925
y[1] (numeric) = -1.0119159862788760698727965858923
absolute error = 2e-31
relative error = 1.9764486648289947699740695019256e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.6
y[1] (closed_form) = -1.0121970114513341832598134752381
y[1] (numeric) = -1.0121970114513341832598134752379
absolute error = 2e-31
relative error = 1.9758999259761781895900260792693e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.601
y[1] (closed_form) = -1.0124777841303891681244785954202
y[1] (numeric) = -1.01247778413038916812447859542
absolute error = 2e-31
relative error = 1.9753519843576493704147962259709e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.602
y[1] (closed_form) = -1.0127583046119669443004108100369
y[1] (numeric) = -1.0127583046119669443004108100368
absolute error = 1e-31
relative error = 9.8740241916174143633657699528886e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.603
y[1] (closed_form) = -1.0130385731916208203353216053524
y[1] (numeric) = -1.0130385731916208203353216053522
absolute error = 2e-31
relative error = 1.9742584862281359244106437022219e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.604
y[1] (closed_form) = -1.0133185901645318371434230606528
y[1] (numeric) = -1.0133185901645318371434230606526
absolute error = 2e-31
relative error = 1.9737129264304342686742565813469e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.605
y[1] (closed_form) = -1.0135983558255091122005929693204
y[1] (numeric) = -1.0135983558255091122005929693203
absolute error = 1e-31
relative error = 9.8658407864677903223812695475112e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.606
y[1] (closed_form) = -1.0138778704689901842764935268911
y[1] (numeric) = -1.013877870468990184276493526891
absolute error = 1e-31
relative error = 9.8631208859251392065285307720563e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.607
y[1] (closed_form) = -1.0141571343890413586978700768424
y[1] (numeric) = -1.0141571343890413586978700768423
absolute error = 1e-31
relative error = 9.8604049223834525347674332765327e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.608
y[1] (closed_form) = -1.0144361478793580531372863542673
y[1] (numeric) = -1.0144361478793580531372863542671
absolute error = 2e-31
relative error = 1.9715385775447054084176211713667e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.609
y[1] (closed_form) = -1.0147149112332651439215824923232
y[1] (numeric) = -1.014714911233265143921582492323
absolute error = 2e-31
relative error = 1.9709969547695304456570508232268e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.61
y[1] (closed_form) = -1.0149934247437173128543717568226
y[1] (numeric) = -1.0149934247437173128543717568224
absolute error = 2e-31
relative error = 1.9704561145359082379630157539480e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.611
y[1] (closed_form) = -1.015271688703299394546921550942
y[1] (numeric) = -1.0152716887032993945469215509418
absolute error = 2e-31
relative error = 1.9699160552328523427184102412606e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.612
y[1] (closed_form) = -1.015549703404226724251793685188
y[1] (numeric) = -1.0155497034042267242517936851878
absolute error = 2e-31
relative error = 1.9693767752536335263165970467481e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.613
y[1] (closed_form) = -1.0158274691383454861936482378634
y[1] (numeric) = -1.0158274691383454861936482378632
absolute error = 2e-31
relative error = 1.9688382729957660870122995291303e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.614
y[1] (closed_form) = -1.0161049861971330623916445387347
y[1] (numeric) = -1.0161049861971330623916445387345
absolute error = 2e-31
relative error = 1.9683005468609942294783145168151e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.615
y[1] (closed_form) = -1.0163822548716983819679018938144
y[1] (numeric) = -1.0163822548716983819679018938142
absolute error = 2e-31
relative error = 1.9677635952552784908429071680757e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.616
y[1] (closed_form) = -1.016659275452782270936511632536
y[1] (numeric) = -1.0166592754527822709365116325358
absolute error = 2e-31
relative error = 1.9672274165887822179838610839669e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.617
y[1] (closed_form) = -1.0169360482307578024676209005257
y[1] (numeric) = -1.0169360482307578024676209005254
absolute error = 3e-31
relative error = 2.9500380139137871437843942262857e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.618
y[1] (closed_form) = -1.0172125734956306476211373420518
y[1] (numeric) = -1.0172125734956306476211373420516
absolute error = 2e-31
relative error = 1.9661573717350347266321996807807e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.619
y[1] (closed_form) = -1.0174888515370394265446324164765
y[1] (numeric) = -1.0174888515370394265446324164762
absolute error = 3e-31
relative error = 2.9484352535835048891474651394292e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.62
y[1] (closed_form) = -1.0177648826442560601300495730236
y[1] (numeric) = -1.0177648826442560601300495730234
absolute error = 2e-31
relative error = 1.9650903996646040704248800094666e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.621
y[1] (closed_form) = -1.0180406671061861221238518683366
y[1] (numeric) = -1.0180406671061861221238518683364
absolute error = 2e-31
relative error = 1.9645580619928134930879272594581e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.622
y[1] (closed_form) = -1.018316205211369191685271852
y[1] (numeric) = -1.0183162052113691916852718519997
absolute error = 3e-31
relative error = 2.9460397317130958975901869036881e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.623
y[1] (closed_form) = -1.0185914972479792063873546668637
y[1] (numeric) = -1.0185914972479792063873546668635
absolute error = 2e-31
relative error = 1.9634956755515640247208153631386e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.624
y[1] (closed_form) = -1.0188665435038248156555133140183
y[1] (numeric) = -1.018866543503824815655513314018
memory used=37.1MB, alloc=40.3MB, time=0.52
absolute error = 3e-31
relative error = 2.9444484354969282859046589788524e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.625
y[1] (closed_form) = -1.0191413442663497346383429170231
y[1] (numeric) = -1.0191413442663497346383429170228
absolute error = 3e-31
relative error = 2.9436544958929253351456167073972e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.626
y[1] (closed_form) = -1.0194158998226330985054685868957
y[1] (numeric) = -1.0194158998226330985054685868954
absolute error = 3e-31
relative error = 2.9428616921925254058438186787245e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.627
y[1] (closed_form) = -1.0196902104593898171672291388033
y[1] (numeric) = -1.019690210459389817167229138803
absolute error = 3e-31
relative error = 2.9420700220790027889587574966974e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.628
y[1] (closed_form) = -1.0199642764629709304110264437729
y[1] (numeric) = -1.0199642764629709304110264437726
absolute error = 3e-31
relative error = 2.9412794832416984583141692345269e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.629
y[1] (closed_form) = -1.0202380981193639634491976144342
y[1] (numeric) = -1.0202380981193639634491976144339
absolute error = 3e-31
relative error = 2.9404900733760007562066346540415e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.63
y[1] (closed_form) = -1.0205116757141932828732945232312
y[1] (numeric) = -1.020511675714193282873294523231
absolute error = 2e-31
relative error = 1.9598011934555507675764509282270e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.631
y[1] (closed_form) = -1.0207850095327204530096823350723
y[1] (numeric) = -1.0207850095327204530096823350721
absolute error = 2e-31
relative error = 1.9592764209140667126308369757500e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.632
y[1] (closed_form) = -1.0210580998598445926713958044295
y[1] (numeric) = -1.0210580998598445926713958044293
absolute error = 2e-31
relative error = 1.9587523964351585281760648568171e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.633
y[1] (closed_form) = -1.0213309469801027323012190398388
y[1] (numeric) = -1.0213309469801027323012190398385
absolute error = 3e-31
relative error = 2.9373436777476254359297959247823e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.634
y[1] (closed_form) = -1.0216035511776701715009812769787
y[1] (numeric) = -1.0216035511776701715009812769784
absolute error = 3e-31
relative error = 2.9365598783811009901091554311984e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.635
y[1] (closed_form) = -1.0218759127363608369420879254161
y[1] (numeric) = -1.0218759127363608369420879254158
absolute error = 3e-31
relative error = 2.9357771942844354355827290059646e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.636
y[1] (closed_form) = -1.0221480319396276406523327640814
y[1] (numeric) = -1.0221480319396276406523327640811
absolute error = 3e-31
relative error = 2.9349956231948139293070104440877e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.637
y[1] (closed_form) = -1.0224199090705628386740636569746
y[1] (numeric) = -1.0224199090705628386740636569742
absolute error = 4e-31
relative error = 3.9122868838070894135642903667542e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.638
y[1] (closed_form) = -1.022691544411898390088800543882
y[1] (numeric) = -1.0226915444118983900888005438816
absolute error = 4e-31
relative error = 3.9112477480198695662161152183968e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.639
y[1] (closed_form) = -1.0229629382460063164034307314038
y[1] (numeric) = -1.0229629382460063164034307314034
absolute error = 4e-31
relative error = 3.9102100872378463627927445843385e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.64
y[1] (closed_form) = -1.0232340908548990612931326677265
y[1] (numeric) = -1.023234090854899061293132667726
absolute error = 5e-31
relative error = 4.8864673730940332819661931569450e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.641
y[1] (closed_form) = -1.0235050025202298506962054307213
y[1] (numeric) = -1.0235050025202298506962054307208
absolute error = 5e-31
relative error = 4.8851739734424733892712655592292e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.642
y[1] (closed_form) = -1.0237756735232930532560070934894
y[1] (numeric) = -1.0237756735232930532560070934889
absolute error = 5e-31
relative error = 4.8838824063797599767954636528409e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.643
y[1] (closed_form) = -1.0240461041450245411052309547881
y[1] (numeric) = -1.0240461041450245411052309547875
absolute error = 6e-31
relative error = 5.8591112018431985428149941102425e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.644
y[1] (closed_form) = -1.0243162946660020509877743342532
y[1] (numeric) = -1.0243162946660020509877743342526
absolute error = 6e-31
relative error = 5.8575657062610869937352233128663e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.645
y[1] (closed_form) = -1.0245862453664455457134802343583
y[1] (numeric) = -1.0245862453664455457134802343577
absolute error = 6e-31
relative error = 5.8560223964885324780135003647156e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.646
y[1] (closed_form) = -1.0248559565262175759410576630018
y[1] (numeric) = -1.0248559565262175759410576630013
absolute error = 5e-31
relative error = 4.8787343900967915295825162404301e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.647
y[1] (closed_form) = -1.0251254284248236422845117928801
y[1] (numeric) = -1.0251254284248236422845117928796
absolute error = 5e-31
relative error = 4.8774519306216478963057071131223e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.648
y[1] (closed_form) = -1.025394661341412557738440406758
y[1] (numeric) = -1.0253946613414125577384404067574
absolute error = 6e-31
relative error = 5.8514055379914413938122377877707e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.649
y[1] (closed_form) = -1.0256636555547768104175782417792
y[1] (numeric) = -1.0256636555547768104175782417786
absolute error = 6e-31
