|\^/| 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(-0.05) * c(x) * c(x) - c(0.2) * c(x) - cos(c(0.3) * c(x) + c(0.1)) / c(0.3));
> end;
exact_soln_y := proc(x)
return
c(-0.05)*c(x)*c(x) - c(0.2)*c(x) - cos(c(0.3)*c(x) + c(0.1))/c(0.3)
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_0D3,
> array_const_0D1,
> array_const_0D2,
#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_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> 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_0D3,
array_const_0D1, array_const_0D2, 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_g, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, 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_0D3,
> array_const_0D1,
> array_const_0D2,
#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_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> 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_0D3,
array_const_0D1, array_const_0D2, 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_g, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, 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_0D3,
> array_const_0D1,
> array_const_0D2,
#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_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> 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_0D3,
array_const_0D1, array_const_0D2, 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_g, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, 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_0D3,
> array_const_0D1,
> array_const_0D2,
#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_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> 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_0D3,
array_const_0D1, array_const_0D2, 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_g, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, 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_0D3,
> array_const_0D1,
> array_const_0D2,
#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_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> 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)*29*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_0D3,
array_const_0D1, array_const_0D2, 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_g, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, 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)*29*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_0D3,
> array_const_0D1,
> array_const_0D2,
#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_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> 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_0D3,
array_const_0D1, array_const_0D2, 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_g, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, 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_0D3,
> array_const_0D1,
> array_const_0D2,
#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_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> 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_0D3,
array_const_0D1, array_const_0D2, 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_g, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, 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_0D3,
> array_const_0D1,
> array_const_0D2,
#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_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D3[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D1[1];
> #emit pre sin 1 $eq_no = 1
> array_tmp3[1] := sin(array_tmp2[1]);
> array_tmp3_g[1] := cos(array_tmp2[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp5[1] := array_const_0D1[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp6[1] := array_tmp5[1] + array_const_0D2[1];
> #emit pre sub FULL - LINEAR $eq_no = 1 i = 1
> array_tmp7[1] := array_tmp4[1] - array_tmp6[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_tmp7[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D3[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre sin ID_LINEAR iii = 2 $eq_no = 1
> array_tmp3[2] := array_tmp3_g[1] * array_tmp2[2] / c(1);
> array_tmp3_g[2] := neg(array_tmp3[1]) * array_tmp2[2] / c(1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[2];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp5[2] := array_const_0D1[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp6[2] := array_tmp5[2];
> #emit pre sub FULL - LINEAR $eq_no = 1 i = 2
> array_tmp7[2] := array_tmp4[2] - array_tmp6[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_tmp7[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sin ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := array_tmp3_g[2] * array_tmp2[2] / c(2);
> array_tmp3_g[3] := neg(array_tmp3[2]) * array_tmp2[2] / c(2);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp3[3];
> #emit pre sub FULL - LINEAR $eq_no = 1 i = 3
> array_tmp7[3] := array_tmp4[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_tmp7[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sin ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := array_tmp3_g[3] * array_tmp2[2] / c(3);
> array_tmp3_g[4] := neg(array_tmp3[3]) * array_tmp2[2] / c(3);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp3[4];
> #emit pre sub FULL - LINEAR $eq_no = 1 i = 4
> array_tmp7[4] := array_tmp4[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_tmp7[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sin ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := array_tmp3_g[4] * array_tmp2[2] / c(4);
> array_tmp3_g[5] := neg(array_tmp3[4]) * array_tmp2[2] / c(4);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp3[5];
> #emit pre sub FULL - LINEAR $eq_no = 1 i = 5
> array_tmp7[5] := array_tmp4[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_tmp7[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit sin LINEAR $eq_no = 1
> array_tmp3[kkk] := array_tmp3_g[kkk - 1] * array_tmp2[2] / c(kkk - 1);
> array_tmp3_g[kkk] := neg(array_tmp3[kkk - 1]) * array_tmp2[2] / c(kkk - 1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp4[kkk] := array_tmp3[kkk];
> #emit FULL - NOT FULL sub $eq_no = 1
> array_tmp7[kkk] := array_tmp4[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_tmp7[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_0D3,
array_const_0D1, array_const_0D2, 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_g, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
array_tmp1[1] := array_const_0D3[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D1[1];
array_tmp3[1] := sin(array_tmp2[1]);
array_tmp3_g[1] := cos(array_tmp2[1]);
array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
array_tmp5[1] := array_const_0D1[1]*array_x[1];
array_tmp6[1] := array_tmp5[1] + array_const_0D2[1];
array_tmp7[1] := array_tmp4[1] - array_tmp6[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp7[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_const_0D3[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp3_g[1]*array_tmp2[2]/c(1);
array_tmp3_g[2] := neg(array_tmp3[1])*array_tmp2[2]/c(1);
array_tmp4[2] := array_tmp3[2];
array_tmp5[2] := array_const_0D1[1]*array_x[2];
array_tmp6[2] := array_tmp5[2];
array_tmp7[2] := array_tmp4[2] - array_tmp6[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp7[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp3[3] := array_tmp3_g[2]*array_tmp2[2]/c(2);
array_tmp3_g[3] := neg(array_tmp3[2])*array_tmp2[2]/c(2);
array_tmp4[3] := array_tmp3[3];
array_tmp7[3] := array_tmp4[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp7[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_tmp3[4] := array_tmp3_g[3]*array_tmp2[2]/c(3);
array_tmp3_g[4] := neg(array_tmp3[3])*array_tmp2[2]/c(3);
array_tmp4[4] := array_tmp3[4];
