|\^/| Maple 2016 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number 0
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
> if (years_int > 0) then # if number 1
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 2
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 7
# Begin Function number 8
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 8
# Begin Function number 9
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 9
# Begin Function number 10
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 7
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 7;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 10
# Begin Function number 11
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 7
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 11
# Begin Function number 12
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 12
# Begin Function number 13
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 16
# Begin Function number 17
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 17
# Begin Function number 18
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 6
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 7
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 8
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 9
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 10
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 11
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 12
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 12
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 19
# Begin Function number 20
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 20
# Begin Function number 21
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 12
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 12;
> if (errflag) then # if number 12
> quit;
> fi;# end if 12
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 21
# Begin Function number 22
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 12
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 13
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 13
> fi;# end if 12;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 22
# Begin Function number 23
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 12
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 12;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 23
# Begin Function number 24
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 24
# Begin Function number 25
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 25
# Begin Function number 26
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalf(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalf(in_val); ret end proc
# End Function number 26
# Begin Function number 27
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 12
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 27
# Begin Function number 28
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 28
# Begin Function number 29
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 12
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 13
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 15
> if (rcs > glob__0) then # if number 16
> rad_c := sqrt(rcs) * float_abs(glob_h);
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 16
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> fi;# end if 13
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 12;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := sqrt(rcs)*float_abs(glob_h)
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 29
# Begin Function number 30
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 30
# Begin Function number 31
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 31
# Begin Function number 32
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 12
> if (array_fact_1[nnn] = 0) then # if number 13
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 13;
> else
> ret := factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 32
# Begin Function number 33
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 12
> if (array_fact_2[mmm,nnn] = 0) then # if number 13
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 13;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 33
# Begin Function number 34
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 34
# Begin Function number 35
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 35
# Begin Function number 36
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 36
# Begin Function number 37
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 37
# Begin Function number 38
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 38
# Begin Function number 39
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 39
# Begin Function number 40
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 40
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(-2.0)/exp(c(x)));
> end;
exact_soln_y := proc(x) return c(-2.0)/exp(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_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y[1]) < min_size) then # if number 3
> min_size := float_abs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < glob__1) then # if number 3
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_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_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y[1]) < min_size then
min_size := float_abs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#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_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_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_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := float_abs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#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_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
> est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
> fi;# end if 3;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 3
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_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_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y[no_terms - 3]))
+ c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#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_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_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_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#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_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)*19*ATS_MAX_TERMS/float_abs(numeric_val));
> if (evalf(est_rel_err) > glob_prec) then # if number 6
> glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
> else
> glob_est_digits := Digits;
> fi;# end if 6;
> else
> relerr := glob__m1 ;
> glob_est_digits := -16;
> fi;# end if 5;
> array_est_digits[1] := glob_est_digits;
> if (glob_iter = 1) then # if number 5
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 5;
> array_est_rel_error[1] := est_rel_err;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," ");
> omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," ");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 4;
> #BOTTOM DISPLAY ALOT
> fi;# end if 3;
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_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_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)*19*ATS_MAX_TERMS/float_abs(numeric_val))
;
if glob_prec < evalf(est_rel_err) then
glob_est_digits := -int_trunc(log10(est_rel_err)) + 3
else glob_est_digits := Digits
end if
else relerr := glob__m1; glob_est_digits := -16
end if;
array_est_digits[1] := glob_est_digits;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
array_est_rel_error[1] := est_rel_err;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Desired digits ", 32,
glob_desired_digits_correct, 4, " ");
omniout_int(INFO, "Estimated correct digits ", 32,
glob_est_digits, 4, " ");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#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_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr((glob_clock_sec));
> if (c(percent_done) < glob__100) then # if number 3
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 3;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr((left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_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_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(glob_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(left_sec);
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#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_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 3;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 4
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_rad_test_poles[1,1]) then # if number 6
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,2]) then # if number 8
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 9
> glob_min_pole_est := rad_c;
> fi;# end if 9;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[1,3]) then # if number 10
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 11
> glob_min_pole_est := rad_c;
> fi;# end if 11;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test1
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 10;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 9;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 9
> display_poles();
> fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_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_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4],
array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
if
float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_poles() end if
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#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_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 exp 1 $eq_no = 1
> array_tmp1[1] := exp(array_x[1]);
> #emit pre div CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_2D0[1] / array_tmp1[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D0[1] + array_tmp2[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_tmp3[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 exp ID_LINEAR iii = 2 $eq_no = 1
> array_tmp1[2] := array_tmp1[1] * array_x[2] / c(1);
> #emit pre div CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := neg(ats(2,array_tmp1,array_tmp2,2)) / array_tmp1[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp3[2] := array_tmp2[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_tmp3[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 exp ID_LINEAR iii = 3 $eq_no = 1
> array_tmp1[3] := array_tmp1[2] * array_x[2] / c(2);
> #emit pre div CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := neg(ats(3,array_tmp1,array_tmp2,2)) / array_tmp1[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp3[3] := array_tmp2[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_tmp3[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 exp ID_LINEAR iii = 4 $eq_no = 1
> array_tmp1[4] := array_tmp1[3] * array_x[2] / c(3);
> #emit pre div CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := neg(ats(4,array_tmp1,array_tmp2,2)) / array_tmp1[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp3[4] := array_tmp2[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_tmp3[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 exp ID_LINEAR iii = 5 $eq_no = 1
> array_tmp1[5] := array_tmp1[4] * array_x[2] / c(4);
> #emit pre div CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := neg(ats(5,array_tmp1,array_tmp2,2)) / array_tmp1[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp3[5] := array_tmp2[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_tmp3[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 exp LINEAR $eq_no = 1
> array_tmp1[kkk] := array_tmp1[kkk - 1] * array_x[2] / c(kkk - 1);
> #emit div CONST FULL $eq_no = 1 i = 1
> array_tmp2[kkk] := neg(ats(kkk,array_tmp1,array_tmp2,2)) / array_tmp1[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp3[kkk] := array_tmp2[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_tmp3[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_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_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] := exp(array_x[1]);
array_tmp2[1] := array_const_2D0[1]/array_tmp1[1];
array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_tmp1[1]*array_x[2]/c(1);
array_tmp2[2] := neg(ats(2, array_tmp1, array_tmp2, 2))/array_tmp1[1];
array_tmp3[2] := array_tmp2[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp1[3] := array_tmp1[2]*array_x[2]/c(2);
array_tmp2[3] := neg(ats(3, array_tmp1, array_tmp2, 2))/array_tmp1[1];
array_tmp3[3] := array_tmp2[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp1[4] := array_tmp1[3]*array_x[2]/c(3);
array_tmp2[4] := neg(ats(4, array_tmp1, array_tmp2, 2))/array_tmp1[1];
array_tmp3[4] := array_tmp2[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp1[5] := array_tmp1[4]*array_x[2]/c(4);
array_tmp2[5] := neg(ats(5, array_tmp1, array_tmp2, 2))/array_tmp1[1];
array_tmp3[5] := array_tmp2[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp1[kkk] := array_tmp1[kkk - 1]*array_x[2]/c(kkk - 1);
array_tmp2[kkk] :=
neg(ats(kkk, array_tmp1, array_tmp2, 2))/array_tmp1[1];
array_tmp3[kkk] := array_tmp2[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_tmp3[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> #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_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 30;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(30),[]);
> array_norms:= Array(0..(30),[]);
> array_fact_1:= Array(0..(30),[]);
> array_1st_rel_error:= Array(0..(2),[]);
> array_last_rel_error:= Array(0..(2),[]);
> array_est_rel_error:= Array(0..(2),[]);
> array_max_est_error:= Array(0..(2),[]);
> array_type_pole:= Array(0..(2),[]);
> array_type_real_pole:= Array(0..(2),[]);
> array_type_complex_pole:= Array(0..(2),[]);
> array_est_digits:= Array(0..(2),[]);
> array_y:= Array(0..(30),[]);
> array_x:= Array(0..(30),[]);
> array_tmp0:= Array(0..(30),[]);
> array_tmp1:= Array(0..(30),[]);
> array_tmp2:= Array(0..(30),[]);
> array_tmp3:= Array(0..(30),[]);
> array_m1:= Array(0..(30),[]);
> array_y_higher := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..30+ 1),[]);
> array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(30) ,(0..30+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 30) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=30) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_2D0);