relative error = 5.8498709274773193220925944018235e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.65
y[1] (closed_form) = -1.0259324113433529266059959014387
y[1] (numeric) = -1.0259324113433529266059959014381
absolute error = 6e-31
relative error = 5.8483384808397050113481824659516e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.651
y[1] (closed_form) = -1.0262009289852218341113849511525
y[1] (numeric) = -1.0262009289852218341113849511519
absolute error = 6e-31
relative error = 5.8468081937259726466353609559315e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.652
y[1] (closed_form) = -1.0264692087581092259198856528828
y[1] (numeric) = -1.0264692087581092259198856528822
absolute error = 6e-31
relative error = 5.8452800617947413938089092945662e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.653
y[1] (closed_form) = -1.0267372509393859241469385263886
y[1] (numeric) = -1.026737250939385924146938526388
absolute error = 6e-31
relative error = 5.8437540807158400772927127893318e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.654
y[1] (closed_form) = -1.0270050558060682442796655497461
y[1] (numeric) = -1.0270050558060682442796655497455
absolute error = 6e-31
relative error = 5.8422302461702719883807880573529e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.655
y[1] (closed_form) = -1.0272726236348183597063113302
y[1] (numeric) = -1.0272726236348183597063113301994
absolute error = 6e-31
relative error = 5.8407085538501798235133217256992e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.656
y[1] (closed_form) = -1.0275399547019446665282989885398
y[1] (numeric) = -1.0275399547019446665282989885392
absolute error = 6e-31
relative error = 5.8391889994588107519750743080505e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.657
y[1] (closed_form) = -1.0278070492834021486504798064199
y[1] (numeric) = -1.0278070492834021486504798064193
absolute error = 6e-31
relative error = 5.8376715787104816124661652932972e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.658
y[1] (closed_form) = -1.0280739076547927431451798867289
y[1] (numeric) = -1.0280739076547927431451798867283
absolute error = 6e-31
relative error = 5.8361562873305442379979052245236e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.659
y[1] (closed_form) = -1.0283405300913657058856711726431
y[1] (numeric) = -1.0283405300913657058856711726425
absolute error = 6e-31
relative error = 5.8346431210553509085689759842852e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.66
y[1] (closed_form) = -1.0286069168680179774447181617342
y[1] (numeric) = -1.0286069168680179774447181617336
absolute error = 6e-31
relative error = 5.8331320756322199310798817199252e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.661
y[1] (closed_form) = -1.0288730682592945492538755378225
y[1] (numeric) = -1.0288730682592945492538755378219
absolute error = 6e-31
relative error = 5.8316231468194013459461999259718e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.662
y[1] (closed_form) = -1.0291389845393888300192357255379
y[1] (numeric) = -1.0291389845393888300192357255373
absolute error = 6e-31
relative error = 5.8301163303860427598737552340514e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.663
y[1] (closed_form) = -1.0294046659821430123893490511472
y[1] (numeric) = -1.0294046659821430123893490511466
absolute error = 6e-31
relative error = 5.8286116221121553042614175282429e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.664
y[1] (closed_form) = -1.0296701128610484398710627684934
y[1] (numeric) = -1.0296701128610484398710627684928
absolute error = 6e-31
relative error = 5.8271090177885797186997911888878e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.665
y[1] (closed_form) = -1.0299353254492459739890486812413
y[1] (numeric) = -1.0299353254492459739890486812407
absolute error = 6e-31
relative error = 5.8256085132169525590366136534791e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.666
y[1] (closed_form) = -1.0302003040195263616848124624
y[1] (numeric) = -1.0302003040195263616848124623995
absolute error = 5e-31
relative error = 4.8534250868413937745685159598058e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.667
y[1] (closed_form) = -1.0304650488443306029510010396658
y[1] (numeric) = -1.0304650488443306029510010396652
absolute error = 6e-31
relative error = 5.8226137865898669382309475054841e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.668
y[1] (closed_form) = -1.0307295601957503186968475808608
y[1] (numeric) = -1.0307295601957503186968475808602
absolute error = 6e-31
relative error = 5.8211195561913582760768883624261e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.669
y[1] (closed_form) = -1.0309938383455281188406166780065
y[1] (numeric) = -1.0309938383455281188406166780059
absolute error = 6e-31
relative error = 5.8196274088586309175048482407590e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.67
y[1] (closed_form) = -1.0312578835650579706249352917186
y[1] (numeric) = -1.031257883565057970624935291718
absolute error = 6e-31
relative error = 5.8181373404467979437399113726815e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.671
y[1] (closed_form) = -1.0315216961253855671509178800198
y[1] (numeric) = -1.0315216961253855671509178800191
absolute error = 7e-31
relative error = 6.7860909046251627684483415760003e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.672
y[1] (closed_form) = -1.0317852762972086961270168976902
y[1] (numeric) = -1.0317852762972086961270168976895
absolute error = 7e-31
relative error = 6.7843573278357482633180789215599e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.673
y[1] (closed_form) = -1.0320486243508776088285525142806
y[1] (numeric) = -1.0320486243508776088285525142799
absolute error = 7e-31
relative error = 6.7826261620209556625426058135853e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.674
y[1] (closed_form) = -1.0323117405563953892638979612579
y[1] (numeric) = -1.0323117405563953892638979612572
absolute error = 7e-31
relative error = 6.7808974023942999526831584289193e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.675
y[1] (closed_form) = -1.0325746251834183235433193818035
y[1] (numeric) = -1.0325746251834183235433193818028
absolute error = 7e-31
relative error = 6.7791710441815048593343211878944e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.676
y[1] (closed_form) = -1.0328372785012562694464914208908
y[1] (numeric) = -1.0328372785012562694464914208901
absolute error = 7e-31
relative error = 6.7774470826204649818949108479010e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.677
y[1] (closed_form) = -1.0330997007788730261847320588002
y[1] (numeric) = -1.0330997007788730261847320587995
absolute error = 7e-31
relative error = 6.7757255129612080664845880109801e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.678
y[1] (closed_form) = -1.0333618922848867043540223585378
y[1] (numeric) = -1.033361892284886704354022358537
absolute error = 8e-31
relative error = 7.7417215205324084759155327089157e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.679
y[1] (closed_form) = -1.0336238532875700960748988670659
y[1] (numeric) = -1.0336238532875700960748988670652
absolute error = 7e-31
relative error = 6.7722895304085944397157490564181e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.68
y[1] (closed_form) = -1.0338855840548510453153283821921
y[1] (numeric) = -1.0338855840548510453153283821914
absolute error = 7e-31
relative error = 6.7705751080756213329076747582604e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.681
y[1] (closed_form) = -1.0341470848543128183926966717421
y[1] (numeric) = -1.0341470848543128183926966717414
absolute error = 7e-31
relative error = 6.7688630587651239008397739730989e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.682
y[1] (closed_form) = -1.034408355953194474651064509632
y[1] (numeric) = -1.0344083559531944746510645096313
absolute error = 7e-31
relative error = 6.7671533777872345116324203706343e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.683
y[1] (closed_form) = -1.0346693976183912373098660749934
y[1] (numeric) = -1.0346693976183912373098660749926
absolute error = 8e-31
relative error = 7.7319383548159944987352582000105e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.684
y[1] (closed_form) = -1.034930210116454864480246345955
y[1] (numeric) = -1.0349302101164548644802463459542
absolute error = 8e-31
relative error = 7.7299898310049380835028842974328e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.685
y[1] (closed_form) = -1.0351907937135940203452556094
y[1] (numeric) = -1.0351907937135940203452556093992
absolute error = 8e-31
relative error = 7.7280439978616714901181196049292e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.686
y[1] (closed_form) = -1.0354511486756746465001406023373
y[1] (numeric) = -1.0354511486756746465001406023366
absolute error = 7e-31
relative error = 6.7603382438204712356794081887588e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.687
y[1] (closed_form) = -1.0357112752682203334489930998183
y[1] (numeric) = -1.0357112752682203334489930998176
absolute error = 7e-31
relative error = 6.7586403345731610730982651991830e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.688
y[1] (closed_form) = -1.0359711737564126922540379689265
y[1] (numeric) = -1.0359711737564126922540379689258
absolute error = 7e-31
relative error = 6.7569447657680733731319198084786e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.689
y[1] (closed_form) = -1.0362308444050917263338638186339
y[1] (numeric) = -1.0362308444050917263338638186332
absolute error = 7e-31
relative error = 6.7552515327979404314656769942663e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.69
y[1] (closed_form) = -1.0364902874787562034069203915875
y[1] (numeric) = -1.0364902874787562034069203915868
absolute error = 7e-31
relative error = 6.7535606310671495494601254348885e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.691
y[1] (closed_form) = -1.0367495032415640275766277665203
y[1] (numeric) = -1.0367495032415640275766277665196
absolute error = 7e-31
relative error = 6.7518720559917071814333503771844e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.692
y[1] (closed_form) = -1.0370084919573326115544632693128
y[1] (numeric) = -1.0370084919573326115544632693121
absolute error = 7e-31
relative error = 6.7501858029992032116706275548249e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.693
y[1] (closed_form) = -1.0372672538895392490174127271123
y[1] (numeric) = -1.0372672538895392490174127271116
absolute error = 7e-31
relative error = 6.7485018675287753606214018388441e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.694
y[1] (closed_form) = -1.0375257893013214870961933436928
y[1] (numeric) = -1.0375257893013214870961933436921
absolute error = 7e-31
relative error = 6.7468202450310737197459034022100e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.695
y[1] (closed_form) = -1.037784098455477498990676025748
y[1] (numeric) = -1.0377840984554774989906760257473
absolute error = 7e-31
relative error = 6.7451409309682254144762898073551e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.696
y[1] (closed_form) = -1.0380421816144664567089554494038
y[1] (numeric) = -1.0380421816144664567089554494031
absolute error = 7e-31
relative error = 6.7434639208137993947597246585187e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.697
y[1] (closed_form) = -1.038300039040408903926536524248
y[1] (numeric) = -1.0383000390404089039265365242473
absolute error = 7e-31
relative error = 6.7417892100527713526533123780750e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.698
y[1] (closed_form) = -1.038557670995087128962126188953
y[1] (numeric) = -1.0385576709950871289621261889522
absolute error = 8e-31
relative error = 7.7029906219217014473637763950644e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.699
y[1] (closed_form) = -1.0388150777399455378665396584461
y[1] (numeric) = -1.0388150777399455378665396584453
absolute error = 8e-31
relative error = 7.7010819070944412237296847526919e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.7
y[1] (closed_form) = -1.0390722595360910276212503379073
y[1] (numeric) = -1.0390722595360910276212503379065