array_tmp7[4] := array_tmp4[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp7[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_tmp3[5] := array_tmp3_g[4]*array_tmp2[2]/c(4);
array_tmp3_g[5] := neg(array_tmp3[4])*array_tmp2[2]/c(4);
array_tmp4[5] := array_tmp3[5];
array_tmp7[5] := array_tmp4[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp7[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_tmp3[kkk] := array_tmp3_g[kkk - 1]*array_tmp2[2]/c(kkk - 1);
array_tmp3_g[kkk] :=
neg(array_tmp3[kkk - 1])*array_tmp2[2]/c(kkk - 1);
array_tmp4[kkk] := array_tmp3[kkk];
array_tmp7[kkk] := array_tmp4[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_tmp7[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_0D3,
> array_const_0D1,
> array_const_0D2,
> #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_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 40;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=40;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(40),[]);
> array_norms:= Array(0..(40),[]);
> array_fact_1:= Array(0..(40),[]);
> array_1st_rel_error:= Array(0..(2),[]);
> array_last_rel_error:= Array(0..(2),[]);
> array_est_rel_error:= Array(0..(2),[]);
> array_max_est_error:= Array(0..(2),[]);
> array_type_pole:= Array(0..(2),[]);
> array_type_real_pole:= Array(0..(2),[]);
> array_type_complex_pole:= Array(0..(2),[]);
> array_est_digits:= Array(0..(2),[]);
> array_y:= Array(0..(40),[]);
> array_x:= Array(0..(40),[]);
> array_tmp0:= Array(0..(40),[]);
> array_tmp1:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_tmp3_g:= Array(0..(40),[]);
> array_tmp3:= Array(0..(40),[]);
> array_tmp4:= Array(0..(40),[]);
> array_tmp5:= Array(0..(40),[]);
> array_tmp6:= Array(0..(40),[]);
> array_tmp7:= Array(0..(40),[]);
> array_m1:= Array(0..(40),[]);
> array_y_higher := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..40+ 1),[]);
> array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(40) ,(0..40+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 40) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp3_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp6[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp7[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=40) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3_g);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> zero_ats_ar(array_tmp6);
> zero_ats_ar(array_tmp7);
> zero_ats_ar(array_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_0D3);
> array_const_0D3[1] := c(0.3);
> zero_ats_ar(array_const_0D1);
> array_const_0D1[1] := c(0.1);
> zero_ats_ar(array_const_0D2);
> array_const_0D2[1] := c(0.2);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_h := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 1000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> array_y_set_initial[1,31] := false;
> array_y_set_initial[1,32] := false;
> array_y_set_initial[1,33] := false;
> array_y_set_initial[1,34] := false;
> array_y_set_initial[1,35] := false;
> array_y_set_initial[1,36] := false;
> array_y_set_initial[1,37] := false;
> array_y_set_initial[1,38] := false;
> array_y_set_initial[1,39] := false;
> array_y_set_initial[1,40] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 40;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/sub_full_linpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=40;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := c(0.1);");
> 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,"");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=100000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=false;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"return(c(-0.05) * c(x) * c(x) - c(0.2) * c(x) - cos(c(0.3) * c(x) + c(0.1)) / c(0.3));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := c(0.1);
> 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 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2016-08-26T17:01:48-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sub_full_lin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ; ")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 308.maple.seems.ok | ")
> ;
> logitem_str(html_log_file,"sub_full_lin diffeq.mxt")
> ;
> logitem_str(html_log_file,"sub_full_lin 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_0D3,
array_const_0D1, array_const_0D2, 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_g, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
ATS_MAX_TERMS := 40;
Digits := 32;
max_terms := 40;
glob_html_log := true;
array_y_init := Array(0 .. 40, []);
array_norms := Array(0 .. 40, []);
array_fact_1 := Array(0 .. 40, []);
array_1st_rel_error := Array(0 .. 2, []);
array_last_rel_error := Array(0 .. 2, []);
array_est_rel_error := Array(0 .. 2, []);
array_max_est_error := Array(0 .. 2, []);
array_type_pole := Array(0 .. 2, []);
array_type_real_pole := Array(0 .. 2, []);
array_type_complex_pole := Array(0 .. 2, []);
array_est_digits := Array(0 .. 2, []);
array_y := Array(0 .. 40, []);
array_x := Array(0 .. 40, []);
array_tmp0 := Array(0 .. 40, []);
array_tmp1 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_tmp3_g := Array(0 .. 40, []);
array_tmp3 := Array(0 .. 40, []);
array_tmp4 := Array(0 .. 40, []);
array_tmp5 := Array(0 .. 40, []);
array_tmp6 := Array(0 .. 40, []);
array_tmp7 := Array(0 .. 40, []);
array_m1 := Array(0 .. 40, []);
array_y_higher := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 41, []);
array_y_set_initial := Array(0 .. 2, 0 .. 41, []);
array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
array_fact_2 := Array(0 .. 40, 0 .. 41, []);
term := 1;
while term <= 40 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 40 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp3_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp6[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp7[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 40 do
term := 1;
while term <= 40 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3_g);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
zero_ats_ar(array_tmp6);
zero_ats_ar(array_tmp7);
zero_ats_ar(array_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_0D3);
array_const_0D3[1] := c(0.3);
zero_ats_ar(array_const_0D1);
array_const_0D1[1] := c(0.1);
zero_ats_ar(array_const_0D2);
array_const_0D2[1] := c(0.2);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_h := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 1000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
array_y_set_initial[1, 31] := false;
array_y_set_initial[1, 32] := false;
array_y_set_initial[1, 33] := false;
array_y_set_initial[1, 34] := false;
array_y_set_initial[1, 35] := false;
array_y_set_initial[1, 36] := false;
array_y_set_initial[1, 37] := false;
array_y_set_initial[1, 38] := false;
array_y_set_initial[1, 39] := false;
array_y_set_initial[1, 40] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 40;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/sub_full_linpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( 0.3 * x \
+ 0.1 ) - ( 0.1 * x + 0.2 ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=40;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := c(0.1);");
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, "");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=100000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=false;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "return(c(-0.05) * c(x) * c(x) - c(0.2) * c(x) - \
cos(c(0.3) * c(x) + c(0.1)) / c(0.3));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := c(0.1);
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 ) = sin ( 0.3 * \
x + 0.1 ) - ( 0.1 * x + 0.2 ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2016-08-26T17:01:48-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sub_full_lin");
logitem_str(html_log_file, "diff ( y , x , 1 ) = s\
in ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ;\
");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 308.maple.seems.ok | ");
logitem_str(html_log_file, "sub_full_lin diffeq.mxt");
logitem_str(html_log_file, "sub_full_lin 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/sub_full_linpostode.ode#################
diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(0.1);
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(-0.05) * c(x) * c(x) - c(0.2) * c(x) - cos(c(0.3) * c(x) + c(0.1)) / c(0.3));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (closed_form) = -3.3257063123826267986483739038394
y[1] (numeric) = -3.3257063123826267986483739038394
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
memory used=4.0MB, alloc=40.3MB, time=0.09
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (closed_form) = -3.3265000994836904604552861567236
y[1] (numeric) = -3.3265000994836904604552861567236
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (closed_form) = -3.3272741515511600542791827214267
y[1] (numeric) = -3.3272741515511600542791827214267
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (closed_form) = -3.328028480653557921497890021765
y[1] (numeric) = -3.3280284806535579214978900217649
absolute error = 1e-31
relative error = 3.0047819777179914446189806112699e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (closed_form) = -3.328763099126912888504819883098
y[1] (numeric) = -3.328763099126912888504819883098
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (closed_form) = -3.3294780195746492425328001612199
y[1] (numeric) = -3.3294780195746492425328001612199
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (closed_form) = -3.330173254867473300920562735326
y[1] (numeric) = -3.3301732548674733009205627353261
absolute error = 1e-31
relative error = 3.0028467694236999600770245876212e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (closed_form) = -3.330848818143257574842764701004
y[1] (numeric) = -3.3308488181432575748427647010043
absolute error = 3e-31
relative error = 9.0067131947234838775620419486395e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (closed_form) = -3.3315047228069225285460684111671
y[1] (numeric) = -3.3315047228069225285460684111674
absolute error = 3e-31
relative error = 9.0049399583992878637027243414734e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=31.0MB, alloc=40.3MB, time=0.42
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (closed_form) = -3.3321409825303159351554464420811
y[1] (numeric) = -3.3321409825303159351554464420814
absolute error = 3e-31
relative error = 9.0032204991575739701335859785753e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (closed_form) = -3.3327576112520898301365084133945
y[1] (numeric) = -3.3327576112520898301365084133948
absolute error = 3e-31
relative error = 9.0015547181450273192814964049539e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (closed_form) = -3.3333546231775750635212676706652
y[1] (numeric) = -3.3333546231775750635212676706655
absolute error = 3e-31
relative error = 8.9999425177876835325588742208404e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (closed_form) = -3.333932032778653452026376951713
y[1] (numeric) = -3.3339320327786534520263769517132
absolute error = 2e-31
relative error = 5.9989225345218190279098536687192e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (closed_form) = -3.3344898547936275322144631097015
y[1] (numeric) = -3.3344898547936275322144631097018
absolute error = 3e-31
relative error = 8.9968784750903697121222693254074e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (closed_form) = -3.3350281042270879158707815617738
y[1] (numeric) = -3.3350281042270879158707815617741
absolute error = 3e-31
relative error = 8.9954264439257772912848530923519e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (closed_form) = -3.3355467963497782487889911779985
y[1] (numeric) = -3.3355467963497782487889911779989
absolute error = 4e-31
relative error = 1.1992036821001460283915923318513e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (closed_form) = -3.3360459466984577741814196271259
y[1] (numeric) = -3.3360459466984577741814196271266
absolute error = 7e-31
relative error = 2.0982924431624213998661402716664e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (closed_form) = -3.336525571075761501950747559069
y[1] (numeric) = -3.3365255710757615019507475590696
absolute error = 6e-31
relative error = 1.7982778408814897615091800849879e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (closed_form) = -3.3369856855500579850815872350936
y[1] (numeric) = -3.3369856855500579850815872350944
absolute error = 8e-31
relative error = 2.3973731846204505778630713292160e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (closed_form) = -3.3374263064553047044319671215027
y[1] (numeric) = -3.3374263064553047044319671215035
absolute error = 8e-31
relative error = 2.3970566734391314586207740875616e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (closed_form) = -3.3378474503909010632262583472997
y[1] (numeric) = -3.3378474503909010632262583473004
absolute error = 7e-31
relative error = 2.0971599523460000980189850417057e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=71.5MB, alloc=44.3MB, time=0.90
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (closed_form) = -3.3382491342215389925725915972059
y[1] (numeric) = -3.3382491342215389925725915972065
absolute error = 6e-31
relative error = 1.7973493765015733034348375910385e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (closed_form) = -3.3386313750770511693493137748686
y[1] (numeric) = -3.3386313750770511693493137748692
absolute error = 6e-31
relative error = 1.7971435974603599309693322528451e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (closed_form) = -3.3389941903522568478265224336202
y[1] (numeric) = -3.3389941903522568478265224336207
absolute error = 5e-31
relative error = 1.4974569331228787016793710372934e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (closed_form) = -3.3393375977068053064101923403414
y[1] (numeric) = -3.3393375977068053064101923403419
absolute error = 5e-31
relative error = 1.4973029391917747863681109665927e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (closed_form) = -3.3396616150650169109178724185576
y[1] (numeric) = -3.3396616150650169109178724185581
absolute error = 5e-31
relative error = 1.4971576693414968729346594019007e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (closed_form) = -3.3399662606157217958163825166702
y[1] (numeric) = -3.3399662606157217958163825166708
absolute error = 6e-31
relative error = 1.7964253324205442028243664337701e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (closed_form) = -3.3402515528120961648733777731541
y[1] (numeric) = -3.3402515528120961648733777731548
absolute error = 7e-31
relative error = 2.0956505488656472979168661930487e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (closed_form) = -3.3405175103714962126960736096685
y[1] (numeric) = -3.3405175103714962126960736096691
absolute error = 6e-31
relative error = 1.7961288876263800577212924769385e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (closed_form) = -3.3407641522752896686518363825296
y[1] (numeric) = -3.3407641522752896686518363825303
absolute error = 7e-31
relative error = 2.0953289968801058826532484123183e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (closed_form) = -3.340991497768684964686743270149
y[1] (numeric) = -3.3409914977686849646867432701498
absolute error = 8e-31
relative error = 2.3944987604257242456848137331339e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (closed_form) = -3.3411995663605580285795998762834
y[1] (numeric) = -3.3411995663605580285795998762841
absolute error = 7e-31
relative error = 2.0950559405300158477030396116140e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (closed_form) = -3.341388377823276704190275093791