> array_const_2D0[1] := c(2.0);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_h := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 1000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 30;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/div_c_exppostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = 2.0 / exp ( x ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := c(1.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"x_end := c(5.0) ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 3;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=100000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=false;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(c(-2.0)/exp(c(x)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := c(1.0);
> x_end := c(5.0) ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_type_given_pole := 3;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=100000;
> glob_upper_ratio_limit:=c(1.000001);
> glob_lower_ratio_limit:=c(0.999999);
> glob_look_poles:=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 ) = 2.0 / exp ( x ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2016-08-26T16:29:03-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"div_c_exp")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = 2.0 / exp ( x ) ; ")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 308.maple.seems.ok | ")
> ;
> logitem_str(html_log_file,"div_c_exp diffeq.mxt")
> ;
> logitem_str(html_log_file,"div_c_exp maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> fi;# end if 14
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_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_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
ATS_MAX_TERMS := 30;
Digits := 32;
max_terms := 30;
glob_html_log := true;
array_y_init := Array(0 .. 30, []);
array_norms := Array(0 .. 30, []);
array_fact_1 := Array(0 .. 30, []);
array_1st_rel_error := Array(0 .. 2, []);
array_last_rel_error := Array(0 .. 2, []);
array_est_rel_error := Array(0 .. 2, []);
array_max_est_error := Array(0 .. 2, []);
array_type_pole := Array(0 .. 2, []);
array_type_real_pole := Array(0 .. 2, []);
array_type_complex_pole := Array(0 .. 2, []);
array_est_digits := Array(0 .. 2, []);
array_y := Array(0 .. 30, []);
array_x := Array(0 .. 30, []);
array_tmp0 := Array(0 .. 30, []);
array_tmp1 := Array(0 .. 30, []);
array_tmp2 := Array(0 .. 30, []);
array_tmp3 := Array(0 .. 30, []);
array_m1 := Array(0 .. 30, []);
array_y_higher := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []);
array_y_set_initial := Array(0 .. 2, 0 .. 31, []);
array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
array_fact_2 := Array(0 .. 30, 0 .. 31, []);
term := 1;
while term <= 30 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 30 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 30 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 30 do
term := 1;
while term <= 30 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_2D0);
array_const_2D0[1] := c(2.0);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_h := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 1000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 30;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/div_c_exppostode.ode#################");
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = 2.0 / exp ( x ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := c(1.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "x_end := c(5.0) ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 3;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=100000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=false;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(c(-2.0)/exp(c(x)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := c(1.0);
x_end := c(5.0);
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 3;
glob_desired_digits_correct := 8;
glob_max_minutes := 3.0;
glob_subiter_method := 3;
glob_max_iter := 100000;
glob_upper_ratio_limit := c(1.000001);
glob_lower_ratio_limit := c(0.999999);
glob_look_poles := 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 ) = 2.0 / exp ( x ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2016-08-26T16:29:03-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"div_c_exp");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = 2.0 / exp ( x ) ; ");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 308.maple.seems.ok | ");
logitem_str(html_log_file, "div_c_exp diffeq.mxt");
logitem_str(html_log_file, "div_c_exp 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/div_c_exppostode.ode#################
diff ( y , x , 1 ) = 2.0 / exp ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(1.0);
x_end := c(5.0) ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 3;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=100000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=false;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(-2.0)/exp(c(x)));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (closed_form) = -0.73575888234288464319104754032291
y[1] (numeric) = -0.73575888234288464319104754032291
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 14
Correct digits = 32
h = 0.001
memory used=4.5MB, alloc=40.3MB, time=0.09
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (closed_form) = -0.72843795914304663951409259127469
y[1] (numeric) = -0.72843795914304663951409259127468
absolute error = 1e-32
relative error = 1.3728005075084582469948881583302e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (closed_form) = -0.72118988034615659656268326930804
y[1] (numeric) = -0.72118988034615659656268326930801
absolute error = 3e-32
relative error = 4.1597921459464468751987996657181e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (closed_form) = -0.71401392113829473953486123130269
y[1] (numeric) = -0.71401392113829473953486123130267
absolute error = 2e-32
relative error = 2.8010658346990791093697628196836e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (closed_form) = -0.70690936391756029630511653061792
y[1] (numeric) = -0.70690936391756029630511653061788
absolute error = 4e-32
relative error = 5.6584340287031190390389720143626e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
memory used=23.8MB, alloc=40.3MB, time=0.33
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (closed_form) = -0.69987549822231070934359774715362
y[1] (numeric) = -0.69987549822231070934359774715362
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] = 1.06
y[1] (closed_form) = -0.69291162066011487940701669618026
y[1] (numeric) = -0.69291162066011487940701669618025
absolute error = 1e-32
relative error = 1.4431854946339791231206876424608e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (closed_form) = -0.68601703483741333626641097879752
y[1] (numeric) = -0.68601703483741333626641097879749
absolute error = 3e-32
relative error = 4.3730692499654950108168061594632e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (closed_form) = -0.67919105128987830243022043049529
y[1] (numeric) = -0.67919105128987830243022043049529
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] = 1.09
y[1] (closed_form) = -0.67243298741346668581101630178611
y[1] (numeric) = -0.67243298741346668581101630178609
absolute error = 2e-32
relative error = 2.9742740725630653163119065891359e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (closed_form) = -0.66574216739615910657769381286262
y[1] (numeric) = -0.66574216739615910657769381286262
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] = 1.11
y[1] (closed_form) = -0.65911792215037813203892896763225
y[1] (numeric) = -0.65911792215037813203892896763224
absolute error = 1e-32
relative error = 1.5171791972178377913293332296919e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (closed_form) = -0.65255958924607896132506964748516
y[1] (numeric) = -0.65255958924607896132506964748513
absolute error = 3e-32
relative error = 4.5972813049395030674529346378482e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (closed_form) = -0.64606651284450586888117122528068
y[1] (numeric) = -0.64606651284450586888117122528066
absolute error = 2e-32
relative error = 3.0956565001247114903930123270235e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
memory used=67.8MB, alloc=52.3MB, time=0.86
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (closed_form) = -0.63963804363260778236032285534765
y[1] (numeric) = -0.63963804363260778236032285534762
absolute error = 3e-32
relative error = 4.6901525477792336341973343617693e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (closed_form) = -0.63327353875810643642039990485905
y[1] (numeric) = -0.63327353875810643642039990485902
absolute error = 3e-32
relative error = 4.7372893645346514408760509420102e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (closed_form) = -0.62697236176521060918551214962199
y[1] (numeric) = -0.62697236176521060918551214962198
absolute error = 1e-32
relative error = 1.5949666380580923363238956180109e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (closed_form) = -0.62073388253097001274222223091491
y[1] (numeric) = -0.6207338825309700127422222309149
absolute error = 1e-32
relative error = 1.6109963192642499637752786362050e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (closed_form) = -0.61455747720226247300654539383636
y[1] (numeric) = -0.61455747720226247300654539383635
absolute error = 1e-32
relative error = 1.6271871014448354239410142814865e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (closed_form) = -0.60844252813340809762720634865897
y[1] (numeric) = -0.60844252813340809762720634865894
absolute error = 3e-32
relative error = 4.9306218110746774164762468054117e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (closed_form) = -0.60238842382440419328995521416645
y[1] (numeric) = -0.60238842382440419328995521416641
absolute error = 4e-32
relative error = 6.6402338454730949790615348592032e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (closed_form) = -0.59639455885977475586320190075193
y[1] (numeric) = -0.59639455885977475586320190075189
absolute error = 4e-32
relative error = 6.7069693050980473620071788547514e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (closed_form) = -0.59046033384802841828302456864059
y[1] (numeric) = -0.59046033384802841828302456864054
absolute error = 5e-32
relative error = 8.4679693340533365847178629701582e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (closed_form) = -0.58458515536171880192188878381439
y[1] (numeric) = -0.58458515536171880192188878381434
absolute error = 5e-32
relative error = 8.5530738407241839344753808786304e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=111.9MB, alloc=52.3MB, time=1.38
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (closed_form) = -0.57876843587810127742626436986212
y[1] (numeric) = -0.57876843587810127742626436986209
absolute error = 3e-32
relative error = 5.1834201971440133970864232411830e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (closed_form) = -0.57300959372038020064977085329567
y[1] (numeric) = -0.57300959372038020064977085329564
absolute error = 3e-32
relative error = 5.2355144361927620641958190445084e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (closed_form) = -0.56730805299954074835648401695181
y[1] (numeric) = -0.56730805299954074835648401695179
absolute error = 2e-32
relative error = 3.5254214873653821649737080556228e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (closed_form) = -0.56166324355675953682950026030951
y[1] (numeric) = -0.56166324355675953682950026030948
absolute error = 3e-32
relative error = 5.3412788435332807865392070843279e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (closed_form) = -0.55607460090638826439862831202818
y[1] (numeric) = -0.55607460090638826439862831202812
absolute error = 6e-32
relative error = 1.0789919176707844387106155221722e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (closed_form) = -0.55054156617950467620394727427232
y[1] (numeric) = -0.55054156617950467620394727427226
absolute error = 6e-32
relative error = 1.0898359667258427271547045107534e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (closed_form) = -0.5450635860680252062446663351267
y[1] (numeric) = -0.54506358606802520624466633512662
absolute error = 8e-32
relative error = 1.4677186670476976881829959664046e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (closed_form) = -0.53964011276937370793091808153778
y[1] (numeric) = -0.53964011276937370793091808153769
absolute error = 9e-32
relative error = 1.6677781704945894106558462555010e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (closed_form) = -0.5342706039317007399654310472076
y[1] (numeric) = -0.53427060393170073996543104720751
absolute error = 9e-32
relative error = 1.6845396197673881558511251234217e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=156.0MB, alloc=52.3MB, time=1.90
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (closed_form) = -0.52895452259964792943801891542745
y[1] (numeric) = -0.52895452259964792943801891542736
absolute error = 9e-32
relative error = 1.7014695244059513356198900037149e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (closed_form) = -0.52369133716065198852399931102871
y[1] (numeric) = -0.52369133716065198852399931102861
absolute error = 1.0e-31
relative error = 1.9095217526831678968590932800393e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (closed_form) = -0.51848052129178301514346522142309
y[1] (numeric) = -0.51848052129178301514346522142299
absolute error = 1.0e-31
relative error = 1.9287127653484871690694194549651e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (closed_form) = -0.51332155390711176136717341008552
y[1] (numeric) = -0.51332155390711176136717341008542
absolute error = 1.0e-31
relative error = 1.9480966508976072853320848856501e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (closed_form) = -0.50821391910560060625202965545668
y[1] (numeric) = -0.50821391910560060625202965545658
absolute error = 1.0e-31
relative error = 1.9676753477352364494605386111894e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (closed_form) = -0.50315710611951302216003002973818
y[1] (numeric) = -0.50315710611951302216003002973809
absolute error = 9e-32
relative error = 1.7887057323726366535091255014228e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (closed_form) = -0.49815060926333637546429785699966
y[1] (numeric) = -0.49815060926333637546429785699954
absolute error = 1.2e-31
relative error = 2.4089100317965211268207395153139e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (closed_form) = -0.49319392788321295387972247966754
y[1] (numeric) = -0.49319392788321295387972247966743
absolute error = 1.1e-31