absolute error = 8e-31
relative error = 7.6991758047430856596457476662046e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.701
y[1] (closed_form) = -1.0393292166442933594431326239748
y[1] (numeric) = -1.039329216644293359443132623974
absolute error = 8e-31
relative error = 7.6972723097593540226204367943251e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.702
y[1] (closed_form) = -1.0395859493249855321919667287672
y[1] (numeric) = -1.0395859493249855321919667287664
absolute error = 8e-31
relative error = 7.6953714170478035430006282420110e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.703
y[1] (closed_form) = -1.0398424578382641558772944880061
y[1] (numeric) = -1.0398424578382641558772944880053
absolute error = 8e-31
relative error = 7.6934731215257901784438578874278e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.704
y[1] (closed_form) = -1.0400987424438898252612348509983
y[1] (numeric) = -1.0400987424438898252612348509974
absolute error = 9e-31
relative error = 8.6530245953888582093599651057326e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.705
y[1] (closed_form) = -1.0403548034012874935538873978328
y[1] (numeric) = -1.0403548034012874935538873978319
absolute error = 9e-31
relative error = 8.6508948395065025646410906194064e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.706
y[1] (closed_form) = -1.0406106409695468461979717882109
y[1] (numeric) = -1.04061064096954684619797178821
absolute error = 9e-31
relative error = 8.6487679883944049172457318367933e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.707
y[1] (closed_form) = -1.0408662554074226747393705171791
y[1] (numeric) = -1.0408662554074226747393705171782
absolute error = 9e-31
relative error = 8.6466440363917467563342684713637e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.708
y[1] (closed_form) = -1.0411216469733352507802617360203
y[1] (numeric) = -1.0411216469733352507802617360194
absolute error = 9e-31
relative error = 8.6445229778518898064259398430795e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.709
y[1] (closed_form) = -1.0413768159253707000115481919974
y[1] (numeric) = -1.0413768159253707000115481919964
absolute error = 1.0e-30
relative error = 9.6026720079359253662998380548771e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.71
y[1] (closed_form) = -1.0416317625212813763213075488757
y[1] (numeric) = -1.0416317625212813763213075488748
absolute error = 9e-31
relative error = 8.6402895186446685828944022342828e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.711
y[1] (closed_form) = -1.0418864870184862359760084715006
y[1] (numeric) = -1.0418864870184862359760084714997
absolute error = 9e-31
relative error = 8.6381771067545409287969596581956e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.712
y[1] (closed_form) = -1.0421409896740712118712558925046
y[1] (numeric) = -1.0421409896740712118712558925037
absolute error = 9e-31
relative error = 8.6360675658816021006387471000434e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.713
y[1] (closed_form) = -1.0423952707447895878488478277957
y[1] (numeric) = -1.0423952707447895878488478277948
absolute error = 9e-31
relative error = 8.6339608904494701198126771603298e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.714
y[1] (closed_form) = -1.0426493304870623730769449701572
y[1] (numeric) = -1.0426493304870623730769449701562
absolute error = 1.0e-30
relative error = 9.5909523054396515173944119685222e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.715
y[1] (closed_form) = -1.0429031691569786764901730673983
y[1] (numeric) = -1.0429031691569786764901730673973
absolute error = 1.0e-30
relative error = 9.5886179040796369965269530555733e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.716
y[1] (closed_form) = -1.0431567870102960812864967833629
y[1] (numeric) = -1.0431567870102960812864967833619
absolute error = 1.0e-30
relative error = 9.5862866680474359155275506951969e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.717
y[1] (closed_form) = -1.0434101843024410194777223470474
y[1] (numeric) = -1.0434101843024410194777223470464
absolute error = 1.0e-30
relative error = 9.5839585912086687022814937407696e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.718
y[1] (closed_form) = -1.0436633612885091464905048174304
y[1] (numeric) = -1.0436633612885091464905048174294
absolute error = 1.0e-30
relative error = 9.5816336674442392815023589292596e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.719
y[1] (closed_form) = -1.0439163182232657158147542296939
y[1] (numeric) = -1.0439163182232657158147542296928
absolute error = 1.1e-30
relative error = 1.0537243079715317642053847310091e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.72
y[1] (closed_form) = -1.0441690553611459536963532426421
y[1] (numeric) = -1.044169055361145953696353242641
absolute error = 1.1e-30
relative error = 1.0534692580211964241002577780581e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.721
y[1] (closed_form) = -1.0444215729562554338711171776211
y[1] (numeric) = -1.04442157295625543387111717762
absolute error = 1.1e-30
relative error = 1.0532145528997727947708964707052e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.722
y[1] (closed_form) = -1.0446738712623704523369455264271
y[1] (numeric) = -1.0446738712623704523369455264261
absolute error = 1.0e-30
relative error = 9.5723653812803117050287233485355e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.723
y[1] (closed_form) = -1.0449259505329384021611321098912
y[1] (numeric) = -1.0449259505329384021611321098902
absolute error = 1.0e-30
relative error = 9.5700561316328200831984887329475e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.724
y[1] (closed_form) = -1.0451778110210781483198190903494
y[1] (numeric) = -1.0451778110210781483198190903483
absolute error = 1.1e-30
relative error = 1.0524524998529807576526655637259e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.725
y[1] (closed_form) = -1.0454294529795804025665979803791
y[1] (numeric) = -1.045429452979580402566597980378
absolute error = 1.1e-30
relative error = 1.0521991673994720363192771087814e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.726
y[1] (closed_form) = -1.0456808766609080983272786473166
y[1] (numeric) = -1.0456808766609080983272786473155
absolute error = 1.1e-30
relative error = 1.0519461764592510851022434392873e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.727
y[1] (closed_form) = -1.0459320823171967656178650884773
y[1] (numeric) = -1.0459320823171967656178650884761
absolute error = 1.2e-30
relative error = 1.1473020287717682870413953957898e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.728
y[1] (closed_form) = -1.0461830702002549059827944460079
y[1] (numeric) = -1.0461830702002549059827944460068
absolute error = 1.1e-30
relative error = 1.0514412164875156487151503342649e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.729
y[1] (closed_form) = -1.0464338405615643674505133432104
y[1] (numeric) = -1.0464338405615643674505133432092
absolute error = 1.2e-30
relative error = 1.1467519048849041348955587742930e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.73
y[1] (closed_form) = -1.0466843936522807195034831563044
y[1] (numeric) = -1.0466843936522807195034831563032
absolute error = 1.2e-30
relative error = 1.1464773978455365179394934670042e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.731
y[1] (closed_form) = -1.0469347297232336280597232872656
y[1] (numeric) = -1.0469347297232336280597232872644
absolute error = 1.2e-30
relative error = 1.1462032597936936505289293761292e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.732
y[1] (closed_form) = -1.0471848490249272304630188748779
y[1] (numeric) = -1.0471848490249272304630188748767
absolute error = 1.2e-30
relative error = 1.1459294900201856830989130780254e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.733
y[1] (closed_form) = -1.0474347518075405104789366728037
y[1] (numeric) = -1.0474347518075405104789366728025
absolute error = 1.2e-30
relative error = 1.1456560878175754720691843853528e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.734
y[1] (closed_form) = -1.0476844383209276732938100356012
y[1] (numeric) = -1.0476844383209276732938100356
absolute error = 1.2e-30
relative error = 1.1453830524801733114388171002851e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.735
y[1] (closed_form) = -1.0479339088146185205138710865148
y[1] (numeric) = -1.0479339088146185205138710865136
absolute error = 1.2e-30
relative error = 1.1451103833040316830055258442015e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.736
y[1] (closed_form) = -1.0481831635378188251617251948455
y[1] (numeric) = -1.0481831635378188251617251948443
absolute error = 1.2e-30
relative error = 1.1448380795869400251338956766369e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.737
y[1] (closed_form) = -1.0484322027394107066673798660733
y[1] (numeric) = -1.0484322027394107066673798660721
absolute error = 1.2e-30
relative error = 1.1445661406284195199971401120796e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.738
y[1] (closed_form) = -1.048681026667953005851057044964
y[1] (numeric) = -1.0486810266679530058510570449628
absolute error = 1.2e-30
relative error = 1.1442945657297178992173402398693e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.739
y[1] (closed_form) = -1.0489296355716816598950346509516
y[1] (numeric) = -1.0489296355716816598950346509504
absolute error = 1.2e-30
relative error = 1.1440233541938042678294629602534e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.74
y[1] (closed_form) = -1.0491780296985100773017799064475
y[1] (numeric) = -1.0491780296985100773017799064463
absolute error = 1.2e-30
relative error = 1.1437525053253639464947998788342e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.741
y[1] (closed_form) = -1.0494262092960295128356536826984
y[1] (numeric) = -1.0494262092960295128356536826972
absolute error = 1.2e-30
relative error = 1.1434820184307933318898101623329e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.742
y[1] (closed_form) = -1.0496741746115094424454816746877
y[1] (numeric) = -1.0496741746115094424454816746865
absolute error = 1.2e-30
relative error = 1.1432118928181947751966906609218e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.743
y[1] (closed_form) = -1.0499219258918979381653047266663
y[1] (numeric) = -1.0499219258918979381653047266651
absolute error = 1.2e-30
relative error = 1.1429421277973714786223348563426e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.744
y[1] (closed_form) = -1.0501694633838220429906370634934
y[1] (numeric) = -1.0501694633838220429906370634922
absolute error = 1.2e-30
relative error = 1.1426727226798224098726787106318e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.745
y[1] (closed_form) = -1.0504167873335881457275775403811
y[1] (numeric) = -1.0504167873335881457275775403799
absolute error = 1.2e-30
relative error = 1.1424036767787372345097662773971e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.746
y[1] (closed_form) = -1.0506638979871823558121353051524
y[1] (numeric) = -1.0506638979871823558121353051512
absolute error = 1.2e-30
relative error = 1.1421349894089912661192010060941e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.747
y[1] (closed_form) = -1.0509107955902708780971474730531
y[1] (numeric) = -1.050910795590270878097147473052
absolute error = 1.1e-30
relative error = 1.0467111048965453980313150269618e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.748
y[1] (closed_form) = -1.0511574803882003876041825447895
y[1] (numeric) = -1.0511574803882003876041825447883
absolute error = 1.2e-30
relative error = 1.1415986875314162698170383844273e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.749
y[1] (closed_form) = -1.0514039526259984042378393540978
y[1] (numeric) = -1.0514039526259984042378393540966
absolute error = 1.2e-30
relative error = 1.1413310716617209086091580892417e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.75
y[1] (closed_form) = -1.0516502125483736674598673120863
y[1] (numeric) = -1.0516502125483736674598673120851
absolute error = 1.2e-30