y[1] (numeric) = -3.3413883778232767041902750937918
absolute error = 8e-31
relative error = 2.3942143490699342615127076249658e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=111.9MB, alloc=44.3MB, time=1.38
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (closed_form) = -3.3415579521925228002825698087188
y[1] (numeric) = -3.3415579521925228002825698087195
absolute error = 7e-31
relative error = 2.0948312434345287161713024964251e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (closed_form) = -3.3417083097671117695231788377313
y[1] (numeric) = -3.3417083097671117695231788377321
absolute error = 8e-31
relative error = 2.3939851292878195465682832821997e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (closed_form) = -3.3418394711088100192796338910574
y[1] (numeric) = -3.3418394711088100192796338910583
absolute error = 9e-31
relative error = 2.6931275657636041900849128902517e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (closed_form) = -3.3419514570421498558614291463175
y[1] (numeric) = -3.3419514570421498558614291463184
absolute error = 9e-31
relative error = 2.6930373213636085633529519743813e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (closed_form) = -3.3420442886542420638698300139739
y[1] (numeric) = -3.3420442886542420638698300139747
absolute error = 8e-31
relative error = 2.3937444596885939544785479446141e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (closed_form) = -3.3421179872945861223431496810361
y[1] (numeric) = -3.342117987294586122343149681037
absolute error = 9e-31
relative error = 2.6929031333467127257652002713092e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (closed_form) = -3.3421725745748780594055468444938
y[1] (numeric) = -3.3421725745748780594055468444947
absolute error = 9e-31
relative error = 2.6928591505017641130661364943187e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (closed_form) = -3.342208072368815947148651498314
y[1] (numeric) = -3.3422080723688159471486514983148
absolute error = 8e-31
relative error = 2.3936271550950859332592964138675e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (closed_form) = -3.3422245028119030384965635264639
y[1] (numeric) = -3.3422245028119030384965635264648
absolute error = 9e-31
relative error = 2.6928173114726610434918053223394e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (closed_form) = -3.3422218883012485478259909881449
y[1] (numeric) = -3.3422218883012485478259909881458
absolute error = 9e-31
relative error = 2.6928194179753968689158681733645e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (closed_form) = -3.3422002514953660771345011692623
y[1] (numeric) = -3.3422002514953660771345011692631
absolute error = 8e-31
relative error = 2.3936327562720524526179475256419e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (closed_form) = -3.3421596153139696895710475252506
y[1] (numeric) = -3.3421596153139696895710475252513
absolute error = 7e-31
relative error = 2.0944541271833915352565922461580e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (closed_form) = -3.3421000029377676321641093640055
y[1] (numeric) = -3.3421000029377676321641093640061
absolute error = 6e-31
relative error = 1.7952784161832049245127714884805e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=152.4MB, alloc=44.3MB, time=1.86
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (closed_form) = -3.3420214378082537096039383232972
y[1] (numeric) = -3.3420214378082537096039383232978
absolute error = 6e-31
relative error = 1.7953206200660661557878448998954e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (closed_form) = -3.341923943627496310956546194218
y[1] (numeric) = -3.3419239436274963109565461942185
absolute error = 5e-31
relative error = 1.4961441625666509243266328312195e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (closed_form) = -3.3418075443579250912081922407056
y[1] (numeric) = -3.3418075443579250912081922407061
absolute error = 5e-31
relative error = 1.4961962751091550626310388699704e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (closed_form) = -3.3416722642221153095602346748574
y[1] (numeric) = -3.3416722642221153095602346748579
absolute error = 5e-31
relative error = 1.4962568452726213990058276826591e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (closed_form) = -3.3415181277025698264153001786549
y[1] (numeric) = -3.3415181277025698264153001786556
absolute error = 7e-31
relative error = 2.0948562098068837548792875450240e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (closed_form) = -3.3413451595414987610167971250549
y[1] (numeric) = -3.3413451595414987610167971250555
absolute error = 6e-31
relative error = 1.7956839875899930473307672613218e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (closed_form) = -3.3411533847405968117248522555154
y[1] (numeric) = -3.3411533847405968117248522555159
absolute error = 5e-31
relative error = 1.4964892132266457060995897063174e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (closed_form) = -3.340942828560818240932786827441
y[1] (numeric) = -3.3409428285608182409327868274415
absolute error = 5e-31
relative error = 1.4965835264394080374527331834264e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (closed_form) = -3.3407135165221495266492664644088
y[1] (numeric) = -3.3407135165221495266492664644093
absolute error = 5e-31
relative error = 1.4966862543799478496596254120956e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (closed_form) = -3.3404654744033796827922589352268
y[1] (numeric) = -3.3404654744033796827922589352274
absolute error = 6e-31
relative error = 1.7961568667527161554025244979507e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (closed_form) = -3.3401987282418682502619156658658
y[1] (numeric) = -3.3401987282418682502619156658665
absolute error = 7e-31
relative error = 2.0956836911570492198922278137600e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (closed_form) = -3.3399133043333109608804557622718
y[1] (numeric) = -3.3399133043333109608804557622725
absolute error = 7e-31
relative error = 2.0958627850962403188253487614697e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=193.0MB, alloc=44.3MB, time=2.35
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (closed_form) = -3.3396092292315030763080755033352
y[1] (numeric) = -3.3396092292315030763080755033359
absolute error = 7e-31
relative error = 2.0960536157132404247094982905480e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (closed_form) = -3.3392865297481004040648314633692
y[1] (numeric) = -3.3392865297481004040648314633699
absolute error = 7e-31
relative error = 2.0962561725806877922661156534563e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (closed_form) = -3.3389452329523779928093514540074
y[1] (numeric) = -3.3389452329523779928093514540082
absolute error = 8e-31
relative error = 2.3959662234190652029542329913893e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (closed_form) = -3.3385853661709865090461141483171
y[1] (numeric) = -3.3385853661709865090461141483179
absolute error = 8e-31
relative error = 2.3962244850953671676768263845014e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (closed_form) = -3.3382069569877062974539053771537
y[1] (numeric) = -3.3382069569877062974539053771545
absolute error = 8e-31
relative error = 2.3964961139554241874338768468833e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (closed_form) = -3.3378100332431991270489064815571
y[1] (numeric) = -3.337810033243199127048906481558
absolute error = 9e-31
relative error = 2.6963787364660495180128854550467e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (closed_form) = -3.3373946230347576254166975776839
y[1] (numeric) = -3.3373946230347576254166975776847
absolute error = 8e-31