relative error = 2.2303599817645710229732598923757e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (closed_form) = -0.48828656630687416347879194624471
y[1] (numeric) = -0.48828656630687416347879194624461
absolute error = 1.0e-31
relative error = 2.0479777020355881670203686398563e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (closed_form) = -0.48342803379407288877059956197097
y[1] (numeric) = -0.48342803379407288877059956197085
absolute error = 1.2e-31
relative error = 2.4822722641508356477345804854116e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=200.0MB, alloc=52.3MB, time=2.42
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (closed_form) = -0.4786178444875090590377256987904
y[1] (numeric) = -0.47861784448750905903772569879026
absolute error = 1.4e-31
relative error = 2.9250894343462723096062742350470e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (closed_form) = -0.4738555173642435134467330551028
y[1] (numeric) = -0.47385551736424351344673305510267
absolute error = 1.3e-31
relative error = 2.7434522810477593366876638040391e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (closed_form) = -0.46914057618759530627829783412195
y[1] (numeric) = -0.46914057618759530627829783412183
absolute error = 1.2e-31
relative error = 2.5578687091012904330331664053486e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (closed_form) = -0.4644725494595176419674141413649
y[1] (numeric) = -0.46447254945951764196741414136478
absolute error = 1.2e-31
relative error = 2.5835757170071236624935939335696e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (closed_form) = -0.45985097037344767750748876862291
y[1] (numeric) = -0.45985097037344767750748876862279
absolute error = 1.2e-31
relative error = 2.6095410846376445451049031519172e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (closed_form) = -0.45527537676762547715927481158951
y[1] (numeric) = -0.45527537676762547715927481158938
absolute error = 1.3e-31
relative error = 2.8554146925971918457269619681562e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (closed_form) = -0.45074531107887745132121401376173
y[1] (numeric) = -0.45074531107887745132121401376162
absolute error = 1.1e-31
relative error = 2.4404025354520155347899257197077e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (closed_form) = -0.44626032029685965786656094152802
y[1] (numeric) = -0.44626032029685965786656094152791
absolute error = 1.1e-31
relative error = 2.4649289886859356524311305030656e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (closed_form) = -0.44181995591875639023929199353893
y[1] (numeric) = -0.44181995591875639023929199353882
absolute error = 1.1e-31
relative error = 2.4897019368728387012463868590964e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=244.1MB, alloc=52.3MB, time=2.94
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (closed_form) = -0.43742377390442952212985753283752
y[1] (numeric) = -0.43742377390442952212985753283741
absolute error = 1.1e-31
relative error = 2.5147238573281875638435300328918e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (closed_form) = -0.43307133463201412362786904627373
y[1] (numeric) = -0.43307133463201412362786904627361
absolute error = 1.2e-31
relative error = 2.7709060933798684854477118246528e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (closed_form) = -0.42876220285395590837633282336661
y[1] (numeric) = -0.4287622028539559083763328233665
absolute error = 1.1e-31
relative error = 2.5655246490434692465363627214341e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (closed_form) = -0.42449594765348611543550999515945
y[1] (numeric) = -0.42449594765348611543550999515933
absolute error = 1.2e-31
relative error = 2.8268821095544447952835838875507e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (closed_form) = -0.42027214240152947330831826638783
y[1] (numeric) = -0.4202721424015294733083182663877
absolute error = 1.3e-31
relative error = 3.0932338093396051402245580778698e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (closed_form) = -0.41609036471404093688776773145513
y[1] (numeric) = -0.416090364714040936887767731455
absolute error = 1.3e-31
relative error = 3.1243213259538658128537408434014e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (closed_form) = -0.41195019640976693096457268007686
y[1] (numeric) = -0.41195019640976693096457268007672
absolute error = 1.4e-31
relative error = 3.3984690678662033215355814449680e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (closed_form) = -0.40785122346842687638409107270102
y[1] (numeric) = -0.40785122346842687638409107270088
absolute error = 1.4e-31
relative error = 3.4326242498286355386324007394226e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (closed_form) = -0.4037930359893108169703585352867
y[1] (numeric) = -0.40379303598931081697035853528656
absolute error = 1.4e-31
relative error = 3.4671226970765803625580004494968e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (closed_form) = -0.39977522815028900694540718427019
y[1] (numeric) = -0.39977522815028900694540718427003
absolute error = 1.6e-31
relative error = 4.0022489822668701596159067562513e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=288.1MB, alloc=52.3MB, time=3.45
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (closed_form) = -0.39579739816722935976845242258825
y[1] (numeric) = -0.39579739816722935976845242258809
absolute error = 1.6e-31
relative error = 4.0424722532510937659248743399240e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (closed_form) = -0.39185914825381870010601272007459
y[1] (numeric) = -0.39185914825381870010601272007444
absolute error = 1.5e-31
relative error = 3.8279060389025443016524908263419e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (closed_form) = -0.38796008458178380102467698857468
y[1] (numeric) = -0.38796008458178380102467698857454
absolute error = 1.4e-31
relative error = 3.6086186585642767320668588127085e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (closed_form) = -0.38409981724150822847708958234667
y[1] (numeric) = -0.38409981724150822847708958234654
absolute error = 1.3e-31
relative error = 3.3845368876669016794772496102630e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (closed_form) = -0.38027796020304105473278211658868
y[1] (numeric) = -0.38027796020304105473278211658854
absolute error = 1.4e-31
relative error = 3.6815175911128291139543293308576e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (closed_form) = -0.37649413127749354159270234015759
y[1] (numeric) = -0.37649413127749354159270234015745
absolute error = 1.4e-31
relative error = 3.7185174580268169468433113321819e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (closed_form) = -0.37274795207881993302359197748017
y[1] (numeric) = -0.37274795207881993302359197748002
absolute error = 1.5e-31
relative error = 4.0241669783414810775174264501924e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (closed_form) = -0.3690390479859785352596275318049
y[1] (numeric) = -0.36903904798597853525962753180475
absolute error = 1.5e-31
relative error = 4.0646105288484046631661444046899e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (closed_form) = -0.36536704810546930044780167551788
y[1] (numeric) = -0.36536704810546930044780167551771
absolute error = 1.7e-31
relative error = 4.6528552829681197966722332635577e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=332.2MB, alloc=52.3MB, time=3.97
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (closed_form) = -0.36173158523424416756419098130371
y[1] (numeric) = -0.36173158523424416756419098130353
absolute error = 1.8e-31
relative error = 4.9760653298616036502909671163148e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (closed_form) = -0.35813229582298645160429346866125
y[1] (numeric) = -0.35813229582298645160429346866109
absolute error = 1.6e-31
relative error = 4.4676227714208432061169483784155e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (closed_form) = -0.35456881993975560895575438851885
y[1] (numeric) = -0.35456881993975560895575438851869
absolute error = 1.6e-31
relative error = 4.5125231267426566381208773742464e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (closed_form) = -0.35104080123399374339972138868441
y[1] (numeric) = -0.35104080123399374339972138868425
absolute error = 1.6e-31
relative error = 4.5578747381375928095496790690881e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (closed_form) = -0.34754788690089025336143451733274
y[1] (numeric) = -0.34754788690089025336143451733258
absolute error = 1.6e-31
relative error = 4.6036821408045843494931997638742e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (closed_form) = -0.34408972764610105684507989725189
y[1] (numeric) = -0.34408972764610105684507989725172
absolute error = 1.7e-31
relative error = 4.9405717852422003523982895307823e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (closed_form) = -0.34066597765081886594599981232611
y[1] (numeric) = -0.34066597765081886594599981232593
absolute error = 1.8e-31
relative error = 5.2837680252443409865046285242457e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (closed_form) = -0.33727629453719101793860222566362
y[1] (numeric) = -0.33727629453719101793860222566341
absolute error = 2.1e-31
relative error = 6.2263492395207032071475251611492e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (closed_form) = -0.33392033933408140469425995016587
y[1] (numeric) = -0.33392033933408140469425995016567
absolute error = 2.0e-31
relative error = 5.9894524663831133289584667268155e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=376.3MB, alloc=52.3MB, time=4.49
x[1] = 1.8
y[1] (closed_form) = -0.33059777644317307659360944086443
y[1] (numeric) = -0.33059777644317307659360944086423
absolute error = 2.0e-31
relative error = 6.0496474644129460837310239530277e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (closed_form) = -0.32730827360540813116539251467187
y[1] (numeric) = -0.32730827360540813116539251467168
absolute error = 1.9e-31
relative error = 5.8049250606190793334925888796950e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (closed_form) = -0.3240515018677615304127380290285
y[1] (numeric) = -0.32405150186776153041273802902832
absolute error = 1.8e-31
relative error = 5.5546726048951978143573944813097e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (closed_form) = -0.32082713555034552418092756975611
y[1] (numeric) = -0.32082713555034552418092756975592
absolute error = 1.9e-31
relative error = 5.9221923255984814385112320814742e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (closed_form) = -0.31763485221384138998156885278391
y[1] (numeric) = -0.31763485221384138998156885278372
absolute error = 1.9e-31
relative error = 5.9817113479753239763514138481736e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (closed_form) = -0.31447433262725523242001894980624
y[1] (numeric) = -0.31447433262725523242001894980604
absolute error = 2.0e-31
relative error = 6.3598195226018317043472218706368e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (closed_form) = -0.31134526073599461777912982348316
y[1] (numeric) = -0.31134526073599461777912982348297
absolute error = 1.9e-31
relative error = 6.1025499328576773408670470782642e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (closed_form) = -0.30824732363026285139617165354796
y[1] (numeric) = -0.30824732363026285139617165354776
absolute error = 2.0e-31
relative error = 6.4882963992867111150290313243490e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (closed_form) = -0.30518021151376773723433345617434
y[1] (numeric) = -0.30518021151376773723433345617415
absolute error = 1.9e-31
relative error = 6.2258296190815911199365372342538e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (closed_form) = -0.3021436176727416904986820260546
y[1] (numeric) = -0.30214361767274169049868202605439
absolute error = 2.1e-31
relative error = 6.9503371150952312179909511215980e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=420.5MB, alloc=52.3MB, time=5.01
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (closed_form) = -0.29913723844527010528202413820747
y[1] (numeric) = -0.29913723844527010528202413820725
absolute error = 2.2e-31
relative error = 7.3544838865071963576797838004621e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (closed_form) = -0.29616077319092491005187681690838
y[1] (numeric) = -0.29616077319092491005187681690816
absolute error = 2.2e-31
relative error = 7.4283976783844153507287237107371e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (closed_form) = -0.29321392426070027430878891399001
y[1] (numeric) = -0.29321392426070027430878891398978
absolute error = 2.3e-31
relative error = 7.8441022396843623101885886578832e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.93
y[1] (closed_form) = -0.29029639696724745996162616737418
y[1] (numeric) = -0.29029639696724745996162616737394
absolute error = 2.4e-31
relative error = 8.2674122898975516807348230807925e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (closed_form) = -0.28740789955540584088015289513921
y[1] (numeric) = -0.28740789955540584088015289513897
absolute error = 2.4e-31
relative error = 8.3505011647647265213582417510513e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (closed_form) = -0.28454814317302714370230801772766
y[1] (numeric) = -0.28454814317302714370230801772741
absolute error = 2.5e-31
relative error = 8.7858594757366166678636024169556e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (closed_form) = -0.28171684184208999229594292219192
y[1] (numeric) = -0.28171684184208999229594292219168
absolute error = 2.4e-31
relative error = 8.5191924781879592057297225664985e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (closed_form) = -0.27891371243010186730539604907824
y[1] (numeric) = -0.278913712430101867305396049078
absolute error = 2.4e-31
relative error = 8.6048117860159359358534009246771e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (closed_form) = -0.27613847462178562095502707959073
y[1] (numeric) = -0.27613847462178562095502707959049
absolute error = 2.4e-31
relative error = 8.6912915821932146502149217037737e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=464.5MB, alloc=52.3MB, time=5.52
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (closed_form) = -0.27339085089104771573759642680838
y[1] (numeric) = -0.27339085089104771573759642680812
absolute error = 2.6e-31
relative error = 9.5101938910024364648657220835680e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (closed_form) = -0.27067056647322538378799898994497
y[1] (numeric) = -0.27067056647322538378799898994474
absolute error = 2.3e-31
relative error = 8.4974145137702477613149915796612e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (closed_form) = -0.26797734933760993163516210074751