relative error = 1.1410638115996221116412232880962e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.751
y[1] (closed_form) = -1.0518962603997165109205496221103
y[1] (numeric) = -1.0518962603997165109205496221091
absolute error = 1.2e-30
relative error = 1.1407969066683483034701272988026e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.752
y[1] (closed_form) = -1.0521420964240992370448069713523
y[1] (numeric) = -1.0521420964240992370448069713511
absolute error = 1.2e-30
relative error = 1.1405303561927836276899603564519e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.753
y[1] (closed_form) = -1.0523877208652764915704949638652
y[1] (numeric) = -1.052387720865276491570494963864
absolute error = 1.2e-30
relative error = 1.1402641594994630197744281559983e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.754
y[1] (closed_form) = -1.0526331339666856380363842448938
y[1] (numeric) = -1.0526331339666856380363842448926
absolute error = 1.2e-30
relative error = 1.1399983159165672971627709629272e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.755
y[1] (closed_form) = -1.0528783359714471322173278781071
y[1] (numeric) = -1.0528783359714471322173278781059
absolute error = 1.2e-30
relative error = 1.1397328247739182665197710950808e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.756
y[1] (closed_form) = -1.053123327122364896504136076245
y[1] (numeric) = -1.0531233271223648965041360762438
absolute error = 1.2e-30
relative error = 1.1394676854029738481007529890746e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.757
y[1] (closed_form) = -1.0533681076619266942256938518897
y[1] (numeric) = -1.0533681076619266942256938518885
absolute error = 1.2e-30
relative error = 1.1392028971368232171527948607892e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.758
y[1] (closed_form) = -1.0536126778323045039108725489141
y[1] (numeric) = -1.0536126778323045039108725489129
absolute error = 1.2e-30
relative error = 1.1389384593101819622836841602977e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.759
y[1] (closed_form) = -1.0538570378753548934878015369111
y[1] (numeric) = -1.0538570378753548934878015369099
absolute error = 1.2e-30
relative error = 1.1386743712593872607304606163541e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.76
y[1] (closed_form) = -1.0541011880326193944180816008678
y[1] (numeric) = -1.0541011880326193944180816008665
absolute error = 1.3e-30
relative error = 1.2332781850159258263313423960294e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.761
y[1] (closed_form) = -1.0543451285453248757635367367935
y[1] (numeric) = -1.0543451285453248757635367367923
absolute error = 1.2e-30
relative error = 1.1381472418387653390320055524683e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.762
y[1] (closed_form) = -1.0545888596543839181831161712323
y[1] (numeric) = -1.0545888596543839181831161712311
absolute error = 1.2e-30
relative error = 1.1378841991496772291634620316908e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.763
y[1] (closed_form) = -1.0548323816003951878575734588655
y[1] (numeric) = -1.0548323816003951878575734588643
absolute error = 1.2e-30
relative error = 1.1376215035979043609171503341428e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.764
y[1] (closed_form) = -1.0550756946236438103395644780314
y[1] (numeric) = -1.0550756946236438103395644780301
absolute error = 1.3e-30
relative error = 1.2321390840718050763295837082145e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.765
y[1] (closed_form) = -1.0553187989641017443268210392272
y[1] (numeric) = -1.0553187989641017443268210392259
absolute error = 1.3e-30
relative error = 1.2318552472258399090806495514683e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.766
y[1] (closed_form) = -1.0555616948614281553560716468066
y[1] (numeric) = -1.0555616948614281553560716468054
absolute error = 1.2e-30
relative error = 1.1368354932181708160146262519330e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.767
y[1] (closed_form) = -1.055804382554969789415395709414
y[1] (numeric) = -1.0558043825549697894153957094128
absolute error = 1.2e-30
relative error = 1.1365741796752986642279567410751e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.768
y[1] (closed_form) = -1.0560468622837613464727121804917
y[1] (numeric) = -1.0560468622837613464727121804905
absolute error = 1.2e-30
relative error = 1.1363132100074913470208715889938e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.769
y[1] (closed_form) = -1.0562891342865258539181182267354
y[1] (numeric) = -1.0562891342865258539181182267342
absolute error = 1.2e-30
relative error = 1.1360525835670402374863106655475e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.77
y[1] (closed_form) = -1.0565311988016750399178080699299
y[1] (numeric) = -1.0565311988016750399178080699286
absolute error = 1.3e-30
relative error = 1.2304416580167901816117083418069e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.771
y[1] (closed_form) = -1.0567730560673097066773166264532
y[1] (numeric) = -1.0567730560673097066773166264519
absolute error = 1.3e-30
relative error = 1.2301600542673168680609462834830e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.772
y[1] (closed_form) = -1.0570147063212201036118469791709
y[1] (numeric) = -1.0570147063212201036118469791696
absolute error = 1.3e-30
relative error = 1.2298788202526088581481295451807e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.773
y[1] (closed_form) = -1.057256149800886300421455058718
y[1] (numeric) = -1.0572561498008863004214550587167
absolute error = 1.3e-30
relative error = 1.2295979552777534544202629982869e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.774
y[1] (closed_form) = -1.0574973867434785600688791855726
y[1] (numeric) = -1.0574973867434785600688791855713
absolute error = 1.3e-30
relative error = 1.2293174586495184263043862600676e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.775
y[1] (closed_form) = -1.057738417385857711657816331125
y[1] (numeric) = -1.0577384173858577116578163311238
absolute error = 1.2e-30
relative error = 1.1344959966243203690479042336732e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.776
y[1] (closed_form) = -1.0579792419645755232094610954174
y[1] (numeric) = -1.0579792419645755232094610954161
absolute error = 1.3e-30
relative error = 1.2287575676683532642855639484393e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.777
y[1] (closed_form) = -1.0582198607158750743351374716394
y[1] (numeric) = -1.0582198607158750743351374716381
absolute error = 1.3e-30
relative error = 1.2284781719373165963312006729232e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.778
y[1] (closed_form) = -1.0584602738756911288028674730938
y[1] (numeric) = -1.0584602738756911288028674730925
absolute error = 1.3e-30
relative error = 1.2281991417966774338495691938642e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.779
y[1] (closed_form) = -1.0587004816796505069957346374499
y[1] (numeric) = -1.0587004816796505069957346374486
absolute error = 1.3e-30
relative error = 1.2279204765615320671177730766535e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.78
y[1] (closed_form) = -1.0589404843630724582599142959644
y[1] (numeric) = -1.0589404843630724582599142959631
absolute error = 1.3e-30
relative error = 1.2276421755486278466429945627031e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.781
y[1] (closed_form) = -1.0591802821609690331402563022281
y[1] (numeric) = -1.0591802821609690331402563022268
absolute error = 1.3e-30
relative error = 1.2273642380763583411250864356140e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.782
y[1] (closed_form) = -1.0594198753080454555013196561638
y[1] (numeric) = -1.0594198753080454555013196561625
absolute error = 1.3e-30
relative error = 1.2270866634647585121181570465233e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.783
y[1] (closed_form) = -1.0596592640387004945317721347226
y[1] (numeric) = -1.0596592640387004945317721347213
absolute error = 1.3e-30
relative error = 1.2268094510354999053249198616471e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.784
y[1] (closed_form) = -1.0598984485870268366300816512671
y[1] (numeric) = -1.0598984485870268366300816512657
absolute error = 1.4e-30
relative error = 1.3208812616589540014161744248589e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.785
y[1] (closed_form) = -1.0601374291868114571694396112554
y[1] (numeric) = -1.060137429186811457169439611254
absolute error = 1.4e-30
relative error = 1.3205835030972195506479804211304e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.786
y[1] (closed_form) = -1.0603762060715359921398700128174
y[1] (numeric) = -1.0603762060715359921398700128161
absolute error = 1.3e-30
relative error = 1.2259799800829351180114552273661e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.787
y[1] (closed_form) = -1.0606147794743771096654914573981
y[1] (numeric) = -1.0606147794743771096654914573968
absolute error = 1.3e-30
relative error = 1.2257042096323211612816813801389e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.788
y[1] (closed_form) = -1.0608531496282068813949125881078
y[1] (numeric) = -1.0608531496282068813949125881065
absolute error = 1.3e-30
relative error = 1.2254287979967877688214522607511e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.789
y[1] (closed_form) = -1.0610913167655931537627547620153
y[1] (numeric) = -1.061091316765593153762754762014
absolute error = 1.3e-30
relative error = 1.2251537445077259315710786745940e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.79
y[1] (closed_form) = -1.061329281118799919120308987613
y[1] (numeric) = -1.0613292811187999191203089876117
absolute error = 1.3e-30
relative error = 1.2248790484981300238961946845943e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.791
y[1] (closed_form) = -1.0615670429197876867333473203349
y[1] (numeric) = -1.0615670429197876867333473203336
absolute error = 1.3e-30
relative error = 1.2246047093025931255953635881365e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.792
y[1] (closed_form) = -1.061804602400213853645122007572
y[1] (numeric) = -1.0618046024002138536451220075707
absolute error = 1.3e-30
relative error = 1.2243307262573023599575942100505e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.793
y[1] (closed_form) = -1.0620419597914330754025987103692
y[1] (numeric) = -1.062041959791433075402598710368
absolute error = 1.2e-30
relative error = 1.1298988603384931518213349609925e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.794
y[1] (closed_form) = -1.0622791153244976366439831021563
y[1] (numeric) = -1.0622791153244976366439831021551
absolute error = 1.2e-30
relative error = 1.1296466085878308407394023429270e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.795
y[1] (closed_form) = -1.0625160692301578215456130557209
y[1] (numeric) = -1.0625160692301578215456130557197
absolute error = 1.2e-30
relative error = 1.1293946837617765759363710250592e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.796
y[1] (closed_form) = -1.0627528217388622841263014784297
y[1] (numeric) = -1.0627528217388622841263014784285
absolute error = 1.2e-30
relative error = 1.1291430852534229696711731850435e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.797
y[1] (closed_form) = -1.0629893730807584184072276426995
y[1] (numeric) = -1.0629893730807584184072276426983
absolute error = 1.2e-30
relative error = 1.1288918124573127624984062536998e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.798
y[1] (closed_form) = -1.0632257234856927284254875841644
y[1] (numeric) = -1.0632257234856927284254875841632
absolute error = 1.2e-30
relative error = 1.1286408647694346076102520513155e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.799
y[1] (closed_form) = -1.0634618731832111980994268041349
y[1] (numeric) = -1.0634618731832111980994268041338
absolute error = 1.1e-30
relative error = 1.0343577214549506304574826157275e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
memory used=85.7MB, alloc=44.3MB, time=1.14
x[1] = -1.8
y[1] (closed_form) = -1.0636978224025596609438911160525
y[1] (numeric) = -1.0636978224025596609438911160514
absolute error = 1.1e-30
relative error = 1.0341282804504056510603587166800e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.801