relative error = 2.3970794297994778099350220991751e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (closed_form) = -3.3369607547160524032682659549249
y[1] (numeric) = -3.3369607547160524032682659549257
absolute error = 8e-31
relative error = 2.3973910956830337191200368452047e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (closed_form) = -3.3365084568968768715958968962261
y[1] (numeric) = -3.336508456896876871595896896227
absolute error = 9e-31
relative error = 2.6974305973647851244913554480150e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (closed_form) = -3.3360377584428897537255907951102
y[1] (numeric) = -3.3360377584428897537255907951111
absolute error = 9e-31
relative error = 2.6978111915018580151806541504728e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (closed_form) = -3.3355486884753552945833963596028
y[1] (numeric) = -3.3355486884753552945833963596036
absolute error = 8e-31
relative error = 2.3984060036781285944733890117958e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (closed_form) = -3.3350412763708811695137747524766
y[1] (numeric) = -3.3350412763708811695137747524773
absolute error = 7e-31
relative error = 2.0989245469301197366390218527536e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=233.5MB, alloc=44.3MB, time=2.84
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (closed_form) = -3.3345155517611540950088135334219
y[1] (numeric) = -3.3345155517611540950088135334225
absolute error = 6e-31
relative error = 1.7993618283864492842250079970282e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (closed_form) = -3.3339715445326731437277920555908
y[1] (numeric) = -3.3339715445326731437277920555912
absolute error = 4e-31
relative error = 1.1997702879496786097843930442925e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (closed_form) = -3.333409284826480766207261340303
y[1] (numeric) = -3.3334092848264807662072613403034
absolute error = 4e-31
relative error = 1.1999726580854646945051710920889e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (closed_form) = -3.3328288030378915216824412235928
y[1] (numeric) = -3.3328288030378915216824412235933
absolute error = 5e-31
relative error = 1.5002270730025115284431067736426e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (closed_form) = -3.3322301298162185204613555509543
y[1] (numeric) = -3.3322301298162185204613555509548
absolute error = 5e-31
relative error = 1.5004966059399275302400420448337e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (closed_form) = -3.3316132960644975803137222065566
y[1] (numeric) = -3.3316132960644975803137222065571
absolute error = 5e-31
relative error = 1.5007744163784858666102673147963e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (closed_form) = -3.3309783329392090993571886149744
y[1] (numeric) = -3.330978332939209099357188614975
absolute error = 6e-31
relative error = 1.8012725993043861037972508299605e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (closed_form) = -3.3303252718499976479440548619566
y[1] (numeric) = -3.3303252718499976479440548619572
absolute error = 6e-31
relative error = 1.8016258203712925824322951016144e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (closed_form) = -3.3296541444593892820721555609705
y[1] (numeric) = -3.3296541444593892820721555609712
absolute error = 7e-31
relative error = 2.1023204502029555288537659585517e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (closed_form) = -3.3289649826825065808640778594523
y[1] (numeric) = -3.3289649826825065808640778594528
absolute error = 5e-31
relative error = 1.5019683373091416692880771584793e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (closed_form) = -3.3282578186867814106793763483029
y[1] (numeric) = -3.3282578186867814106793763483035
absolute error = 6e-31
relative error = 1.8027449575307835346822510128863e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (closed_form) = -3.3275326848916654184449059258564
y[1] (numeric) = -3.3275326848916654184449059258569
absolute error = 5e-31
relative error = 1.5026148421327332957995943479585e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=273.9MB, alloc=44.3MB, time=3.32
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (closed_form) = -3.3267896139683382568088306891525
y[1] (numeric) = -3.326789613968338256808830689153
absolute error = 5e-31
relative error = 1.5029504658203450889088449748795e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (closed_form) = -3.3260286388394135437442804969567
y[1] (numeric) = -3.3260286388394135437442804969572
absolute error = 5e-31
relative error = 1.5032943317483589200822810239893e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (closed_form) = -3.325249792678642559249016786844
y[1] (numeric) = -3.3252497926786425592490167868445
absolute error = 5e-31
relative error = 1.5036464361290189457080460211186e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (closed_form) = -3.3244531089106156818078353493093
y[1] (numeric) = -3.3244531089106156818078353493098
absolute error = 5e-31
relative error = 1.5040067753094106343033481616609e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (closed_form) = -3.3236386212104615673047758819753
y[1] (numeric) = -3.3236386212104615673047758819758
absolute error = 5e-31
relative error = 1.5043753457705974848564788981557e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (closed_form) = -3.3228063635035440730925260834705
y[1] (numeric) = -3.322806363503544073092526083471
absolute error = 5e-31
relative error = 1.5047521441267599307145360289852e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (closed_form) = -3.3219563699651569299467016165777
y[1] (numeric) = -3.321956369965156929946701616578
absolute error = 3e-31
relative error = 9.0308230027460178829873126721220e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (closed_form) = -3.3210886750202161646529522911714
y[1] (numeric) = -3.3210886750202161646529522911718
absolute error = 4e-31
relative error = 1.2044243293129326513531253786326e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (closed_form) = -3.3202033133429502759950891068393
y[1] (numeric) = -3.3202033133429502759950891068398
absolute error = 5e-31
relative error = 1.5059318746856332192168859945893e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (closed_form) = -3.3193003198565881669326461707355
y[1] (numeric) = -3.319300319856588166932646170736
absolute error = 5e-31
relative error = 1.5063415533958154179306135021300e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (closed_form) = -3.318379729733044835776485786148
y[1] (numeric) = -3.3183797297330448357764857861485
absolute error = 5e-31
relative error = 1.5067594450386295046153800121488e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (closed_form) = -3.3174415783926048291912240097545
y[1] (numeric) = -3.317441578392604829191224009755
absolute error = 5e-31
relative error = 1.5071855470089823766467115005241e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (closed_form) = -3.316485901503603459873397519041
y[1] (numeric) = -3.3164859015036034598733975190417
absolute error = 7e-31
relative error = 2.1106677995604903955531594275296e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=314.4MB, alloc=44.3MB, time=3.80
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (closed_form) = -3.3155127349821057917744105346046
y[1] (numeric) = -3.3155127349821057917744105346052
absolute error = 6e-31
relative error = 1.8096748465761458456666869725594e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (closed_form) = -3.3145221149915833957573926239669
y[1] (numeric) = -3.3145221149915833957573926239673
absolute error = 4e-31
relative error = 1.2068104725890951691971487693277e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (closed_form) = -3.3135140779425888785971642932799
y[1] (numeric) = -3.3135140779425888785971642932803
absolute error = 4e-31