y[1] (numeric) = -0.26797734933760993163516210074728
absolute error = 2.3e-31
relative error = 8.5828149494170734247022295054701e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (closed_form) = -0.2653109301602434426396855294633
y[1] (numeric) = -0.26531093016024344263968552946307
absolute error = 2.3e-31
relative error = 8.6690736737112104278080429786192e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (closed_form) = -0.2626710422969861567647978241762
y[1] (numeric) = -0.26267104229698615676479782417597
absolute error = 2.3e-31
relative error = 8.7561993125969706941858521045567e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (closed_form) = -0.2600574217568518343961621541422
y[1] (numeric) = -0.26005742175685183439616215414198
absolute error = 2.2e-31
relative error = 8.4596701187668978391694287176327e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (closed_form) = -0.25746980717560843772469303348974
y[1] (numeric) = -0.25746980717560843772469303348951
absolute error = 2.3e-31
relative error = 8.9330862722527875886813637670309e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (closed_form) = -0.25490793978964148973852270144483
y[1] (numeric) = -0.2549079397896414897385227014446
absolute error = 2.3e-31
relative error = 9.0228652818662160895552397271991e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (closed_form) = -0.25237156341007749713823574894352
y[1] (numeric) = -0.25237156341007749713823574894328
absolute error = 2.4e-31
relative error = 9.5097877414193850544201872652156e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (closed_form) = -0.24986042439716484949609962897764
y[1] (numeric) = -0.24986042439716484949609962897739
absolute error = 2.5e-31
relative error = 1.0005586142870440680299979909837e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=508.7MB, alloc=52.3MB, time=6.04
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (closed_form) = -0.24737427163490963272785765185998
y[1] (numeric) = -0.24737427163490963272785765185973
absolute error = 2.5e-31
relative error = 1.0106143955381325218716800895552e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (closed_form) = -0.24491285650596382043729475214525
y[1] (numeric) = -0.24491285650596382043729475214501
absolute error = 2.4e-31
relative error = 9.7994038950811800881396728925745e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (closed_form) = -0.24247593286676333193178390681564
y[1] (numeric) = -0.24247593286676333193178390681541
absolute error = 2.3e-31
relative error = 9.4854774773206601667733867165789e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (closed_form) = -0.24006325702291347069389640532458
y[1] (numeric) = -0.24006325702291347069389640532434
absolute error = 2.4e-31
relative error = 9.9973649852252303250007793393364e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (closed_form) = -0.23767458770481928183241092954488
y[1] (numeric) = -0.23767458770481928183241092954463
absolute error = 2.5e-31
relative error = 1.0518583514300161680965592443436e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (closed_form) = -0.23530968604355839152815844137813
y[1] (numeric) = -0.23530968604355839152815844137787
absolute error = 2.6e-31
relative error = 1.1049268917551960093939185782390e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (closed_form) = -0.23296831554699391573854142836567
y[1] (numeric) = -0.23296831554699391573854142836541
absolute error = 2.6e-31
relative error = 1.1160315916331262026111983896122e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (closed_form) = -0.23065024207612504943169198345969
y[1] (numeric) = -0.23065024207612504943169198345942
absolute error = 2.7e-31
relative error = 1.1706035838925664093223131687804e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (closed_form) = -0.22835523382167297138948422676448
y[1] (numeric) = -0.2283552338216729713894842267642
absolute error = 2.8e-31
relative error = 1.2261597657037168135139395376261e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=552.7MB, alloc=52.3MB, time=6.57
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (closed_form) = -0.2260830612808997231503695594535
y[1] (numeric) = -0.22608306128089972315036955945322
absolute error = 2.8e-31
relative error = 1.2384828762209235257261010382875e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (closed_form) = -0.22383349723465774396061136811429
y[1] (numeric) = -0.22383349723465774396061136811401
absolute error = 2.8e-31
relative error = 1.2509298360578248340446264203398e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (closed_form) = -0.22160631672466776666828885169988
y[1] (numeric) = -0.2216063167246677666682888516996
absolute error = 2.8e-31
relative error = 1.2635018899207769297060488033644e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (closed_form) = -0.21940129703102280233072422159711
y[1] (numeric) = -0.21940129703102280233072422159682
absolute error = 2.9e-31
relative error = 1.3217788769908443849089296341665e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (closed_form) = -0.21721821764991596391504727554914
y[1] (numeric) = -0.21721821764991596391504727554886
absolute error = 2.8e-31
relative error = 1.2890263212235151342309001640711e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (closed_form) = -0.21505686027158990185570719310607
y[1] (numeric) = -0.21505686027158990185570719310579
absolute error = 2.8e-31
relative error = 1.3019812511277019472350548032446e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (closed_form) = -0.2129170087585056463941117721627
y[1] (numeric) = -0.21291700875850564639411177216242
absolute error = 2.8e-31
relative error = 1.3150663802419895229947292839419e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (closed_form) = -0.2107984491237286735664353784814
y[1] (numeric) = -0.21079844912372867356643537848112
absolute error = 2.8e-31
relative error = 1.3282830170901936008770516662316e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (closed_form) = -0.20870096950953003342818271727923
y[1] (numeric) = -0.20870096950953003342818271727895
absolute error = 2.8e-31
relative error = 1.3416324833470129020429259399415e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (closed_form) = -0.20662436016620040061049843066899
y[1] (numeric) = -0.20662436016620040061049843066871
absolute error = 2.8e-31
relative error = 1.3551161139701977007184017078550e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=596.9MB, alloc=52.3MB, time=7.09
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (closed_form) = -0.20456841343107492859562313519417
y[1] (numeric) = -0.20456841343107492859562313519389
absolute error = 2.8e-31
relative error = 1.3687352573340467116905969084545e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (closed_form) = -0.20253292370776681017944409869335
y[1] (numeric) = -0.20253292370776681017944409869306
absolute error = 2.9e-31
relative error = 1.4318659637701115596791770528258e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (closed_form) = -0.20051768744560746745988138759597
y[1] (numeric) = -0.20051768744560746745988138759568
absolute error = 2.9e-31
relative error = 1.4462564559481345072938541977518e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (closed_form) = -0.19852250311929131535297509114374
y[1] (numeric) = -0.19852250311929131535297509114345
absolute error = 2.9e-31
relative error = 1.4607915749769699990355910170042e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (closed_form) = -0.19654717120872306309606247764772
y[1] (numeric) = -0.19654717120872306309606247764744
absolute error = 2.8e-31
relative error = 1.4245944028502668836051896046145e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (closed_form) = -0.19459149417906553845140142910307
y[1] (numeric) = -0.19459149417906553845140142910281
absolute error = 2.6e-31
relative error = 1.3361323992956482079209580356936e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (closed_form) = -0.19265527646098603937603364791825
y[1] (numeric) = -0.19265527646098603937603364791799
absolute error = 2.6e-31
relative error = 1.3495607531551398234516820977154e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (closed_form) = -0.1907383244310992377765931935996
y[1] (numeric) = -0.19073832443109923777659319359933
absolute error = 2.7e-31
relative error = 1.4155519128382225343567755177797e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (closed_form) = -0.18884044639260467962313819571542
y[1] (numeric) = -0.18884044639260467962313819571514
absolute error = 2.8e-31
relative error = 1.4827332033407292722440592169944e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=641.0MB, alloc=52.3MB, time=7.62
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (closed_form) = -0.18696145255611694515588165595398
y[1] (numeric) = -0.18696145255611694515588165595371
absolute error = 2.7e-31
relative error = 1.4441479583549920710207064971543e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (closed_form) = -0.18510115502068655218486709261196
y[1] (numeric) = -0.18510115502068655218486709261168
absolute error = 2.8e-31
relative error = 1.5126864009503762082273406461002e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (closed_form) = -0.18325936775500970455710302844059
y[1] (numeric) = -0.18325936775500970455710302844032
absolute error = 2.7e-31
relative error = 1.4733216823106664551616055323560e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (closed_form) = -0.18143590657882500675034444015938
y[1] (numeric) = -0.18143590657882500675034444015911
absolute error = 2.7e-31
relative error = 1.4881288113866162230521218689052e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (closed_form) = -0.17963058914449528424947775826781
y[1] (numeric) = -0.17963058914449528424947775826754
absolute error = 2.7e-31
relative error = 1.5030847545838161290856479436467e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (closed_form) = -0.17784323491877266787219852147351
y[1] (numeric) = -0.17784323491877266787219852147324
absolute error = 2.7e-31
relative error = 1.5181910075090492207948145427467e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (closed_form) = -0.17607366516474511853721843978805
y[1] (numeric) = -0.17607366516474511853721843978777
absolute error = 2.8e-31
relative error = 1.5902434912002038893163399614863e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (closed_form) = -0.1743217029239625871124340741545
y[1] (numeric) = -0.17432170292396258711243407415423
absolute error = 2.7e-31
relative error = 1.5488605002773025075645754157787e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (closed_form) = -0.17258717299874102194414703303231
y[1] (numeric) = -0.17258717299874102194414703303203
absolute error = 2.8e-31
relative error = 1.6223685406912744691126988670312e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (closed_form) = -0.17086990193464245445334189841079
y[1] (numeric) = -0.17086990193464245445334189841052
absolute error = 2.7e-31
relative error = 1.5801495578974154073127050217092e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=685.1MB, alloc=52.3MB, time=8.14
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (closed_form) = -0.16916971800312941079298153170792
y[1] (numeric) = -0.16916971800312941079298153170766
absolute error = 2.6e-31
relative error = 1.5369180907140269154967259290836e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (closed_form) = -0.16748645118439191499303078395017
y[1] (numeric) = -0.16748645118439191499303078394991
absolute error = 2.6e-31
relative error = 1.5523643743203834455367761996215e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (closed_form) = -0.1658199331503453662792122341894
y[1] (numeric) = -0.16581993315034536627921223418913
absolute error = 2.7e-31
relative error = 1.6282722762600368932931489122066e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (closed_form) = -0.16416999724779759033905734893432
y[1] (numeric) = -0.16416999724779759033905734893403
absolute error = 2.9e-31
relative error = 1.7664616243020036485201755129194e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (closed_form) = -0.16253647848178338122635216367639
y[1] (numeric) = -0.16253647848178338122635216367609
absolute error = 3.0e-31
relative error = 1.8457395090765617454441627741077e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (closed_form) = -0.16091921349906486734428000303859
y[1] (numeric) = -0.16091921349906486734428000303828
absolute error = 3.1e-31
relative error = 1.9264324828545192331788087821054e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (closed_form) = -0.15931804057179605153010981297284
y[1] (numeric) = -0.15931804057179605153010981297251
absolute error = 3.3e-31
relative error = 2.0713285125502581823252838280124e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (closed_form) = -0.15773279958134989168182564520009
y[1] (numeric) = -0.15773279958134989168182564519977
absolute error = 3.2e-31
relative error = 2.0287473553334201894631054489830e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (closed_form) = -0.15616333200230630462128247910557
y[1] (numeric) = -0.15616333200230630462128247910526
absolute error = 3.1e-31
relative error = 1.9851010863127699669658943316767e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=729.2MB, alloc=52.3MB, time=8.66
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (closed_form) = -0.15460948088659949198093132207952
y[1] (numeric) = -0.15460948088659949198093132207921
absolute error = 3.1e-31
relative error = 2.0050516839091768218262744328810e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (closed_form) = -0.15307109084782300283349165501697
y[1] (numeric) = -0.15307109084782300283349165501665
absolute error = 3.2e-31
relative error = 2.0905319105495293597155520782475e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (closed_form) = -0.15154800804569096355775503214886
y[1] (numeric) = -0.15154800804569096355775503214854
absolute error = 3.2e-31
relative error = 2.1115421055453372016929623260559e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (closed_form) = -0.15004008017065392105055739728929
y[1] (numeric) = -0.15004008017065392105055739728898
absolute error = 3.1e-31
relative error = 2.0661145984953449933309239773734e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (closed_form) = -0.14854715642866776085642114033995
y[1] (numeric) = -0.14854715642866776085642114033963
absolute error = 3.2e-31
relative error = 2.1541980856002704636401320532135e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (closed_form) = -0.14706908752611417709398724772342
y[1] (numeric) = -0.1470690875261141770939872477231
absolute error = 3.2e-31