y[1] (closed_form) = -1.0639335713726841696335440179519
y[1] (numeric) = -1.0639335713726841696335440179507
absolute error = 1.2e-30
relative error = 1.1278899663366795523907842416577e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.802
y[1] (closed_form) = -1.0641691203222313654124114547175
y[1] (numeric) = -1.0641691203222313654124114547163
absolute error = 1.2e-30
relative error = 1.1276403130703876487463288400568e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.803
y[1] (closed_form) = -1.0644044694795488473478272553968
y[1] (numeric) = -1.0644044694795488473478272553956
absolute error = 1.2e-30
relative error = 1.1273909819138132105239175865596e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.804
y[1] (closed_form) = -1.0646396190726855414269648922663
y[1] (numeric) = -1.0646396190726855414269648922651
absolute error = 1.2e-30
relative error = 1.1271419722715326410188634923689e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.805
y[1] (closed_form) = -1.0648745693293920694941535099859
y[1] (numeric) = -1.0648745693293920694941535099847
absolute error = 1.2e-30
relative error = 1.1268932835495391469270362159918e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.806
y[1] (closed_form) = -1.0651093204771211180271884152658
y[1] (numeric) = -1.0651093204771211180271884152645
absolute error = 1.3e-30
relative error = 1.2205319914181751894412204725296e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.807
y[1] (closed_form) = -1.0653438727430278067508584002558
y[1] (numeric) = -1.0653438727430278067508584002546
absolute error = 1.2e-30
relative error = 1.1263968664974456311092044455682e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.808
y[1] (closed_form) = -1.0655782263539700570859243966009
y[1] (numeric) = -1.0655782263539700570859243965997
absolute error = 1.2e-30
relative error = 1.1261491369863791921116703299326e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.809
y[1] (closed_form) = -1.0658123815365089604317960220182
y[1] (numeric) = -1.065812381536508960431796022017
absolute error = 1.2e-30
relative error = 1.1259017260336588597175593081175e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.81
y[1] (closed_form) = -1.0660463385169091462811645876063
y[1] (numeric) = -1.0660463385169091462811645876051
absolute error = 1.2e-30
relative error = 1.1256546330523006070506268172978e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.811
y[1] (closed_form) = -1.0662800975211391501648630821168
y[1] (numeric) = -1.0662800975211391501648630821156
absolute error = 1.2e-30
relative error = 1.1254078574567128074005017442789e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.812
y[1] (closed_form) = -1.0665136587748717814252355393604
y[1] (numeric) = -1.0665136587748717814252355393592
absolute error = 1.2e-30
relative error = 1.1251613986626922152621228322583e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.813
y[1] (closed_form) = -1.0667470225034844908163100270173
y[1] (numeric) = -1.0667470225034844908163100270161
absolute error = 1.2e-30
relative error = 1.1249152560874199610161427405635e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.814
y[1] (closed_form) = -1.0669801889320597379290812696193
y[1] (numeric) = -1.066980188932059737929081269618
absolute error = 1.3e-30
relative error = 1.2183918815785790224634887178037e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.815
y[1] (closed_form) = -1.0672131582853853584402206356041
y[1] (numeric) = -1.0672131582853853584402206356028
absolute error = 1.3e-30
relative error = 1.2181259103744715078208034726732e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.816
y[1] (closed_form) = -1.0674459307879549311825428783578
y[1] (numeric) = -1.0674459307879549311825428783565
absolute error = 1.3e-30
relative error = 1.2178602798554686390499721120509e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.817
y[1] (closed_form) = -1.0676785066639681450355706242843
y[1] (numeric) = -1.067678506663968145035570624283
absolute error = 1.3e-30
relative error = 1.2175949893961391721470509679900e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.818
y[1] (closed_form) = -1.0679108861373311656345491474241
y[1] (numeric) = -1.0679108861373311656345491474228
absolute error = 1.3e-30
relative error = 1.2173300383725301278259935216776e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.819
y[1] (closed_form) = -1.0681430694316570018962754602112
y[1] (numeric) = -1.0681430694316570018962754602099
absolute error = 1.3e-30
relative error = 1.2170654261621625398865253540464e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.82
y[1] (closed_form) = -1.0683750567702658723601171838498
y[1] (numeric) = -1.0683750567702658723601171838485
absolute error = 1.3e-30
relative error = 1.2168011521440272179613534529675e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.821
y[1] (closed_form) = -1.068606848376185571342608039746
y[1] (numeric) = -1.0686068483761855713426080397447
absolute error = 1.3e-30
relative error = 1.2165372156985805245867972303321e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.822
y[1] (closed_form) = -1.068838444472151834904018125674
y[1] (numeric) = -1.0688384444721518349040181256727
absolute error = 1.3e-30
relative error = 1.2162736162077401665411746366238e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.823
y[1] (closed_form) = -1.0690698452806087066253084071283
y[1] (numeric) = -1.069069845280608706625308407127
absolute error = 1.3e-30
relative error = 1.2160103530548810003955215840690e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.824
y[1] (closed_form) = -1.0693010510237089031938900658457
y[1] (numeric) = -1.0693010510237089031938900658444
absolute error = 1.3e-30
relative error = 1.2157474256248308522214665087121e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.825
y[1] (closed_form) = -1.0695320619233141797966205039994
y[1] (numeric) = -1.0695320619233141797966205039981
absolute error = 1.3e-30
relative error = 1.2154848333038663514013243233856e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.826
y[1] (closed_form) = -1.0697628782009956953184789043136
y[1] (numeric) = -1.0697628782009956953184789043123
absolute error = 1.3e-30
relative error = 1.2152225754797087784857152440232e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.827
y[1] (closed_form) = -1.0699935000780343773453752935366
y[1] (numeric) = -1.0699935000780343773453752935353
absolute error = 1.3e-30
relative error = 1.2149606515415199270442540176164e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.828
y[1] (closed_form) = -1.0702239277754212869695580495882
y[1] (numeric) = -1.0702239277754212869695580495869
absolute error = 1.3e-30
relative error = 1.2146990608798979794550939477536e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.829
y[1] (closed_form) = -1.0704541615138579833960957314775
y[1] (numeric) = -1.0704541615138579833960957314762
absolute error = 1.3e-30
relative error = 1.2144378028868733965793478095406e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.83
y[1] (closed_form) = -1.0706842015137568883489199960067
y[1] (numeric) = -1.0706842015137568883489199960055
absolute error = 1.2e-30
relative error = 1.1207786556516044503999793318153e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.831
y[1] (closed_form) = -1.0709140479952416502749271965605
y[1] (numeric) = -1.0709140479952416502749271965592
absolute error = 1.3e-30
relative error = 1.2139162824818749956383138504535e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.832
y[1] (closed_form) = -1.0711437011781475083446470371482
y[1] (numeric) = -1.0711437011781475083446470371469
absolute error = 1.3e-30
relative error = 1.2136560188610866920949325142078e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.833
y[1] (closed_form) = -1.0713731612820216562479973795565
y[1] (numeric) = -1.0713731612820216562479973795552
absolute error = 1.3e-30
relative error = 1.2133960854912586579951843783232e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.834
y[1] (closed_form) = -1.0716024285261236057836549731896
y[1] (numeric) = -1.0716024285261236057836549731883
absolute error = 1.3e-30
relative error = 1.2131364817715215739532365505973e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.835
y[1] (closed_form) = -1.0718315031294255502405824961646
y[1] (numeric) = -1.0718315031294255502405824961633
absolute error = 1.3e-30
relative error = 1.2128772071024140257020502338883e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.836
y[1] (closed_form) = -1.0720603853106127275702628626984
y[1] (numeric) = -1.0720603853106127275702628626971
absolute error = 1.3e-30
relative error = 1.2126182608858784894702817377044e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.837
y[1] (closed_form) = -1.0722890752880837833482022660042
y[1] (numeric) = -1.0722890752880837833482022660029
absolute error = 1.3e-30
relative error = 1.2123596425252573308206556336959e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.838
y[1] (closed_form) = -1.0725175732799511335232738880207
y[1] (numeric) = -1.0725175732799511335232738880193
absolute error = 1.4e-30
relative error = 1.3053399169195418028131443110131e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.839
y[1] (closed_form) = -1.0727458795040413269534846175545
y[1] (numeric) = -1.0727458795040413269534846175531
absolute error = 1.4e-30
relative error = 1.3050621090684187683450806650268e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.84
y[1] (closed_form) = -1.0729739941778954077267574770421
y[1] (numeric) = -1.0729739941778954077267574770407
absolute error = 1.4e-30
relative error = 1.3047846523742352717919367372552e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.841
y[1] (closed_form) = -1.0732019175187692772653327653487
y[1] (numeric) = -1.0732019175187692772653327653473
absolute error = 1.4e-30
relative error = 1.3045075462004244286776028255922e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.842
y[1] (closed_form) = -1.0734296497436340562124011800399
y[1] (numeric) = -1.0734296497436340562124011800385
absolute error = 1.4e-30
relative error = 1.3042307899119055984457027032584e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.843
y[1] (closed_form) = -1.0736571910691764460995923876043
y[1] (numeric) = -1.073657191069176446099592387603
absolute error = 1.3e-30
relative error = 1.2108147840982887212378714802348e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.844
y[1] (closed_form) = -1.073884541711799090793952664386
y[1] (numeric) = -1.0738845417117990907939526643847
absolute error = 1.3e-30
relative error = 1.2105584441394110729717872556686e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.845
y[1] (closed_form) = -1.0741117018876209377230553347201
y[1] (numeric) = -1.0741117018876209377230553347188
absolute error = 1.3e-30
relative error = 1.2103024273131070048177884446200e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.846
y[1] (closed_form) = -1.0743386718124775988768977861754
y[1] (numeric) = -1.0743386718124775988768977861741
absolute error = 1.3e-30
relative error = 1.2100467330351400297074244269686e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.847
y[1] (closed_form) = -1.0745654517019217115852488450957
y[1] (numeric) = -1.0745654517019217115852488450944
absolute error = 1.3e-30
relative error = 1.2097913607226342673662987159945e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.848
y[1] (closed_form) = -1.0747920417712232990691202490252
y[1] (numeric) = -1.0747920417712232990691202490238
absolute error = 1.4e-30
relative error = 1.3025775643936144792264396952036e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.849
y[1] (closed_form) = -1.0750184422353701307650458563007
y[1] (numeric) = -1.0750184422353701307650458562993
absolute error = 1.4e-30
relative error = 1.3023032396438429808716582247769e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.85
y[1] (closed_form) = -1.0752446533090680824208620873218
y[1] (numeric) = -1.0752446533090680824208620873204
absolute error = 1.4e-30
relative error = 1.3020292597517193265528208672030e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.851