relative error = 1.2071776083968415299518325843398e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (closed_form) = -3.3124886604924281882525471703067
y[1] (numeric) = -3.312488660492428188252547170307
absolute error = 3e-31
relative error = 9.0566347766878869089473567352603e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (closed_form) = -3.3114458995448306983602691159434
y[1] (numeric) = -3.3114458995448306983602691159438
absolute error = 4e-31
relative error = 1.2079315565897704573828486479016e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (closed_form) = -3.3103858322496170749197015922115
y[1] (numeric) = -3.3103858322496170749197015922119
absolute error = 4e-31
relative error = 1.2083183661046985485893633577647e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (closed_form) = -3.3093084960023649281576268821809
y[1] (numeric) = -3.3093084960023649281576268821813
absolute error = 4e-31
relative error = 1.2087117308138508110829642036024e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (closed_form) = -3.3082139284440722525821661220729
y[1] (numeric) = -3.3082139284440722525821661220732
absolute error = 3e-31
relative error = 9.0683373714316225429703589931062e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (closed_form) = -3.3071021674608186582549053884098
y[1] (numeric) = -3.3071021674608186582549053884102
absolute error = 4e-31
relative error = 1.2095181211384182441806007821519e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (closed_form) = -3.3059732511834243963301361043887
y[1] (numeric) = -3.3059732511834243963301361043892
absolute error = 5e-31
relative error = 1.5124139308175504617047195149913e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (closed_form) = -3.3048272179871071819299776107393
y[1] (numeric) = -3.3048272179871071819299776107396
absolute error = 3e-31
relative error = 9.0776303937221556244073409419697e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (closed_form) = -3.3036641064911368174439737085169
y[1] (numeric) = -3.3036641064911368174439737085171
absolute error = 2e-31
relative error = 6.0538842192532253069742542942394e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=354.9MB, alloc=44.3MB, time=4.27
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (closed_form) = -3.3024839555584876193615511461702
y[1] (numeric) = -3.3024839555584876193615511461704
absolute error = 2e-31
relative error = 6.0560475899776998004319131439784e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (closed_form) = -3.3012868042954886517654962126398
y[1] (numeric) = -3.30128680429548865176549621264
absolute error = 2e-31
relative error = 6.0582437048416644431567938965995e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (closed_form) = -3.3000726920514717696343456342736
y[1] (numeric) = -3.3000726920514717696343456342737
absolute error = 1e-31
relative error = 3.0302362805782789636284892124929e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (closed_form) = -3.2988416584184174751212996783347
y[1] (numeric) = -3.298841658418417475121299678335
absolute error = 3e-31
relative error = 9.0941012350326240250056149734363e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (closed_form) = -3.2975937432305985899969485624153
y[1] (numeric) = -3.2975937432305985899969485624157
absolute error = 4e-31
relative error = 1.2130056979308996088178440129798e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (closed_form) = -3.2963289865642217474627577800071
y[1] (numeric) = -3.2963289865642217474627577800075
absolute error = 4e-31
relative error = 1.2134711117439821004675153515651e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (closed_form) = -3.2950474287370667065618836009314
y[1] (numeric) = -3.295047428737066706561883600932
absolute error = 6e-31
relative error = 1.8209146088982681757893450051821e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (closed_form) = -3.2937491103081234924334866146632
y[1] (numeric) = -3.2937491103081234924334866146639
absolute error = 7e-31
relative error = 2.1252377657098370547652140461672e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (closed_form) = -3.2924340720772273656762785784231
y[1] (numeric) = -3.2924340720772273656762785784239
absolute error = 8e-31
relative error = 2.4298132703239598603107935578836e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (closed_form) = -3.2911023550846916241065758341615
y[1] (numeric) = -3.2911023550846916241065758341624
absolute error = 9e-31
relative error = 2.7346460331430191529538474963519e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (closed_form) = -3.2897540006109382402156409933645
y[1] (numeric) = -3.2897540006109382402156409933656
absolute error = 1.1e-30
relative error = 3.3437150613563192277089521832899e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (closed_form) = -3.2883890501761263376505732804125
y[1] (numeric) = -3.2883890501761263376505732804137
absolute error = 1.2e-30
relative error = 3.6492032472122722816893952660950e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=395.4MB, alloc=44.3MB, time=4.75
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (closed_form) = -3.287007545539778510062456698693
y[1] (numeric) = -3.2870075455397785100624566986941
absolute error = 1.1e-30
relative error = 3.3465088983218705733007580618726e-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) = -3.2856095287004049856848938637889
y[1] (numeric) = -3.2856095287004049856848938637899
absolute error = 1.0e-30
relative error = 3.0435752978703514056355085984826e-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) = -3.2841950418951256410254417600485
y[1] (numeric) = -3.2841950418951256410254417600496
absolute error = 1.1e-30
relative error = 3.3493747660164890814519231853643e-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) = -3.2827641275992898670718236462092
y[1] (numeric) = -3.2827641275992898670718236462104
absolute error = 1.2e-30
relative error = 3.6554560527550574845359666117275e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (closed_form) = -3.2813168285260942914341186882642
y[1] (numeric) = -3.2813168285260942914341186882655
absolute error = 1.3e-30
relative error = 3.9618240722702035196195241191542e-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) = -3.2798531876261983598634274594928
y[1] (numeric) = -3.2798531876261983598634274594941
absolute error = 1.3e-30
relative error = 3.9635920440112081037706677993404e-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) = -3.2783732480873377806067770448384
y[1] (numeric) = -3.2783732480873377806067770448397
absolute error = 1.3e-30
relative error = 3.9653813084231440133026381226972e-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) = -3.2768770533339358350772639462408
y[1] (numeric) = -3.2768770533339358350772639462421
absolute error = 1.3e-30
relative error = 3.9671918684814973039780080258301e-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) = -3.2753646470267125583376361339824
y[1] (numeric) = -3.2753646470267125583376361339836
absolute error = 1.2e-30
relative error = 3.6637142099256873429991972430618e-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) = -3.2738360730622917929146872537802
y[1] (numeric) = -3.2738360730622917929146872537817
absolute error = 1.5e-30
relative error = 4.5817810254528870068999466831805e-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) = -3.2722913755728061194809760076898
y[1] (numeric) = -3.2722913755728061194809760076912
absolute error = 1.4e-30
relative error = 4.2783476143072180744472948977689e-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) = -3.2707305989254996679594919066284
y[1] (numeric) = -3.2707305989254996679594919066297
absolute error = 1.3e-30
relative error = 3.9746471336620508166780007364504e-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) = -3.2691537877223288126259647715032
y[1] (numeric) = -3.2691537877223288126259647715045