relative error = 2.1758481362929481454709090411882e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (closed_form) = -0.14560572565487118621366387301155
y[1] (numeric) = -0.14560572565487118621366387301124
absolute error = 3.1e-31
relative error = 2.1290371556870783230689456010562e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (closed_form) = -0.14415692447753219162542581259969
y[1] (numeric) = -0.14415692447753219162542581259937
absolute error = 3.2e-31
relative error = 2.2198031843407849102318934106801e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (closed_form) = -0.14272253911277212109091017917259
y[1] (numeric) = -0.14272253911277212109091017917228
absolute error = 3.1e-31
relative error = 2.1720465591987100398413474586178e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=773.3MB, alloc=52.3MB, time=9.18
x[1] = 2.65
y[1] (closed_form) = -0.14130242612085917348135255637331
y[1] (numeric) = -0.14130242612085917348135255637299
absolute error = 3.2e-31
relative error = 2.2646461832601284146634623692636e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (closed_form) = -0.13989644348931072606396584367654
y[1] (numeric) = -0.13989644348931072606396584367622
absolute error = 3.2e-31
relative error = 2.2874062557884161799375592817761e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (closed_form) = -0.13850445061869196789553697891176
y[1] (numeric) = -0.13850445061869196789553697891144
absolute error = 3.2e-31
relative error = 2.3103950708484610205709424528951e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (closed_form) = -0.13712630830855583917474638648806
y[1] (numeric) = -0.13712630830855583917474638648774
absolute error = 3.2e-31
relative error = 2.3336149273409263507889795646483e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (closed_form) = -0.13576187874352287053542862700309
y[1] (numeric) = -0.13576187874352287053542862700279
absolute error = 3.0e-31
relative error = 2.2097513880663856519076219455086e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (closed_form) = -0.13441102547949953025310340171193
y[1] (numeric) = -0.13441102547949953025310340171163
absolute error = 3.0e-31
relative error = 2.2319597587309251167803489529203e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (closed_form) = -0.13307361343003370118801281601234
y[1] (numeric) = -0.13307361343003370118801281601204
absolute error = 3.0e-31
relative error = 2.2543913272313103396731481974885e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (closed_form) = -0.13174950885280592300098873189073
y[1] (numeric) = -0.13174950885280592300098873189043
absolute error = 3.0e-31
relative error = 2.2770483367430843951686537471095e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (closed_form) = -0.13043857933625504875511446038598
y[1] (numeric) = -0.13043857933625504875511446038568
absolute error = 3.0e-31
relative error = 2.2999330529860793648684767840416e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (closed_form) = -0.12914069378633697845769563692426
y[1] (numeric) = -0.12914069378633697845769563692395
absolute error = 3.1e-31
relative error = 2.4004826899326898823311034951793e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=817.4MB, alloc=52.3MB, time=9.70
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (closed_form) = -0.1278557224134151454048600511159
y[1] (numeric) = -0.12785572241341514540486005111558
absolute error = 3.2e-31
relative error = 2.5028211014701074576340316873851e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (closed_form) = -0.12658353671928144436649625986908
y[1] (numeric) = -0.12658353671928144436649625986874
absolute error = 3.4e-31
relative error = 2.6859733012042675469260736316065e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (closed_form) = -0.12532400948430630369353354844936
y[1] (numeric) = -0.12532400948430630369353354844903
absolute error = 3.3e-31
relative error = 2.6331746116160147483679053831070e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (closed_form) = -0.12407701475471661634406565854311
y[1] (numeric) = -0.12407701475471661634406565854278
absolute error = 3.3e-31
relative error = 2.6596384564245450286925317175126e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (closed_form) = -0.12284242783000025761081913621326
y[1] (numeric) = -0.12284242783000025761081913621294
absolute error = 3.2e-31
relative error = 2.6049631682861483944451962899630e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (closed_form) = -0.12162012525043592999124277636788
y[1] (numeric) = -0.12162012525043592999124277636756
absolute error = 3.2e-31
relative error = 2.6311434833755279794396825617480e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (closed_form) = -0.12040998478474708817431334210487
y[1] (numeric) = -0.12040998478474708817431334210456
absolute error = 3.1e-31
relative error = 2.5745373239119384955986481306985e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (closed_form) = -0.11921188541787870952626780936569
y[1] (numeric) = -0.11921188541787870952626780936537
absolute error = 3.2e-31
relative error = 2.6842961075423797433771520167190e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (closed_form) = -0.11802570733889568774212465157395
y[1] (numeric) = -0.11802570733889568774212465157363
absolute error = 3.2e-31
relative error = 2.7112737319265626086153473122359e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=861.5MB, alloc=52.3MB, time=10.29
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (closed_form) = -0.11685133192900163949227461081453
y[1] (numeric) = -0.1168513319290016394922746108142
absolute error = 3.3e-31
relative error = 2.8241013136290698267382826631828e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (closed_form) = -0.1156886417496769259348212535548
y[1] (numeric) = -0.11568864174967692593482125355448
absolute error = 3.2e-31
relative error = 2.7660450944908222801668849205514e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (closed_form) = -0.11453752053093470288593752994038
y[1] (numeric) = -0.11453752053093470288593752994005
absolute error = 3.3e-31
relative error = 2.8811519445356984188124362612449e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (closed_form) = -0.11339785315969382524346871484118
y[1] (numeric) = -0.11339785315969382524346871484085
absolute error = 3.3e-31
relative error = 2.9101080029731578880385397508125e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (closed_form) = -0.11226952566826744294453481233074
y[1] (numeric) = -0.11226952566826744294453481233041
absolute error = 3.3e-31
relative error = 2.9393550746360127591788553354033e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (closed_form) = -0.11115242522296613730713531516097
y[1] (numeric) = -0.11115242522296613730713531516064
absolute error = 3.3e-31
relative error = 2.9688960842558019586815535776000e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (closed_form) = -0.11004644011281445805989306166835
y[1] (numeric) = -0.11004644011281445805989306166803
absolute error = 3.2e-31
relative error = 2.9078632591108897508282010518605e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (closed_form) = -0.10895145973837973270423724734572
y[1] (numeric) = -0.1089514597383797327042372473454
absolute error = 3.2e-31
relative error = 2.9370877707228676664602070110965e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (closed_form) = -0.10786737460071203108065245281805
y[1] (numeric) = -0.10786737460071203108065245281773
absolute error = 3.2e-31
relative error = 2.9666059935594991697196251805445e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (closed_form) = -0.10679407629039417912623358620798
y[1] (numeric) = -0.10679407629039417912623358620767
absolute error = 3.1e-31
relative error = 2.9027827269843019458830639344394e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=905.8MB, alloc=52.3MB, time=10.82
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (closed_form) = -0.10573145747670072681579747643322
y[1] (numeric) = -0.1057314574767007268157974764329
absolute error = 3.2e-31
relative error = 3.0265354099608063694604721313068e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (closed_form) = -0.10467941189686478617431100509864
y[1] (numeric) = -0.10467941189686478617431100509832
absolute error = 3.2e-31
relative error = 3.0569525965170635434671960477701e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (closed_form) = -0.10363783434545166603549268832574
y[1] (numeric) = -0.10363783434545166603549268832543
absolute error = 3.1e-31
relative error = 2.9911856221029276183360992642769e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (closed_form) = -0.10260662066383824090120823479189
y[1] (numeric) = -0.10260662066383824090120823479156
absolute error = 3.3e-31
relative error = 3.2161667333451343908529559677371e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (closed_form) = -0.10158566772979700182977879769406
y[1] (numeric) = -0.10158566772979700182977879769372
absolute error = 3.4e-31
relative error = 3.3469288296096079657896770572952e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (closed_form) = -0.10057487344718374774961076493595
y[1] (numeric) = -0.10057487344718374774961076493562
absolute error = 3.3e-31
relative error = 3.2811376111081799345890220510380e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (closed_form) = -0.099574136735727885958684831300122
y[1] (numeric) = -0.099574136735727885958684831299798
absolute error = 3.24e-31
relative error = 3.2538569815564021740304218040423e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (closed_form) = -0.098583357520924320831446190234969
y[1] (numeric) = -0.098583357520924320831446190234643
absolute error = 3.26e-31
relative error = 3.3068461878142716880577881929101e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (closed_form) = -0.097602436724025919913543080119995
y[1] (numeric) = -0.097602436724025919913543080119666
absolute error = 3.29e-31
relative error = 3.3708174820497387144956601129644e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=949.9MB, alloc=52.3MB, time=11.33
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (closed_form) = -0.096631276252135556642683519477524
y[1] (numeric) = -0.096631276252135556642683519477196
absolute error = 3.28e-31
relative error = 3.3943461446598784991541949332050e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (closed_form) = -0.095669778988396738891625658216285
y[1] (numeric) = -0.095669778988396738891625658215954
absolute error = 3.31e-31
relative error = 3.4598177554078510916533728963618e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (closed_form) = -0.094717848782281842387981540479467
y[1] (numeric) = -0.09471784878228184238798154047914
absolute error = 3.27e-31
relative error = 3.4523588130853900641321144326832e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (closed_form) = -0.093775390439976977826083093679625
y[1] (numeric) = -0.093775390439976977826083093679295
absolute error = 3.30e-31
relative error = 3.5190469317344387066514051808769e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (closed_form) = -0.092842309714862530149608892870319
y[1] (numeric) = -0.092842309714862530149608892869992
absolute error = 3.27e-31
relative error = 3.5221010873628951348578815668306e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (closed_form) = -0.091918513298088418050967052756972
y[1] (numeric) = -0.091918513298088418050967052756643
absolute error = 3.29e-31
relative error = 3.5792571941744193054015608687875e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (closed_form) = -0.091003908809243131205530209038912
y[1] (numeric) = -0.091003908809243131205530209038582
absolute error = 3.30e-31
relative error = 3.6262178660009644825796243506120e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (closed_form) = -0.090098404787115612136670184356672
y[1] (numeric) = -0.090098404787115612136670184356341
absolute error = 3.31e-31
relative error = 3.6737609370785903284990297600980e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (closed_form) = -0.089201910680549058892080384870443
y[1] (numeric) = -0.089201910680549058892080384870115
absolute error = 3.28e-31
relative error = 3.6770512817224004589801095913198e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (closed_form) = -0.088314336839385733904031703200168
y[1] (numeric) = -0.088314336839385733904031703199839
absolute error = 3.29e-31
relative error = 3.7253294513023525929501529094831e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=994.0MB, alloc=52.3MB, time=11.85
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (closed_form) = -0.087435594505501873506901935547708
y[1] (numeric) = -0.087435594505501873506901935547376
absolute error = 3.32e-31
relative error = 3.7970806040451745635586964032973e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (closed_form) = -0.086565595803931801595459532304399
y[1] (numeric) = -0.086565595803931801595459532304069
absolute error = 3.30e-31
relative error = 3.8121380316891601594555489557025e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (closed_form) = -0.085704253734080359827870913912309
y[1] (numeric) = -0.085704253734080359827870913911979
absolute error = 3.30e-31
relative error = 3.8504506558555477643577144480947e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (closed_form) = -0.08485148216102277560912865346997
y[1] (numeric) = -0.084851482161022775609128653469636
absolute error = 3.34e-31
relative error = 3.9362895201543767481116840427606e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (closed_form) = -0.084007195806891097834448734719998
y[1] (numeric) = -0.084007195806891097834448734719668
absolute error = 3.30e-31
relative error = 3.9282349188107306024108172063683e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (closed_form) = -0.083171310242346339029033231003973
y[1] (numeric) = -0.08317131024234633902903323100364
absolute error = 3.33e-31
relative error = 4.0037844664187385325794132174604e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (closed_form) = -0.082343741878135471091305809546969
y[1] (numeric) = -0.082343741878135471091305809546637
absolute error = 3.32e-31
relative error = 4.0318789555536962303149783171646e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (closed_form) = -0.081524407956732430332158524288851
y[1] (numeric) = -0.081524407956732430332158524288517
absolute error = 3.34e-31
relative error = 4.0969325429172612234745640425700e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (closed_form) = -0.080713226544062295903747969588037
y[1] (numeric) = -0.080713226544062295903747969587702
absolute error = 3.35e-31
relative error = 4.1504969426184390679357252640163e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1038.1MB, alloc=52.3MB, time=12.38