y[1] (closed_form) = -1.0754706752067414959616928969641
y[1] (numeric) = -1.0754706752067414959616928969626
absolute error = 1.5e-30
relative error = 1.3947381686735900488719044211419e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.852
y[1] (closed_form) = -1.0756965081425335391248523335068
y[1] (numeric) = -1.0756965081425335391248523335053
absolute error = 1.5e-30
relative error = 1.3944453557724524734866374723127e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.853
y[1] (closed_form) = -1.0759221523303065648623874465032
y[1] (numeric) = -1.0759221523303065648623874465018
absolute error = 1.4e-30
relative error = 1.3012093830095265094341292846830e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.854
y[1] (closed_form) = -1.0761476079836424705099939644419
y[1] (numeric) = -1.0761476079836424705099939644404
absolute error = 1.5e-30
relative error = 1.3938608317965987800263523021779e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.855
y[1] (closed_form) = -1.0763728753158430567210467730395
y[1] (numeric) = -1.0763728753158430567210467730381
absolute error = 1.4e-30
relative error = 1.3006645114400473394855742149126e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.856
y[1] (closed_form) = -1.0765979545399303861644967867803
y[1] (numeric) = -1.0765979545399303861644967867788
absolute error = 1.5e-30
relative error = 1.3932777725190874682354813338574e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.857
y[1] (closed_form) = -1.0768228458686471419853953200687
y[1] (numeric) = -1.0768228458686471419853953200672
absolute error = 1.5e-30
relative error = 1.3929867904966169301615300232325e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.858
y[1] (closed_form) = -1.0770475495144569860268165303173
y[1] (numeric) = -1.0770475495144569860268165303158
absolute error = 1.5e-30
relative error = 1.3926961726770688046507706711353e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.859
y[1] (closed_form) = -1.0772720656895449168119579236318
y[1] (numeric) = -1.0772720656895449168119579236302
absolute error = 1.6e-30
relative error = 1.4852329796334829759205290302676e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.86
y[1] (closed_form) = -1.0774963946058176272852082847049
y[1] (numeric) = -1.0774963946058176272852082847033
absolute error = 1.6e-30
relative error = 1.4849237621675112628769070303755e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.861
y[1] (closed_form) = -1.0777205364749038623109817162831
y[1] (numeric) = -1.0777205364749038623109817162815
absolute error = 1.6e-30
relative error = 1.4846149310965255979660649237662e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.862
y[1] (closed_form) = -1.0779444915081547759291257503268
y[1] (numeric) = -1.0779444915081547759291257503252
absolute error = 1.6e-30
relative error = 1.4843064857276983572755170309824e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.863
y[1] (closed_form) = -1.0781682599166442883657207229581
y[1] (numeric) = -1.0781682599166442883657207229565
absolute error = 1.6e-30
relative error = 1.4839984253698024321462122879002e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.864
y[1] (closed_form) = -1.0783918419111694427980967886686
y[1] (numeric) = -1.078391841911169442798096788667
absolute error = 1.6e-30
relative error = 1.4836907493332067287454294922454e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.865
y[1] (closed_form) = -1.0786152377022507618729040862557
y[1] (numeric) = -1.0786152377022507618729040862541
absolute error = 1.6e-30
relative error = 1.4833834569298716825204050091492e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.866
y[1] (closed_form) = -1.07883844750013260397608065976
y[1] (numeric) = -1.0788384475001326039760806597584
absolute error = 1.6e-30
relative error = 1.4830765474733447874761369747427e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.867
y[1] (closed_form) = -1.0790614715147835192535717824957
y[1] (numeric) = -1.0790614715147835192535717824941
absolute error = 1.6e-30
relative error = 1.4827700202787561402210531860616e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.868
y[1] (closed_form) = -1.0792843099558966053816633312927
y[1] (numeric) = -1.0792843099558966053816633312911
absolute error = 1.6e-30
relative error = 1.4824638746628139987244718462296e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.869
y[1] (closed_form) = -1.0795069630328898630858008115048
y[1] (numeric) = -1.0795069630328898630858008115032
absolute error = 1.6e-30
relative error = 1.4821581099438003557300251522223e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.87
y[1] (closed_form) = -1.0797294309549065514067745413803
y[1] (numeric) = -1.0797294309549065514067745413787
absolute error = 1.6e-30
relative error = 1.4818527254415665267694553746682e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.871
y[1] (closed_form) = -1.0799517139308155427131603672314
y[1] (numeric) = -1.0799517139308155427131603672298
absolute error = 1.6e-30
relative error = 1.4815477204775287527214315912738e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.872
y[1] (closed_form) = -1.0801738121692116774589140986807
y[1] (numeric) = -1.0801738121692116774589140986791
absolute error = 1.6e-30
relative error = 1.4812430943746638168602726036612e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.873
y[1] (closed_form) = -1.0803957258784161186850266262912
y[1] (numeric) = -1.0803957258784161186850266262896
absolute error = 1.6e-30
relative error = 1.4809388464575046763396977977773e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.874
y[1] (closed_form) = -1.0806174552664767062641554123057
y[1] (numeric) = -1.0806174552664767062641554123041
absolute error = 1.6e-30
relative error = 1.4806349760521361080569628065910e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.875
y[1] (closed_form) = -1.0808390005411683108871567292172
y[1] (numeric) = -1.0808390005411683108871567292156
absolute error = 1.6e-30
relative error = 1.4803314824861903688429708065635e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.876
y[1] (closed_form) = -1.0810603619099931877904516606612
y[1] (numeric) = -1.0810603619099931877904516606596
absolute error = 1.6e-30
relative error = 1.4800283650888428699241831323101e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.877
y[1] (closed_form) = -1.0812815395801813302231674748537
y[1] (numeric) = -1.0812815395801813302231674748521
absolute error = 1.6e-30
relative error = 1.4797256231908078656023846329226e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.878
y[1] (closed_form) = -1.0815025337586908226530045326886
y[1] (numeric) = -1.081502533758690822653004532687
absolute error = 1.6e-30
relative error = 1.4794232561243341560985898244704e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.879
y[1] (closed_form) = -1.0817233446522081937097874008434
y[1] (numeric) = -1.0817233446522081937097874008418
absolute error = 1.6e-30
relative error = 1.4791212632232008045076054221314e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.88
y[1] (closed_form) = -1.0819439724671487688656673050121
y[1] (numeric) = -1.0819439724671487688656673050105
absolute error = 1.6e-30
relative error = 1.4788196438227128678099932680413e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.881
y[1] (closed_form) = -1.0821644174096570228509514798842
y[1] (numeric) = -1.0821644174096570228509514798827
absolute error = 1.5e-30
relative error = 1.3861109974309660705203796997697e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.882
y[1] (closed_form) = -1.0823846796856069318045433508962
y[1] (numeric) = -1.0823846796856069318045433508947
absolute error = 1.5e-30
relative error = 1.3858289276929668004645182827774e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.883
y[1] (closed_form) = -1.0826047595006023251579858182959
y[1] (numeric) = -1.0826047595006023251579858182943
absolute error = 1.6e-30
relative error = 1.4779170200009727681207723198626e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.884
y[1] (closed_form) = -1.0828246570599772372521082068612
y[1] (numeric) = -1.0828246570599772372521082068596
absolute error = 1.6e-30
relative error = 1.4776168879864883067042244070112e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.885
y[1] (closed_form) = -1.0830443725687962586852856948912
y[1] (numeric) = -1.0830443725687962586852856948896
absolute error = 1.6e-30
relative error = 1.4773171261719160161442729993185e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.886
y[1] (closed_form) = -1.0832639062318548873923282440222
y[1] (numeric) = -1.0832639062318548873923282440206
absolute error = 1.6e-30
relative error = 1.4770177339016280485484634856434e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.887
y[1] (closed_form) = -1.0834832582536798794530242172078
y[1] (numeric) = -1.0834832582536798794530242172062
absolute error = 1.6e-30
relative error = 1.4767187105214930561750150058526e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.888
y[1] (closed_form) = -1.0837024288385295996293719960113
y[1] (numeric) = -1.0837024288385295996293719960097
absolute error = 1.6e-30
relative error = 1.4764200553788720330138258247768e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.889
y[1] (closed_form) = -1.0839214181903943716305409903873
y[1] (numeric) = -1.0839214181903943716305409903857
absolute error = 1.6e-30
relative error = 1.4761217678226141699556766707607e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.89
y[1] (closed_form) = -1.084140226512996828104611474551
y[1] (numeric) = -1.0841402265129968281046114745494
absolute error = 1.6e-30
relative error = 1.4758238472030527234986013443016e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.891
y[1] (closed_form) = -1.0843588540097922603561506815363
y[1] (numeric) = -1.0843588540097922603561506815347
absolute error = 1.6e-30
relative error = 1.4755262928720008979406106510715e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.892
y[1] (closed_form) = -1.0845773008839689677886905468049
y[1] (numeric) = -1.0845773008839689677886905468032
absolute error = 1.7e-30
relative error = 1.5674309231941694748211821481295e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.893
y[1] (closed_form) = -1.0847955673384486070711804079716
y[1] (numeric) = -1.08479556733844860707118040797
absolute error = 1.6e-30
relative error = 1.4749322804900540528700571717912e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.894
y[1] (closed_form) = -1.0850136535758865410274958435374
y[1] (numeric) = -1.0850136535758865410274958435357
absolute error = 1.7e-30
relative error = 1.5668005599720325777668003215433e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.895
y[1] (closed_form) = -1.0852315597986721872480926686421
y[1] (numeric) = -1.0852315597986721872480926686405
absolute error = 1.6e-30
relative error = 1.4743397255207225932429890712797e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.896
y[1] (closed_form) = -1.0854492862089293664229029004597
y[1] (numeric) = -1.0854492862089293664229029004581
absolute error = 1.6e-30
relative error = 1.4740439929609285518210633885555e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.897
y[1] (closed_form) = -1.085666833008516650394577260115
y[1] (numeric) = -1.0856668330085166503945772601133
absolute error = 1.7e-30
relative error = 1.5658579117583341846438919983248e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.898
y[1] (closed_form) = -1.0858842003990277099311864921022
y[1] (numeric) = -1.0858842003990277099311864921005
absolute error = 1.7e-30
relative error = 1.5655444653999978793097783526534e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.899
y[1] (closed_form) = -1.0861013885817916622175014562941
y[1] (numeric) = -1.0861013885817916622175014562924
absolute error = 1.7e-30
relative error = 1.5652314027697029519196075337459e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.9
y[1] (closed_form) = -1.0863183977578734180639795819257
y[1] (numeric) = -1.086318397757873418063979581924
absolute error = 1.7e-30
relative error = 1.5649187231927083881113939890012e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.901
y[1] (closed_form) = -1.0865352281280740288325928675998