absolute error = 1.3e-30
relative error = 3.9765642255261737812656745783350e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=435.9MB, alloc=44.3MB, time=5.23
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (closed_form) = -3.26756098679956075480255936685
y[1] (numeric) = -3.2675609867995607548025593668514
absolute error = 1.4e-30
relative error = 4.2845413005473584521955773864917e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (closed_form) = -3.2659522412273699967557082141659
y[1] (numeric) = -3.2659522412273699967557082141674
absolute error = 1.5e-30
relative error = 4.5928411967110959697601760115530e-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) = -3.2643275963094327104298147806401
y[1] (numeric) = -3.2643275963094327104298147806415
absolute error = 1.4e-30
relative error = 4.2887852358409280071602131051782e-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) = -3.2626870975825190046675057019428
y[1] (numeric) = -3.2626870975825190046675057019442
absolute error = 1.4e-30
relative error = 4.2909416628929172895936107093774e-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) = -3.2610307908160830945860243046089
y[1] (numeric) = -3.2610307908160830945860243046103
absolute error = 1.4e-30
relative error = 4.2931210706221073341212595088552e-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) = -3.2593587220118513767982382741164
y[1] (numeric) = -3.2593587220118513767982382741178
absolute error = 1.4e-30
relative error = 4.2953234651503617168114177820666e-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) = -3.2576709374034084141855816991013
y[1] (numeric) = -3.2576709374034084141855816991026
absolute error = 1.3e-30
relative error = 3.9905810776461999715435828255239e-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) = -3.255967483455780833949065740627
y[1] (numeric) = -3.2559674834557808339490657406283
absolute error = 1.3e-30
relative error = 3.9926688660300168159137504194239e-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) = -3.2542484068650191426832726587259
y[1] (numeric) = -3.2542484068650191426832726587271
absolute error = 1.2e-30
relative error = 3.6874874009879910838441380740307e-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) = -3.2525137545577774622369947075191
y[1] (numeric) = -3.2525137545577774622369947075203
absolute error = 1.2e-30
relative error = 3.6894540363385979675617445437458e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (closed_form) = -3.2507635736908911901428923163821
y[1] (numeric) = -3.2507635736908911901428923163833
absolute error = 1.2e-30
relative error = 3.6914404040695260817390874007211e-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) = -3.2489979116509525884172248394417
y[1] (numeric) = -3.2489979116509525884172248394429
absolute error = 1.2e-30
relative error = 3.6934465106819028156928378184958e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=476.4MB, alloc=44.3MB, time=5.71
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (closed_form) = -3.2472168160538843045493518110525
y[1] (numeric) = -3.2472168160538843045493518110537
absolute error = 1.2e-30
relative error = 3.6954723628780542881202442542934e-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) = -3.2454203347445108285193129230097
y[1] (numeric) = -3.245420334744510828519312923011
absolute error = 1.3e-30
relative error = 4.0056444648558593522130697038550e-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) = -3.2436085157961278897003706726133
y[1] (numeric) = -3.2436085157961278897003706726144
absolute error = 1.1e-30
relative error = 3.3912847208381753960915325659580e-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) = -3.2417814075100697975219406521301
y[1] (numeric) = -3.2417814075100697975219406521313
absolute error = 1.2e-30
relative error = 3.7016684629630521897194293765536e-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) = -3.2399390584152747297868405928328
y[1] (numeric) = -3.2399390584152747297868405928338
absolute error = 1.0e-30
relative error = 3.0864778070520929417689565033967e-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) = -3.2380815172678479725552603740685
y[1] (numeric) = -3.2380815172678479725552603740694
absolute error = 9e-31
relative error = 2.7794235419971167573925260421605e-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) = -3.2362088330506231155262910935001
y[1] (numeric) = -3.236208833050623115526291093501
absolute error = 9e-31
relative error = 2.7810319000693536209875638405449e-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) = -3.2343210549727212068662518028266
y[1] (numeric) = -3.2343210549727212068662518028274
absolute error = 8e-31
relative error = 2.4734712058656382550578583319761e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (closed_form) = -3.2324182324691078714514174783385
y[1] (numeric) = -3.2324182324691078714514174783392
absolute error = 7e-31
relative error = 2.1655613527006359625486583130494e-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) = -3.2305004152001483965110810523045
y[1] (numeric) = -3.2305004152001483965110810523053
absolute error = 8e-31
relative error = 2.4763965243150582311665565146864e-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) = -3.2285676530511607886751757144625
y[1] (numeric) = -3.2285676530511607886751757144632
absolute error = 7e-31
relative error = 2.1681441283674646406522951973879e-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) = -3.2266199961319668064489410381473
y[1] (numeric) = -3.2266199961319668064489410381479
absolute error = 6e-31
relative error = 1.8595310285043568014495021078474e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=516.9MB, alloc=44.3MB, time=6.19
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (closed_form) = -3.2246574947764409721553376285322
y[1] (numeric) = -3.2246574947764409721553376285328
absolute error = 6e-31
relative error = 1.8606627245588970526772759842258e-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) = -3.2226801995420575674040997670831
y[1] (numeric) = -3.2226801995420575674040997670838
absolute error = 7e-31
relative error = 2.1721050698715619004178171018559e-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) = -3.2206881612094356161644637729721
y[1] (numeric) = -3.2206881612094356161644637729728
absolute error = 7e-31
relative error = 2.1734485456584390085688482625072e-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) = -3.2186814307818818595367213555316
y[1] (numeric) = -3.2186814307818818595367213555323
absolute error = 7e-31
relative error = 2.1748036115209949523015662680150e-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) = -3.2166600594849317263358219288494
y[1] (numeric) = -3.2166600594849317263358219288502
absolute error = 8e-31
relative error = 2.4870517406433682788869734765388e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (closed_form) = -3.2146240987658883036182855376373
y[1] (numeric) = -3.2146240987658883036182855376379
absolute error = 6e-31
relative error = 1.8664701736988261465187583169550e-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) = -3.2125736002933593113016885402071
y[1] (numeric) = -3.2125736002933593113016885402078
absolute error = 7e-31
relative error = 2.1789384060682028047005780845852e-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) = -3.2105086159567920850439473477642
y[1] (numeric) = -3.2105086159567920850439473477649
absolute error = 7e-31
relative error = 2.1803398892028414791545806700414e-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) = -3.2084291978660065715675511675993
y[1] (numeric) = -3.2084291978660065715675511676002
absolute error = 9e-31
relative error = 2.8051109888870505281240470673996e-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) = -3.2063353983507263406317826798036
y[1] (numeric) = -3.2063353983507263406317826798044