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (closed_form) = -0.079910116521307814028787133448768
y[1] (numeric) = -0.079910116521307814028787133448434
absolute error = 3.34e-31
relative error = 4.1796960702834141586759996185392e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (closed_form) = -0.079114997576797448675927960221868
y[1] (numeric) = -0.079114997576797448675927960221531
absolute error = 3.37e-31
relative error = 4.2596221996072474469435336716519e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (closed_form) = -0.078327790197974147479542180731511
y[1] (numeric) = -0.078327790197974147479542180731176
absolute error = 3.35e-31
relative error = 4.2768983926813802208932426919292e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (closed_form) = -0.077548415663444019773799670535193
y[1] (numeric) = -0.077548415663444019773799670534857
absolute error = 3.36e-31
relative error = 4.3327771060884344309654580884553e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (closed_form) = -0.076776796035104131602221620427345
y[1] (numeric) = -0.076776796035104131602221620427011
absolute error = 3.34e-31
relative error = 4.3502727028005630051993403451002e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (closed_form) = -0.076012854150348630475649281811054
y[1] (numeric) = -0.076012854150348630475649281810718
absolute error = 3.36e-31
relative error = 4.4203050096686699266898177427370e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (closed_form) = -0.075256513614352420484609166127661
y[1] (numeric) = -0.075256513614352420484609166127326
absolute error = 3.35e-31
relative error = 4.4514419272288881808842125298084e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (closed_form) = -0.07450769879243161612715564269026
y[1] (numeric) = -0.074507698792431616127155642689925
absolute error = 3.35e-31
relative error = 4.4961796623630095746030340322043e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (closed_form) = -0.073766334802480010891207409483032
y[1] (numeric) = -0.073766334802480010891207409482695
absolute error = 3.37e-31
relative error = 4.5684796581308540314188957005739e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (closed_form) = -0.073032347507480804231933106715629
y[1] (numeric) = -0.073032347507480804231933106715294
absolute error = 3.35e-31
relative error = 4.5870085165437888639349299612541e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1082.3MB, alloc=52.3MB, time=12.90
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (closed_form) = -0.072305663508092838110643563374324
y[1] (numeric) = -0.072305663508092838110643563373989
absolute error = 3.35e-31
relative error = 4.6331087185515558015970769167829e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (closed_form) = -0.071586210135310601712666409183133
y[1] (numeric) = -0.071586210135310601712666409182798
absolute error = 3.35e-31
relative error = 4.6796722352921146967351022179300e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (closed_form) = -0.070873915443197270338558156312127
y[1] (numeric) = -0.070873915443197270338558156311793
absolute error = 3.34e-31
relative error = 4.7125941598032383587357045544722e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (closed_form) = -0.070168708201690051766487050931066
y[1] (numeric) = -0.07016870820169005176648705093073
absolute error = 3.36e-31
relative error = 4.7884592521529027661670380279408e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (closed_form) = -0.069470517889477120614427368210285
y[1] (numeric) = -0.069470517889477120614427368209948
absolute error = 3.37e-31
relative error = 4.8509786631523912012514157617768e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (closed_form) = -0.068779274686945428389665462380541
y[1] (numeric) = -0.068779274686945428389665462380205
absolute error = 3.36e-31
relative error = 4.8851925457099083936435066550098e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (closed_form) = -0.068094909469198684000745677908606
y[1] (numeric) = -0.068094909469198684000745677908267
absolute error = 3.39e-31
relative error = 4.9783457037025594280769645569515e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (closed_form) = -0.067417353799144806524088947411793
y[1] (numeric) = -0.067417353799144806524088947411455
absolute error = 3.38e-31
relative error = 5.0135459336923359304807669912467e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (closed_form) = -0.066746539920652158964800262941896
y[1] (numeric) = -0.066746539920652158964800262941558
absolute error = 3.38e-31
relative error = 5.0639329080100952558395052627004e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1126.4MB, alloc=52.3MB, time=13.42
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (closed_form) = -0.066082400751773878629337943842434
y[1] (numeric) = -0.066082400751773878629337943842097
absolute error = 3.37e-31
relative error = 5.0996936577089137065653582024741e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (closed_form) = -0.065424869878039626537435557928615
y[1] (numeric) = -0.065424869878039626537435557928277
absolute error = 3.38e-31
relative error = 5.1662311385574855410855297496435e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (closed_form) = -0.064773881545814085042627460724618
y[1] (numeric) = -0.064773881545814085042627460724281
absolute error = 3.37e-31
relative error = 5.2027143033205815287628949017919e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (closed_form) = -0.064129370655721539505605401547277
y[1] (numeric) = -0.064129370655721539505605401546942
absolute error = 3.35e-31
relative error = 5.2238154931918349222987322730940e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (closed_form) = -0.06349127275613588647309399855947
y[1] (numeric) = -0.063491272756135886473093998559134
absolute error = 3.36e-31
relative error = 5.2920659078696525953825785894459e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (closed_form) = -0.062859524036735417357637959073097
y[1] (numeric) = -0.062859524036735417357637959072761
absolute error = 3.36e-31
relative error = 5.3452520544641721260486619322790e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (closed_form) = -0.062234061322121733091297992320118
y[1] (numeric) = -0.062234061322121733091297992319781
absolute error = 3.37e-31
relative error = 5.4150411019409062102211720850897e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (closed_form) = -0.061614822065502151639403195435717
y[1] (numeric) = -0.061614822065502151639403195435379
absolute error = 3.38e-31
relative error = 5.4856930308209817314403139486888e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (closed_form) = -0.061001744342434976609846609938077
y[1] (numeric) = -0.061001744342434976609846609937737
absolute error = 3.40e-31
relative error = 5.5736111100594207584363662361522e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (closed_form) = -0.060394766844637001479572584727239
y[1] (numeric) = -0.0603947668446370014795725847269
absolute error = 3.39e-31
relative error = 5.6130691069983471807357257648909e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1170.5MB, alloc=52.3MB, time=13.94
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (closed_form) = -0.059793828873852630183518163993323
y[1] (numeric) = -0.059793828873852630183518163992983
absolute error = 3.40e-31
relative error = 5.6862055232706350181478160237895e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (closed_form) = -0.059198870335784000972958310966756
y[1] (numeric) = -0.059198870335784000972958310966415
absolute error = 3.41e-31
relative error = 5.7602450530863489368965169599966e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (closed_form) = -0.058609831734081506550582555054073
y[1] (numeric) = -0.058609831734081506550582555053732
absolute error = 3.41e-31
relative error = 5.8181364783156192462177451514844e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (closed_form) = -0.05802665416439410952930865344351
y[1] (numeric) = -0.058026654164394109529308653443168
absolute error = 3.42e-31
relative error = 5.8938431816366130373373181205633e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (closed_form) = -0.057449279308478858241421061568647
y[1] (numeric) = -0.057449279308478858241421061568306
absolute error = 3.41e-31
relative error = 5.9356706316361446530207545494507e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (closed_form) = -0.056877649428369013844706373088932
y[1] (numeric) = -0.056877649428369013844706373088591
absolute error = 3.41e-31
relative error = 5.9953251132406772572946627935802e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (closed_form) = -0.056311707360600205533436432653193
y[1] (numeric) = -0.056311707360600205533436432652852
absolute error = 3.41e-31
relative error = 6.0555791323526548440388070802763e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (closed_form) = -0.055751396510494036464908666394755
y[1] (numeric) = -0.055751396510494036464908666394414
absolute error = 3.41e-31
relative error = 6.1164387144242004609777506700317e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (closed_form) = -0.055196660846498568757372606584414
y[1] (numeric) = -0.055196660846498568757372606584073
absolute error = 3.41e-31
relative error = 6.1779099454642377501208386643529e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1214.6MB, alloc=52.3MB, time=14.45
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (closed_form) = -0.054647444894585121603126124871106
y[1] (numeric) = -0.054647444894585121603126124870766
absolute error = 3.40e-31
relative error = 6.2216998554252579179411102028612e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (closed_form) = -0.054103693732700822171923333263377
y[1] (numeric) = -0.054103693732700822171923333263037
absolute error = 3.40e-31
relative error = 6.2842289785198260074760062690714e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (closed_form) = -0.053565352985276354555161603984964
y[1] (numeric) = -0.053565352985276354555161603984623
absolute error = 3.41e-31
relative error = 6.3660553136601478444576198756851e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (closed_form) = -0.053032368817788357521165235770362
y[1] (numeric) = -0.053032368817788357521165235770022
absolute error = 3.40e-31
relative error = 6.4111788249208973469460232252782e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (closed_form) = -0.052504687931375927316809944658597
y[1] (numeric) = -0.052504687931375927316809944658258
absolute error = 3.39e-31
relative error = 6.4565663249551330876884432613075e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (closed_form) = -0.051982257557510687161282079114776
y[1] (numeric) = -0.051982257557510687161282079114439
absolute error = 3.37e-31
relative error = 6.4829812292619129642735156504697e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (closed_form) = -0.051465025452719890434480311840354
y[1] (numeric) = -0.051465025452719890434480311840018
absolute error = 3.36e-31
relative error = 6.5287056023838541807723546518650e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (closed_form) = -0.050952939893362029865981219773543
y[1] (numeric) = -0.050952939893362029865981219773206
absolute error = 3.37e-31
relative error = 6.6139461374613082321571210071014e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (closed_form) = -0.050445949670454430281133975316452
y[1] (numeric) = -0.050445949670454430281133975316117
absolute error = 3.35e-31
relative error = 6.6407710071559097395474166227363e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1258.6MB, alloc=52.3MB, time=14.96
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (closed_form) = -0.049944004084552307659248404512019
y[1] (numeric) = -0.049944004084552307659248404511683
absolute error = 3.36e-31
relative error = 6.7275342888241689837922475910279e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (closed_form) = -0.049447052940678782405514765966805
y[1] (numeric) = -0.04944705294067878240551476596647
absolute error = 3.35e-31
relative error = 6.7749234803112879135897766975391e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (closed_form) = -0.048955046543305339833757439474213
y[1] (numeric) = -0.048955046543305339833757439473879
absolute error = 3.34e-31
relative error = 6.8225856900073745849531601528489e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (closed_form) = -0.048467935691382235901887836166041
y[1] (numeric) = -0.048467935691382235901887836165708
absolute error = 3.33e-31
relative error = 6.8705216190836973183539760793506e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (closed_form) = -0.047985671673418351236488733125186
y[1] (numeric) = -0.047985671673418351236488733124851
absolute error = 3.35e-31
relative error = 6.9812506174749066155880051962944e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (closed_form) = -0.047508206262610001427832355579656
y[1] (numeric) = -0.047508206262610001427832355579321
absolute error = 3.35e-31
relative error = 7.0514133526369808490719755185811e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (closed_form) = -0.047035491712018216472302370200866
y[1] (numeric) = -0.04703549171201821647230237020053
absolute error = 3.36e-31
relative error = 7.1435417760105475533270530004294e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (closed_form) = -0.046567480749794007086145084511088
y[1] (numeric) = -0.046567480749794007086145084510752
absolute error = 3.36e-31
relative error = 7.2153355644321881852575498786667e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (closed_form) = -0.046104126574451140413202269518292
y[1] (numeric) = -0.046104126574451140413202269517956
absolute error = 3.36e-31
relative error = 7.2878508924230717156679764837675e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (closed_form) = -0.045645382850185952400257012152537
y[1] (numeric) = -0.045645382850185952400257012152203
absolute error = 3.34e-31
relative error = 7.3172789698408529048455102653508e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1302.7MB, alloc=52.3MB, time=15.48
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (closed_form) = -0.045191203702243728817329962734743
y[1] (numeric) = -0.045191203702243728817329962734409
absolute error = 3.34e-31
relative error = 7.3908188460892225973472848369108e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (closed_form) = -0.044741543712331191557166645081646
y[1] (numeric) = -0.044741543712331191557166645081312
absolute error = 3.34e-31
relative error = 7.4650978103812374472721573977538e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (closed_form) = -0.044296357914074631458722837151075
y[1] (numeric) = -0.044296357914074631458722837150742
absolute error = 3.33e-31