y[1] (numeric) = -1.0865352281280740288325928675982
absolute error = 1.6e-30
relative error = 1.4725707538784024872958324960372e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.902
y[1] (closed_form) = -1.0867518798929310330786401665586
y[1] (numeric) = -1.0867518798929310330786401665569
absolute error = 1.7e-30
relative error = 1.5642945105072994188892231903819e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.903
y[1] (closed_form) = -1.0869683532527188029076940123762
y[1] (numeric) = -1.0869683532527188029076940123746
absolute error = 1.6e-30
relative error = 1.4719839774654432568522325148782e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.904
y[1] (closed_form) = -1.0871846484074488900468397170265
y[1] (numeric) = -1.0871846484074488900468397170249
absolute error = 1.6e-30
relative error = 1.4716911265659824548855360042562e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.905
y[1] (closed_form) = -1.0874007655568703716293719111304
y[1] (numeric) = -1.0874007655568703716293719111288
absolute error = 1.6e-30
relative error = 1.4713986330335363488618336481126e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.906
y[1] (closed_form) = -1.0876167049004701956921210952779
y[1] (numeric) = -1.0876167049004701956921210952762
absolute error = 1.7e-30
relative error = 1.5630506522567342559733994164967e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.907
y[1] (closed_form) = -1.0878324666374735263845901318031
y[1] (numeric) = -1.0878324666374735263845901318014
absolute error = 1.7e-30
relative error = 1.5627406352880391201694830181141e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.908
y[1] (closed_form) = -1.0880480509668440888890879284541
y[1] (numeric) = -1.0880480509668440888890879284524
absolute error = 1.7e-30
relative error = 1.5624309960294242769810222316422e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.909
y[1] (closed_form) = -1.0882634580872845140510548491992
y[1] (numeric) = -1.0882634580872845140510548491975
absolute error = 1.7e-30
relative error = 1.5621217338197631217117929937654e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.91
y[1] (closed_form) = -1.0884786881972366827187816331298
y[1] (numeric) = -1.0884786881972366827187816331282
absolute error = 1.6e-30
relative error = 1.4699415039994550761112291030266e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.911
y[1] (closed_form) = -1.0886937414948820697917308102142
y[1] (numeric) = -1.0886937414948820697917308102126
absolute error = 1.6e-30
relative error = 1.4696511415625893647823642563933e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.912
y[1] (closed_form) = -1.088908618178142087976676772703
y[1] (numeric) = -1.0889086181781420879766767727014
absolute error = 1.6e-30
relative error = 1.4693611321370265249653267381869e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.913
y[1] (closed_form) = -1.089123318444678431250887793451
y[1] (numeric) = -1.0891233184446784312508877934493
absolute error = 1.7e-30
relative error = 1.5608884423002561920359877819782e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.914
y[1] (closed_form) = -1.0893378424918934180315803774641
y[1] (numeric) = -1.0893378424918934180315803774624
absolute error = 1.7e-30
relative error = 1.5605810554705401031218969546954e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.915
y[1] (closed_form) = -1.0895521905169303340508833907792
y[1] (numeric) = -1.0895521905169303340508833907775
absolute error = 1.7e-30
relative error = 1.5602740417542063940829453144530e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.916
y[1] (closed_form) = -1.0897663627166737749355564314937
y[1] (numeric) = -1.089766362716673774935556431492
absolute error = 1.7e-30
relative error = 1.5599674005004866119247211968327e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.917
y[1] (closed_form) = -1.0899803592877499884907138915571
y[1] (numeric) = -1.0899803592877499884907138915555
absolute error = 1.6e-30
relative error = 1.4679163586447772722615038376239e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.918
y[1] (closed_form) = -1.0901941804265272166868131049712
y[1] (numeric) = -1.0901941804265272166868131049696
absolute error = 1.6e-30
relative error = 1.4676284543860035284910147565873e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.919
y[1] (closed_form) = -1.0904078263291160373491718884929
y[1] (numeric) = -1.0904078263291160373491718884913
absolute error = 1.6e-30
relative error = 1.4673408988510639852375433842773e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.92
y[1] (closed_form) = -1.0906212971913697055492876549513
y[1] (numeric) = -1.0906212971913697055492876549497
absolute error = 1.6e-30
relative error = 1.4670536914329579308091205664846e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.921
y[1] (closed_form) = -1.0908345932088844946972371170395
y[1] (numeric) = -1.0908345932088844946972371170379
absolute error = 1.6e-30
relative error = 1.4667668315260470948027719247437e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.922
y[1] (closed_form) = -1.0910477145770000373344424010914
y[1] (numeric) = -1.0910477145770000373344424010898
absolute error = 1.6e-30
relative error = 1.4664803185260519243068072230340e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.923
y[1] (closed_form) = -1.0912606614907996656260961560552
y[1] (numeric) = -1.0912606614907996656260961560535
absolute error = 1.7e-30
relative error = 1.5578312863194258640764422486332e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.924
y[1] (closed_form) = -1.0914734341451107515525449727968
y[1] (numeric) = -1.0914734341451107515525449727952
absolute error = 1.6e-30
relative error = 1.4659083308364616966070695095250e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.925
y[1] (closed_form) = -1.0916860327345050467989371231669
y[1] (numeric) = -1.0916860327345050467989371231653
absolute error = 1.6e-30
relative error = 1.4656228549450677741555835530680e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.926
y[1] (closed_form) = -1.0918984574532990223424472870959
y[1] (numeric) = -1.0918984574532990223424472870942
absolute error = 1.7e-30
relative error = 1.5569213312792959489153245056649e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.927
y[1] (closed_form) = -1.0921107084955542077363975595155
y[1] (numeric) = -1.0921107084955542077363975595139
absolute error = 1.6e-30
relative error = 1.4650529360746702366108781816132e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.928
y[1] (closed_form) = -1.0923227860550775300906006172872
y[1] (numeric) = -1.0923227860550775300906006172855
absolute error = 1.7e-30
relative error = 1.5563165226457904631621202478015e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.929
y[1] (closed_form) = -1.0925346903254216527472574797095
y[1] (numeric) = -1.0925346903254216527472574797078
absolute error = 1.7e-30
relative error = 1.5560146648466046749203432462654e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.93
y[1] (closed_form) = -1.0927464214998853136517488147424
y[1] (numeric) = -1.0927464214998853136517488147407
absolute error = 1.7e-30
relative error = 1.5557131705511409163305658866552e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.931
y[1] (closed_form) = -1.0929579797715136634176652269667
y[1] (numeric) = -1.092957979771513663417665226965
absolute error = 1.7e-30
relative error = 1.5554120391301689372329862528745e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.932
y[1] (closed_form) = -1.093169365333098603085428412664
y[1] (numeric) = -1.0931693653330986030854284126624
absolute error = 1.6e-30
relative error = 1.4636341364290477658302625774604e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.933
y[1] (closed_form) = -1.0933805783771791215738614824
y[1] (numeric) = -1.0933805783771791215738614823983
absolute error = 1.7e-30
relative error = 1.5548108624017993163088647059420e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.934
y[1] (closed_form) = -1.0935916190960416328240731322788
y[1] (numeric) = -1.0935916190960416328240731322771
absolute error = 1.7e-30
relative error = 1.5545108158429497282054070453115e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.935
y[1] (closed_form) = -1.0938024876817203126350266917691
y[1] (numeric) = -1.0938024876817203126350266917674
absolute error = 1.7e-30
relative error = 1.5542111296556804252268001434578e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.936
y[1] (closed_form) = -1.0940131843259974351901713888221
y[1] (numeric) = -1.0940131843259974351901713888204
absolute error = 1.7e-30
relative error = 1.5539118032177469057258456188122e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.937
y[1] (closed_form) = -1.0942237092204037092745194520772
y[1] (numeric) = -1.0942237092204037092745194520755
absolute error = 1.7e-30
relative error = 1.5536128359082904574400036646229e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.938
y[1] (closed_form) = -1.0944340625562186141815589154218
y[1] (numeric) = -1.0944340625562186141815589154201
absolute error = 1.7e-30
relative error = 1.5533142271078343988982874655087e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.939
y[1] (closed_form) = -1.0946442445244707353093982021949
y[1] (numeric) = -1.0946442445244707353093982021932
absolute error = 1.7e-30
relative error = 1.5530159761982803328165539205959e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.94
y[1] (closed_form) = -1.094854255315938099445544745049
y[1] (numeric) = -1.0948542553159380994455447450473
absolute error = 1.7e-30
relative error = 1.5527180825629044114372515729076e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.941
y[1] (closed_form) = -1.0950640951211485097397260430628
y[1] (numeric) = -1.0950640951211485097397260430611
absolute error = 1.7e-30
relative error = 1.5524205455863536137698687140217e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.942
y[1] (closed_form) = -1.0952737641303798803641676702742
y[1] (numeric) = -1.0952737641303798803641676702725
absolute error = 1.7e-30
relative error = 1.5521233646546420346885058596089e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.943
y[1] (closed_form) = -1.0954832625336605708607488295345
y[1] (numeric) = -1.0954832625336605708607488295328
absolute error = 1.7e-30
relative error = 1.5518265391551471858431771795986e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.944
y[1] (closed_form) = -1.0956925905207697201744620926103
y[1] (numeric) = -1.0956925905207697201744620926086
absolute error = 1.7e-30
relative error = 1.5515300684766063083416250207191e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.945
y[1] (closed_form) = -1.095901748281237580372609981937
y[1] (numeric) = -1.0959017482812375803726099819352
absolute error = 1.8e-30
relative error = 1.6424830080096487381679404058048e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.946
y[1] (closed_form) = -1.0961107360043458500491770314935
y[1] (numeric) = -1.0961107360043458500491770314918
absolute error = 1.7e-30
relative error = 1.5509381891441120372298201123823e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.947
y[1] (closed_form) = -1.0963195538791280074138219140809
y[1] (numeric) = -1.0963195538791280074138219140791
absolute error = 1.8e-30
relative error = 1.6418570604081869130222797378912e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.948
y[1] (closed_form) = -1.0965282020943696430649401399777
y[1] (numeric) = -1.096528202094369643064940139976
absolute error = 1.7e-30
relative error = 1.5503477217941123586967683838381e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.949
y[1] (closed_form) = -1.0967366808386087924462537176792
y[1] (numeric) = -1.0967366808386087924462537176775
absolute error = 1.7e-30
relative error = 1.5500530160987338473458983194707e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.95
y[1] (closed_form) = -1.0969449903001362679863900213251
y[1] (numeric) = -1.0969449903001362679863900213234
absolute error = 1.7e-30
relative error = 1.5497586615850820550557149541813e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.951
y[1] (closed_form) = -1.0971531306669959909209179316523
y[1] (numeric) = -1.0971531306669959909209179316506
absolute error = 1.7e-30
relative error = 1.5494646576513100639588236706760e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.952
y[1] (closed_form) = -1.0973611021269853227963151079938
y[1] (numeric) = -1.0973611021269853227963151079921
absolute error = 1.7e-30
relative error = 1.5491710036969016057112415162741e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.953
y[1] (closed_form) = -1.0975689048676553966553460081481
y[1] (numeric) = -1.0975689048676553966553460081464
absolute error = 1.7e-30
relative error = 1.5488776991226674781933347114963e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.954
y[1] (closed_form) = -1.0977765390763114479033360009882
y[1] (numeric) = -1.0977765390763114479033360009865
absolute error = 1.7e-30
relative error = 1.5485847433307419735588056060491e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.955
y[1] (closed_form) = -1.0979840049400131448548326136238
y[1] (numeric) = -1.097984004940013144854832613622
absolute error = 1.8e-30
relative error = 1.6393681437083781009781070792184e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.956
y[1] (closed_form) = -1.0981913026455749189601506209025
y[1] (numeric) = -1.0981913026455749189601506209007
absolute error = 1.8e-30
relative error = 1.6390586919271236568109484649050e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.957
y[1] (closed_form) = -1.0983984323795662947113033201895
y[1] (numeric) = -1.0983984323795662947113033201878
absolute error = 1.7e-30
relative error = 1.5477079626899378378815823102339e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.958
y[1] (closed_form) = -1.0986053943283122192268279388266
y[1] (numeric) = -1.0986053943283122192268279388249
absolute error = 1.7e-30
relative error = 1.5474163960749352455269829556577e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.959
y[1] (closed_form) = -1.0988121886778933915150186955938
y[1] (numeric) = -1.098812188677893391515018695592
absolute error = 1.8e-30
relative error = 1.6381325385239727407436411697186e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.96
y[1] (closed_form) = -1.0990188156141465914150865810103
y[1] (numeric) = -1.0990188156141465914150865810085
absolute error = 1.8e-30
relative error = 1.6378245526161766699825207021923e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.961
y[1] (closed_form) = -1.0992252753226650082157704345585
y[1] (numeric) = -1.0992252753226650082157704345567
absolute error = 1.8e-30
relative error = 1.6375169316149781816170392117096e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.962
y[1] (closed_form) = -1.0994315679887985689509293800305
y[1] (numeric) = -1.0994315679887985689509293800288
absolute error = 1.7e-30
relative error = 1.5462535818485068757653268730895e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.963
y[1] (closed_form) = -1.0996376937976542663716521333248
y[1] (numeric) = -1.0996376937976542663716521333231
absolute error = 1.7e-30
relative error = 1.5459637384100250448593660060889e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.964
y[1] (closed_form) = -1.0998436529340964865944241202885
y[1] (numeric) = -1.0998436529340964865944241202868
absolute error = 1.7e-30
relative error = 1.5456742378472091458754063735286e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.965
y[1] (closed_form) = -1.1000494455827473364248987357562
y[1] (numeric) = -1.1000494455827473364248987357546
absolute error = 1.6e-30
relative error = 1.4544800748955476364714973258129e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.966
y[1] (closed_form) = -1.1002550719279869703568244389027
y[1] (numeric) = -1.1002550719279869703568244389011
absolute error = 1.6e-30
relative error = 1.4542082475441857737127976034182e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.967
y[1] (closed_form) = -1.1004605321539539172456847145512
y[1] (numeric) = -1.1004605321539539172456847145496
absolute error = 1.6e-30
relative error = 1.4539367412553063222955460445327e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.968
y[1] (closed_form) = -1.1006658264445454066566132352894
y[1] (numeric) = -1.1006658264445454066566132352878
absolute error = 1.6e-30
relative error = 1.4536655554833040255534953279491e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.969
y[1] (closed_form) = -1.1008709549834176948861518352737
y[1] (numeric) = -1.1008709549834176948861518352721
absolute error = 1.6e-30
relative error = 1.4533946896837700965552160900951e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.97
y[1] (closed_form) = -1.1010759179539863906574241535935
y[1] (numeric) = -1.1010759179539863906574241535919
absolute error = 1.6e-30
relative error = 1.4531241433134890219774038156853e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.971
y[1] (closed_form) = -1.1012807155394267804883030231387
y[1] (numeric) = -1.101280715539426780488303023137
absolute error = 1.7e-30
relative error = 1.5436572855698375870204442162385e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.972
y[1] (closed_form) = -1.1014853479226741537321548702117
y[1] (numeric) = -1.10148534792267415373215487021
absolute error = 1.7e-30
relative error = 1.5433705071121313095916722481597e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.973
y[1] (closed_form) = -1.1016898152864241272907495507763
y[1] (numeric) = -1.1016898152864241272907495507745
absolute error = 1.8e-30
relative error = 1.6338537172843200650866429043227e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.974
y[1] (closed_form) = -1.1018941178131329699989291813655
y[1] (numeric) = -1.1018941178131329699989291813637
absolute error = 1.8e-30
relative error = 1.6335507839649406163319308268784e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.975
y[1] (closed_form) = -1.1020982556850179266806346264257
y[1] (numeric) = -1.102098255685017926680634626424
absolute error = 1.7e-30
relative error = 1.5425121954696784217118346492177e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.976
y[1] (closed_form) = -1.1023022290840575418758933793661
y[1] (numeric) = -1.1023022290840575418758933793643
absolute error = 1.8e-30
relative error = 1.6329459856900448800841416619073e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
memory used=134.5MB, alloc=44.3MB, time=1.76
TOP MAIN SOLVE Loop
x[1] = -1.977
y[1] (closed_form) = -1.1025060381919919832383776219549
y[1] (numeric) = -1.1025060381919919832383776219531
absolute error = 1.8e-30
relative error = 1.6326441195295707011529698953312e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.978
y[1] (closed_form) = -1.1027096831903233646031462660842
y[1] (numeric) = -1.1027096831903233646031462660824
absolute error = 1.8e-30
relative error = 1.6323426078859661765408372132468e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.979
y[1] (closed_form) = -1.1029131642603160687241897734317
y[1] (numeric) = -1.1029131642603160687241897734299
absolute error = 1.8e-30
relative error = 1.6320414501600357956190046734474e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.98
y[1] (closed_form) = -1.103116481582997069681401512326
y[1] (numeric) = -1.1031164815829970696814015123242
absolute error = 1.8e-30
relative error = 1.6317406457538911387594830314367e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.981
y[1] (closed_form) = -1.1033196353391562549566043472836
y[1] (numeric) = -1.1033196353391562549566043472818
absolute error = 1.8e-30
relative error = 1.6314401940709474037351122517970e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.982
y[1] (closed_form) = -1.1035226257093467471782660653698
y[1] (numeric) = -1.1035226257093467471782660653681
absolute error = 1.7e-30
relative error = 1.5405212003761466128109721092467e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.983
y[1] (closed_form) = -1.1037254528738852255345421248616
y[1] (numeric) = -1.1037254528738852255345421248599
absolute error = 1.7e-30
relative error = 1.5402381050228863221097298812694e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.984
y[1] (closed_form) = -1.103928117012852246854289065787
y[1] (numeric) = -1.1039281170128522468542890657853
absolute error = 1.7e-30
relative error = 1.5399553411141244750190744063260e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.985
y[1] (closed_form) = -1.1041306183060925663556967489111
y[1] (numeric) = -1.1041306183060925663556967489094
absolute error = 1.7e-30
relative error = 1.5396729080913120445809351572324e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.986
y[1] (closed_form) = -1.1043329569332154580621923897538
y[1] (numeric) = -1.1043329569332154580621923897521
absolute error = 1.7e-30
relative error = 1.5393908053971149480072241083821e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.987
y[1] (closed_form) = -1.1045351330735950348852741273846
y[1] (numeric) = -1.1045351330735950348852741273829
absolute error = 1.7e-30
relative error = 1.5391090324754108270295569044125e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.988
y[1] (closed_form) = -1.1047371469063705683739366141761
y[1] (numeric) = -1.1047371469063705683739366141744
absolute error = 1.7e-30
relative error = 1.5388275887712858382838113187863e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.989
y[1] (closed_form) = -1.1049389986104468081303558325205
y[1] (numeric) = -1.1049389986104468081303558325188
absolute error = 1.7e-30
relative error = 1.5385464737310314536935888763793e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.99
y[1] (closed_form) = -1.1051406883644943008915050378617
y[1] (numeric) = -1.10514068836449430089150503786
absolute error = 1.7e-30
relative error = 1.5382656868021412708167909474695e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.991
y[1] (closed_form) = -1.1053422163469497092763783943778
y[1] (numeric) = -1.1053422163469497092763783943761
absolute error = 1.7e-30
relative error = 1.5379852274333078331196653966005e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.992
y[1] (closed_form) = -1.1055435827360161301985035103973
y[1] (numeric) = -1.1055435827360161301985035103956
absolute error = 1.7e-30
relative error = 1.5377050950744194601428239919183e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.993
y[1] (closed_form) = -1.105744787709663412943428695263
y[1] (numeric) = -1.1057447877096634129434286952613
absolute error = 1.7e-30
relative error = 1.5374252891765570875238742520274e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.994
y[1] (closed_form) = -1.1059458314456284769108753479934
y[1] (numeric) = -1.1059458314456284769108753479917
absolute error = 1.7e-30
relative error = 1.5371458091919911168414522314267e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.995
y[1] (closed_form) = -1.1061467141214156290212504508558
y[1] (numeric) = -1.1061467141214156290212504508541
absolute error = 1.7e-30
relative error = 1.5368666545741782752455849253989e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.996
y[1] (closed_form) = -1.1063474359142968807862186779712
y[1] (numeric) = -1.1063474359142968807862186779695
absolute error = 1.7e-30
relative error = 1.5365878247777584848394525140598e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.997
y[1] (closed_form) = -1.1065479970013122650430381404474
y[1] (numeric) = -1.1065479970013122650430381404458
absolute error = 1.6e-30
relative error = 1.4459381828315781099084814741756e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.998
y[1] (closed_form) = -1.1067483975592701523523682753958
y[1] (numeric) = -1.1067483975592701523523682753941
absolute error = 1.7e-30
relative error = 1.5360311374735550050470805908754e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
TOP MAIN SOLVE Loop
x[1] = -1.999
y[1] (closed_form) = -1.106948637764747567059262846648
y[1] (numeric) = -1.1069486377647475670592628466464
absolute error = 1.6e-30
relative error = 1.4454148507114720893116507826461e-28 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Finished!
diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ;
Iterations = 500
Total Elapsed Time = 1 Seconds
Elapsed Time(since restart) = 1 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 1 Seconds
Time to Timeout = 2 Minutes 58 Seconds
Percent Done = 0 %
> quit
memory used=141.0MB, alloc=44.3MB, time=1.84