relative error = 7.5175480712420666400664787093907e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (closed_form) = -0.043855601788523233464145468835525
y[1] (numeric) = -0.043855601788523233464145468835192
absolute error = 3.33e-31
relative error = 7.5931006854213147258605729221152e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (closed_form) = -0.043419231259697144438017493467177
y[1] (numeric) = -0.043419231259697144438017493466845
absolute error = 3.32e-31
relative error = 7.6463813468796027025730850606891e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (closed_form) = -0.04298720269017983845193870167105
y[1] (numeric) = -0.042987202690179838451938701670717
absolute error = 3.33e-31
relative error = 7.7464914942249033083506805274516e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (closed_form) = -0.042559472876754338767297894474697
y[1] (numeric) = -0.042559472876754338767297894474363
absolute error = 3.34e-31
relative error = 7.8478415596737399044266895322741e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (closed_form) = -0.042135999046082860134798199089125
y[1] (numeric) = -0.042135999046082860134798199088792
absolute error = 3.33e-31
relative error = 7.9029810029141122723764485920793e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (closed_form) = -0.041716738850429439371365169807746
y[1] (numeric) = -0.041716738850429439371365169807413
absolute error = 3.33e-31
relative error = 7.9824072824564051471784968614820e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1346.8MB, alloc=52.3MB, time=16.00
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (closed_form) = -0.041301650363425126473930878432624
y[1] (numeric) = -0.041301650363425126473930878432289
absolute error = 3.35e-31
relative error = 8.1110560244503170812063084002377e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (closed_form) = -0.040890692075875312785676353468485
y[1] (numeric) = -0.040890692075875312785676353468152
absolute error = 3.33e-31
relative error = 8.1436626062013587966047536237765e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (closed_form) = -0.040483822891608776944055087487307
y[1] (numeric) = -0.040483822891608776944055087486974
absolute error = 3.33e-31
relative error = 8.2255077760707739509802875091132e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (closed_form) = -0.04008100212336803351173327510709
y[1] (numeric) = -0.040081002123368033511733275106756
absolute error = 3.34e-31
relative error = 8.3331249795591127752816586776409e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (closed_form) = -0.039682189488740573321885154718708
y[1] (numeric) = -0.039682189488740573321885154718373
absolute error = 3.35e-31
relative error = 8.4420745003259691315068002726052e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (closed_form) = -0.039287345106130588658487339147276
y[1] (numeric) = -0.039287345106130588658487339146942
absolute error = 3.34e-31
relative error = 8.5014652707566389725473038696385e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (closed_form) = -0.038896429490770780440773257808341
y[1] (numeric) = -0.038896429490770780440773257808007
absolute error = 3.34e-31
relative error = 8.5869064171879952286818787139615e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (closed_form) = -0.038509403550773848589242650711833
y[1] (numeric) = -0.038509403550773848589242650711499
absolute error = 3.34e-31
relative error = 8.6732062614168494845564037880910e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (closed_form) = -0.038126228583223270718972279600075
y[1] (numeric) = -0.038126228583223270718972279599739
absolute error = 3.36e-31
relative error = 8.8128307594486404524884942039095e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (closed_form) = -0.037746866270302978234839492009752
y[1] (numeric) = -0.037746866270302978234839492009415
absolute error = 3.37e-31
relative error = 8.9278934464854330436779003847479e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1391.0MB, alloc=52.3MB, time=16.51
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (closed_form) = -0.037371278675465542793042879942699
y[1] (numeric) = -0.03737127867546554279304287994236
absolute error = 3.39e-31
relative error = 9.0711373015597518193443623195462e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (closed_form) = -0.03699942823963848994437299661867
y[1] (numeric) = -0.036999428239638489944372996618333
absolute error = 3.37e-31
relative error = 9.1082488577205301038246297733667e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (closed_form) = -0.036631277777468360587436042546482
y[1] (numeric) = -0.036631277777468360587436042546146
absolute error = 3.36e-31
relative error = 9.1724892055682321651225238820807e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (closed_form) = -0.036266790473602144634845884059948
y[1] (numeric) = -0.036266790473602144634845884059612
absolute error = 3.36e-31
relative error = 9.2646742546619208275359353058939e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (closed_form) = -0.035905929879005715032652207912938
y[1] (numeric) = -0.035905929879005715032652207912602
absolute error = 3.36e-31
relative error = 9.3577857789016632961692530724956e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (closed_form) = -0.035548659907318893973338772871938
y[1] (numeric) = -0.035548659907318893973338772871603
absolute error = 3.35e-31
relative error = 9.4237026338939128219080101278523e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (closed_form) = -0.035194944831246786805975603183958
y[1] (numeric) = -0.035194944831246786805975603183622
absolute error = 3.36e-31
relative error = 9.5468255913187957628002762648703e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (closed_form) = -0.034844749278987022773908907373465
y[1] (numeric) = -0.034844749278987022773908907373129
absolute error = 3.36e-31
relative error = 9.6427727836349611761704495946023e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (closed_form) = -0.034498038230692545301085182050658
y[1] (numeric) = -0.034498038230692545301085182050322
absolute error = 3.36e-31
relative error = 9.7396842612651608575484934250118e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1435.1MB, alloc=52.3MB, time=17.02
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (closed_form) = -0.034154777014969598103090448554437
y[1] (numeric) = -0.0341547770149695981030904485541
absolute error = 3.37e-31
relative error = 9.8668481967338638443076744094727e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (closed_form) = -0.033814931305410556918597371718443
y[1] (numeric) = -0.033814931305410556918597371718106
absolute error = 3.37e-31
relative error = 9.9660116697051614772807358633207e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (closed_form) = -0.033478467117161260141504088950542
y[1] (numeric) = -0.033478467117161260141504088950205
absolute error = 3.37e-31
relative error = 1.0066171752148467034571010439449e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (closed_form) = -0.033145350803522495083967396166902
y[1] (numeric) = -0.033145350803522495083967396166566
absolute error = 3.36e-31
relative error = 1.0137168316356810875577852910965e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (closed_form) = -0.032815549052585300016124489678115
y[1] (numeric) = -0.03281554905258530001612448967778
absolute error = 3.35e-31
relative error = 1.0208575192911720317206067412654e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (closed_form) = -0.032489028883899745509903311888252
y[1] (numeric) = -0.032489028883899745509903311887918
absolute error = 3.34e-31
relative error = 1.0280393458159562009398628323106e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (closed_form) = -0.032165757645176861962279857041206
y[1] (numeric) = -0.032165757645176861962279857040871
absolute error = 3.35e-31
relative error = 1.0414802091572434269185955620040e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (closed_form) = -0.031845703009023383487986359852932
y[1] (numeric) = -0.031845703009023383487986359852597
absolute error = 3.35e-31
relative error = 1.0519472592741280187921531229804e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (closed_form) = -0.031528832969708981653338582022219
y[1] (numeric) = -0.031528832969708981653338582021883
absolute error = 3.36e-31
relative error = 1.0656912050084718277643620536793e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (closed_form) = -0.031215115839965665771861598480226
y[1] (numeric) = -0.03121511583996566577186159847989
absolute error = 3.36e-31
relative error = 1.0764015796789353647135218303301e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1479.2MB, alloc=52.3MB, time=17.54
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (closed_form) = -0.030904520247819029699076470646538
y[1] (numeric) = -0.030904520247819029699076470646203
absolute error = 3.35e-31
relative error = 1.0839838227990009495198740326541e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (closed_form) = -0.030597015133451028248486648885946
y[1] (numeric) = -0.030597015133451028248486648885611
absolute error = 3.35e-31
relative error = 1.0948780413346661292678301325266e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (closed_form) = -0.030292569746093969503791341104983
y[1] (numeric) = -0.030292569746093969503791341104649
absolute error = 3.34e-31
relative error = 1.1025806090388456886670714939963e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (closed_form) = -0.029991153640955412423968720457457
y[1] (numeric) = -0.029991153640955412423968720457125
absolute error = 3.32e-31
relative error = 1.1069930952793573513073607952563e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (closed_form) = -0.029692736676173662228426886608675
y[1] (numeric) = -0.029692736676173662228426886608343
absolute error = 3.32e-31
relative error = 1.1181185608479352628829302373365e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (closed_form) = -0.029397289009803559109224000018468
y[1] (numeric) = -0.029397289009803559109224000018135
absolute error = 3.33e-31
relative error = 1.1327575134188375248064822558150e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (closed_form) = -0.029104781096832258846716960143819
y[1] (numeric) = -0.029104781096832258846716960143487
absolute error = 3.32e-31
relative error = 1.1407060540858512593769983759424e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (closed_form) = -0.028815183686224706904213334652431
y[1] (numeric) = -0.028815183686224706904213334652099
absolute error = 3.32e-31
relative error = 1.1521703405233361096698919562774e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (closed_form) = -0.028528467817998510546573891712003
y[1] (numeric) = -0.02852846781799851054657389171167
absolute error = 3.33e-31
relative error = 1.1672551155723528373938358019183e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1523.4MB, alloc=52.3MB, time=18.05
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (closed_form) = -0.028244604820327916467539980915243
y[1] (numeric) = -0.02824460482032791646753998091491
absolute error = 3.33e-31
relative error = 1.1789862245137048797264484807965e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (closed_form) = -0.027963566306676604321135135556967
y[1] (numeric) = -0.027963566306676604321135135556635
absolute error = 3.32e-31
relative error = 1.1872591512790391267176509515225e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (closed_form) = -0.027685324172959009434104689735196
y[1] (numeric) = -0.027685324172959009434104689734864
absolute error = 3.32e-31
relative error = 1.1991913041216010301030141937711e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (closed_form) = -0.027409850594729890829299081946433
y[1] (numeric) = -0.027409850594729890829299081946101
absolute error = 3.32e-31
relative error = 1.2112433770939045114522928653678e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (closed_form) = -0.027137118024401863514461149051535
y[1] (numeric) = -0.027137118024401863514461149051204
absolute error = 3.31e-31
relative error = 1.2197315857283104388896602918743e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (closed_form) = -0.026867099188490616787327558519805
y[1] (numeric) = -0.026867099188490616787327558519474
absolute error = 3.31e-31
relative error = 1.2319900919627172137219218243903e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (closed_form) = -0.026599767084887543076579230029926
y[1] (numeric) = -0.026599767084887543076579230029595
absolute error = 3.31e-31
relative error = 1.2443717982329820924452975257146e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (closed_form) = -0.026335094980159504579252024594645
y[1] (numeric) = -0.026335094980159504579252024594312
absolute error = 3.33e-31
relative error = 1.2644723713769689569742234048850e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (closed_form) = -0.02607305640687546766902124030864
y[1] (numeric) = -0.026073056406875467669021240308308
absolute error = 3.32e-31
relative error = 1.2733451530157069183855101463826e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (closed_form) = -0.025813625160959737736572931083345
y[1] (numeric) = -0.025813625160959737736572931083012
absolute error = 3.33e-31
relative error = 1.2900164077055933577648142458067e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1567.5MB, alloc=52.3MB, time=18.57
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (closed_form) = -0.025556775299071529783340440515445
y[1] (numeric) = -0.025556775299071529783340440515112
absolute error = 3.33e-31
relative error = 1.3029812881443528330785433317521e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (closed_form) = -0.025302481136010612723481826091564
y[1] (numeric) = -0.025302481136010612723481826091231
absolute error = 3.33e-31
relative error = 1.3160764677977481031948045752583e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (closed_form) = -0.025050717242148767956366401183318
y[1] (numeric) = -0.025050717242148767956366401182984
absolute error = 3.34e-31
relative error = 1.3332951578649114195343253190371e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (closed_form) = -0.024801458440886805353287185162491
y[1] (numeric) = -0.024801458440886805353287185162157
absolute error = 3.34e-31
relative error = 1.3466949969739660063087167918353e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (closed_form) = -0.024554679806136882357878772473083
y[1] (numeric) = -0.024554679806136882357878772472751
absolute error = 3.32e-31
relative error = 1.3520844198384707495770534746546e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (closed_form) = -0.024310356659829874430052588037247
y[1] (numeric) = -0.024310356659829874430052588036915
absolute error = 3.32e-31
relative error = 1.3656730941697478128857478455390e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (closed_form) = -0.024068464569447547568416724299946
y[1] (numeric) = -0.024068464569447547568416724299613
absolute error = 3.33e-31
relative error = 1.3835531512164237447496725312607e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (closed_form) = -0.023828979345579286126376072142976
y[1] (numeric) = -0.023828979345579286126376072142642
absolute error = 3.34e-31
relative error = 1.4016546624014894793262694831670e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (closed_form) = -0.023591877039503131592658288741304
y[1] (numeric) = -0.023591877039503131592658288740971
absolute error = 3.33e-31
relative error = 1.4115027788692362198618494093800e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
memory used=1611.7MB, alloc=52.3MB, time=19.08
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (closed_form) = -0.023357133940790890438127847222936
y[1] (numeric) = -0.0233571339407908904381278472226
absolute error = 3.36e-31
relative error = 1.4385326592369696482921678156667e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (closed_form) = -0.0231247265749370715376770994238
y[1] (numeric) = -0.023124726574937071537677099423463
absolute error = 3.37e-31
relative error = 1.4573145282731502550699911383636e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (closed_form) = -0.022894631701011416058960648775872
y[1] (numeric) = -0.022894631701011416058960648775535
absolute error = 3.37e-31
relative error = 1.4719607827764809698222653653033e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (closed_form) = -0.022666826309334785069005675152334
y[1] (numeric) = -0.022666826309334785069005675151996
absolute error = 3.38e-31
relative error = 1.4911659682185099810141687945867e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (closed_form) = -0.02244128761917817244552210591857
y[1] (numeric) = -0.022441287619178172445522105918232
absolute error = 3.38e-31
relative error = 1.5061524353493312418324624353527e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (closed_form) = -0.022217993076484612992286268573861
y[1] (numeric) = -0.022217993076484612992286268573524
absolute error = 3.37e-31
relative error = 1.5167886624137925583194454461629e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (closed_form) = -0.021996920351613757947511147117173
y[1] (numeric) = -0.021996920351613757947511147116835
absolute error = 3.38e-31
relative error = 1.5365787328279494296537873782221e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (closed_form) = -0.02177804733710889234087455248789
y[1] (numeric) = -0.021778047337108892340874552487551
absolute error = 3.39e-31
relative error = 1.5566133857297573898000579959443e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (closed_form) = -0.021561352145486170899080084826662
y[1] (numeric) = -0.021561352145486170899080084826322
absolute error = 3.40e-31
relative error = 1.5768955383958995804593910396058e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=1655.8MB, alloc=52.3MB, time=19.60
x[1] = 4.54
y[1] (closed_form) = -0.021346813107045851421699134099529
y[1] (numeric) = -0.021346813107045851421699134099189
absolute error = 3.40e-31
relative error = 1.5927436020310575177719279107891e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (closed_form) = -0.021134408767705306748807525018684
y[1] (numeric) = -0.021134408767705306748807525018343
absolute error = 3.41e-31
relative error = 1.6134825617694555240406242618014e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (closed_form) = -0.020924117886853598619807740544615
y[1] (numeric) = -0.020924117886853598619807740544275
absolute error = 3.40e-31
relative error = 1.6249191571111267466977214627687e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (closed_form) = -0.020715919435227398879034745114834
y[1] (numeric) = -0.020715919435227398879034745114493
absolute error = 3.41e-31
relative error = 1.6460770716270013298160533252040e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (closed_form) = -0.020509792592808045618495896619257
y[1] (numeric) = -0.020509792592808045618495896618916
absolute error = 3.41e-31
relative error = 1.6626204212302707645734673987062e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (closed_form) = -0.02030571674673952396160676205756
y[1] (numeric) = -0.02030571674673952396160676205722
absolute error = 3.40e-31
relative error = 1.6744053127530875461852277366595e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (closed_form) = -0.0201036714892671632842661886631
y[1] (numeric) = -0.02010367148926716328426618866276
absolute error = 3.40e-31
relative error = 1.6912333659128747485027189092886e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (closed_form) = -0.01990363661569684474127497995891
y[1] (numeric) = -0.019903636615696844741274979958569
absolute error = 3.41e-31
relative error = 1.7132547513004385423006234767761e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (closed_form) = -0.019705592122374515017150152549829
y[1] (numeric) = -0.019705592122374515017150152549489
absolute error = 3.40e-31
relative error = 1.7253985462022754605495029198935e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (closed_form) = -0.019509518204685804251026110923004
y[1] (numeric) = -0.019509518204685804251026110922662
absolute error = 3.42e-31
relative error = 1.7529904962894383358210546644731e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
memory used=1700.0MB, alloc=52.3MB, time=20.13
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (closed_form) = -0.019315395255075548095768239755011
y[1] (numeric) = -0.019315395255075548095768239754668
absolute error = 3.43e-31
relative error = 1.7757855610532699286649772572305e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (closed_form) = -0.019123203861087015861854421299449
y[1] (numeric) = -0.019123203861087015861854421299106
absolute error = 3.43e-31
relative error = 1.7936325026475084086294165591792e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (closed_form) = -0.018932924803420648667204884013348
y[1] (numeric) = -0.018932924803420648667204884013003
absolute error = 3.45e-31
relative error = 1.8222224172023763236647847097124e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (closed_form) = -0.018744539054012113465157641806389
y[1] (numeric) = -0.018744539054012113465157641806044
absolute error = 3.45e-31
relative error = 1.8405360569597767997801752884110e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (closed_form) = -0.01855802777412948075439069447478
y[1] (numeric) = -0.018558027774129480754390694474433
absolute error = 3.47e-31
relative error = 1.8698107591137984624261026429699e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (closed_form) = -0.018373372312489335686976291012424
y[1] (numeric) = -0.018373372312489335686976291012078
absolute error = 3.46e-31
relative error = 1.8831600106682964495567203115104e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (closed_form) = -0.018190554203391634184108148582775
y[1] (numeric) = -0.018190554203391634184108148582431
absolute error = 3.44e-31
relative error = 1.8910913661765241807313336478324e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (closed_form) = -0.018009555164873117543558908122057
y[1] (numeric) = -0.018009555164873117543558908121712
absolute error = 3.45e-31
relative error = 1.9156497583733108461273418573307e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (closed_form) = -0.017830357096879100878789746029528
y[1] (numeric) = -0.017830357096879100878789746029183
absolute error = 3.45e-31
relative error = 1.9349023585197087875672331273527e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
memory used=1744.1MB, alloc=52.3MB, time=20.75
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (closed_form) = -0.017652942079453452567032538193552
y[1] (numeric) = -0.01765294207945345256703253819321
absolute error = 3.42e-31
relative error = 1.9373541161620837266655401992646e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (closed_form) = -0.017477292370946583702781029082076
y[1] (numeric) = -0.017477292370946583702781029081732
absolute error = 3.44e-31
relative error = 1.9682682688987292677509539555353e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (closed_form) = -0.017303390406241268354143007914501
y[1] (numeric) = -0.017303390406241268354143007914157
absolute error = 3.44e-31
relative error = 1.9880496938676277198947253947483e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (closed_form) = -0.017131218794996117202600639084614
y[1] (numeric) = -0.017131218794996117202600639084272
absolute error = 3.42e-31
relative error = 1.9963553328727275439187266839797e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (closed_form) = -0.016960760319906528912079146021476
y[1] (numeric) = -0.016960760319906528912079146021134
absolute error = 3.42e-31
relative error = 2.0164190375274683960124503284303e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (closed_form) = -0.016791997934982945321011543333507
y[1] (numeric) = -0.016791997934982945321011543333165
absolute error = 3.42e-31
relative error = 2.0366843857663167940593274361203e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (closed_form) = -0.016624914763846238281483831586441
y[1] (numeric) = -0.016624914763846238281483831586098
absolute error = 3.43e-31
relative error = 2.0631684725741452426932502288221e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (closed_form) = -0.016459494098040057682724053532149
y[1] (numeric) = -0.016459494098040057682724053531805
absolute error = 3.44e-31
relative error = 2.0899791813222399490212276003235e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (closed_form) = -0.016295719395359971892331179358986
y[1] (numeric) = -0.016295719395359971892331179358642
absolute error = 3.44e-31
relative error = 2.1109838212969612293184205694077e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (closed_form) = -0.016133574278199233527895556245215
y[1] (numeric) = -0.016133574278199233527895556244871
absolute error = 3.44e-31
relative error = 2.1321995614129712540070989469706e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
memory used=1788.3MB, alloc=52.3MB, time=21.27
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (closed_form) = -0.01597304253191100513420955114174
y[1] (numeric) = -0.015973042531911005134209551141396
absolute error = 3.44e-31
relative error = 2.1536285232619614664524566250414e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (closed_form) = -0.015814108103186880987271291363368
y[1] (numeric) = -0.015814108103186880987271291363021
absolute error = 3.47e-31
relative error = 2.1942432525174915110833020785319e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (closed_form) = -0.015656755098451542875910667028563
y[1] (numeric) = -0.015656755098451542875910667028217
absolute error = 3.46e-31
relative error = 2.2099087443362992206957912303820e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (closed_form) = -0.015500967782273389325277966639986
y[1] (numeric) = -0.015500967782273389325277966639638
absolute error = 3.48e-31
relative error = 2.2450211166683808795287027147764e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (closed_form) = -0.015346730575790979323793014607349
y[1] (numeric) = -0.015346730575790979323793014607
absolute error = 3.49e-31
relative error = 2.2740999998432065990632878377534e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (closed_form) = -0.015194028055155133196616204361159
y[1] (numeric) = -0.01519402805515513319661620436081
absolute error = 3.49e-31
relative error = 2.2969550848077373788428173936425e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (closed_form) = -0.015042844949986534834430520561019
y[1] (numeric) = -0.01504284494998653483443052056067
absolute error = 3.49e-31
relative error = 2.3200398671948845501421971519827e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (closed_form) = -0.014893166141848681036472092840257
y[1] (numeric) = -0.014893166141848681036472092839907
absolute error = 3.50e-31
relative error = 2.3500711444863709847010259860511e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (closed_form) = -0.014744976662736025261471037686311
y[1] (numeric) = -0.01474497666273602526147103768596
absolute error = 3.51e-31
relative error = 2.3804717228685643258260759246985e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
memory used=1832.4MB, alloc=52.3MB, time=21.78
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (closed_form) = -0.014598261693577164599617798133888
y[1] (numeric) = -0.014598261693577164599617798133538
absolute error = 3.50e-31
relative error = 2.3975457307632073477338157064927e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (closed_form) = -0.014453006562752920283004829557022
y[1] (numeric) = -0.014453006562752920283004829556672
absolute error = 3.50e-31
relative error = 2.4216414659493113860610183920018e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (closed_form) = -0.014309196744629163541359738704192
y[1] (numeric) = -0.014309196744629163541359738703841
absolute error = 3.51e-31
relative error = 2.4529678797780517848135299325848e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (closed_form) = -0.014166817858104240084432800094696
y[1] (numeric) = -0.014166817858104240084432800094345
absolute error = 3.51e-31
relative error = 2.4776206168219186698397966335478e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (closed_form) = -0.014025855665170847952276604894962
y[1] (numeric) = -0.014025855665170847952276604894612
absolute error = 3.50e-31
relative error = 2.4953914281973090220277763864890e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (closed_form) = -0.013886296069492224920004431120137
y[1] (numeric) = -0.013886296069492224920004431119784
absolute error = 3.53e-31
relative error = 2.5420745620967306737053726197700e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (closed_form) = -0.013748125114992503074581296546882
y[1] (numeric) = -0.013748125114992503074581296546529
absolute error = 3.53e-31
relative error = 2.5676228361862161651491668066944e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (closed_form) = -0.013611328984461089597930665007658
y[1] (numeric) = -0.013611328984461089597930665007305
absolute error = 3.53e-31
relative error = 2.5934278746990131073297150259502e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.001
Finished!
diff ( y , x , 1 ) = 2.0 / exp ( x ) ;
Iterations = 4000
Total Elapsed Time = 22 Seconds
Elapsed Time(since restart) = 22 Seconds
Time to Timeout = 2 Minutes 37 Seconds
Percent Done = 100 %
> quit
memory used=1870.8MB, alloc=52.3MB, time=22.21