absolute error = 8e-31
relative error = 2.4950602498151120274431515448794e-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) = -3.2042272699601076178738157318529
y[1] (numeric) = -3.2042272699601076178738157318537
absolute error = 8e-31
relative error = 2.4967018023348884932103696731249e-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) = -3.202104865462266342757391302154
y[1] (numeric) = -3.2021048654622663427573913021549
absolute error = 9e-31
relative error = 2.8106512366517173796762809886461e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=557.4MB, alloc=44.3MB, time=6.67
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (closed_form) = -3.1999682378438032558855470021118
y[1] (numeric) = -3.1999682378438032558855470021129
absolute error = 1.1e-30
relative error = 3.4375341198423893972730497778125e-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) = -3.1978174403093270199516110964921
y[1] (numeric) = -3.1978174403093270199516110964931
absolute error = 1.0e-30
relative error = 3.1271328606653334504353806128225e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (closed_form) = -3.1956525262809753786203692642011
y[1] (numeric) = -3.1956525262809753786203692642022
absolute error = 1.1e-30
relative error = 3.4421764911974141074396873902946e-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) = -3.1934735493979343576489709368039
y[1] (numeric) = -3.1934735493979343576489709368051
absolute error = 1.2e-30
relative error = 3.7576638147707095549230854095175e-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) = -3.1912805635159555125747618812348
y[1] (numeric) = -3.1912805635159555125747618812359
absolute error = 1.1e-30
relative error = 3.4468921741812886733269517899445e-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) = -3.1890736227068712273148105776266
y[1] (numeric) = -3.1890736227068712273148105776277
absolute error = 1.1e-30
relative error = 3.4492775336629732270352243557488e-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) = -3.186852781258108068039437724791
y[1] (numeric) = -3.1868527812581080680394377247921
absolute error = 1.1e-30
relative error = 3.4516812526424304946242560411831e-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) = -3.1846180936721981966995607267213
y[1] (numeric) = -3.1846180936721981966995607267225
absolute error = 1.2e-30
relative error = 3.7681127366084713798965214557444e-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) = -3.182369614666288848605128116062
y[1] (numeric) = -3.1823696146662888486051281160632
absolute error = 1.2e-30
relative error = 3.7707750679546221376231350249069e-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) = -3.1801073991716498784693423976073
y[1] (numeric) = -3.1801073991716498784693423976086
absolute error = 1.3e-30
relative error = 4.0879122520787262124593896024066e-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) = -3.1778315023331793793507535897631
y[1] (numeric) = -3.1778315023331793793507535897644
absolute error = 1.3e-30
relative error = 4.0908399298248936834781435662366e-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) = -3.1755419795089073789426496480555
y[1] (numeric) = -3.1755419795089073789426496480569
absolute error = 1.4e-30
relative error = 4.4086962447163360108574105936838e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (closed_form) = -3.1732388862694976176764738161271
y[1] (numeric) = -3.1732388862694976176764738161285
absolute error = 1.4e-30
relative error = 4.4118960159531476680209510660684e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=597.9MB, alloc=44.3MB, time=7.15
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (closed_form) = -3.1709222783977474131232626104643
y[1] (numeric) = -3.1709222783977474131232626104658
absolute error = 1.5e-30
relative error = 4.7304849135499567305436441053502e-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) = -3.1685922118880856151943214500028
y[1] (numeric) = -3.1685922118880856151943214500041
absolute error = 1.3e-30
relative error = 4.1027684001828755367485087092291e-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) = -3.1662487429460686566595377357267
y[1] (numeric) = -3.1662487429460686566595377357278
absolute error = 1.1e-30
relative error = 3.4741427136785649514287589163208e-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) = -3.1638919279878747035188733137868
y[1] (numeric) = -3.1638919279878747035188733137879
absolute error = 1.1e-30
relative error = 3.4767306375713084690943238585884e-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) = -3.1615218236397959097796795642219
y[1] (numeric) = -3.1615218236397959097796795642231
absolute error = 1.2e-30
relative error = 3.7956404128770629678006182563083e-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) = -3.1591384867377287812095386921676
y[1] (numeric) = -3.1591384867377287812095386921688
absolute error = 1.2e-30
relative error = 3.7985039435202950185980376039300e-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) = -3.1567419743266626526513540059379
y[1] (numeric) = -3.1567419743266626526513540059391
absolute error = 1.2e-30
relative error = 3.8013876641151883457307867565231e-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) = -3.1543323436601662835043898933892
y[1] (numeric) = -3.1543323436601662835043898933905
absolute error = 1.3e-30
relative error = 4.1213158867449263598093864249476e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (closed_form) = -3.1519096521998725759918987017286
y[1] (numeric) = -3.1519096521998725759918987017299
absolute error = 1.3e-30
relative error = 4.1244837049585673901966657117750e-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) = -3.1494739576149614208528666339729
y[1] (numeric) = -3.1494739576149614208528666339741
absolute error = 1.2e-30
relative error = 3.8101600970491525588575479418515e-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) = -3.147025317781640675112263945555
y[1] (numeric) = -3.1470253177816406751122639455563
absolute error = 1.3e-30
relative error = 4.1308851017327650498435467135675e-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) = -3.1445637907826252766009960054276
y[1] (numeric) = -3.1445637907826252766009960054288
absolute error = 1.2e-30
relative error = 3.8161095777972486880721596558633e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=638.5MB, alloc=44.3MB, time=7.69
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (closed_form) = -3.1420894349066144999135210261274
y[1] (numeric) = -3.1420894349066144999135210261286
absolute error = 1.2e-30
relative error = 3.8191147160509293197906848191732e-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) = -3.1396023086477673585078273157203
y[1] (numeric) = -3.1396023086477673585078273157216
absolute error = 1.3e-30
relative error = 4.1406518157387661440138871689838e-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) = -3.1371024707051761576691476107969
y[1] (numeric) = -3.1371024707051761576691476107982
absolute error = 1.3e-30
relative error = 4.1439513440814651851690176204676e-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) = -3.1345899799823382030754302635724
y[1] (numeric) = -3.1345899799823382030754302635738
absolute error = 1.4e-30
relative error = 4.4662938659935621868052515675899e-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) = -3.1320648955866256697191866278861
y[1] (numeric) = -3.1320648955866256697191866278872
absolute error = 1.1e-30
relative error = 3.5120600519804157569707658327276e-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) = -3.1295272768287536359568907690869
y[1] (numeric) = -3.1295272768287536359568907690879
absolute error = 1.0e-30
relative error = 3.1953707750179151504457169749627e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (closed_form) = -3.1269771832222462874736214624423
y[1] (numeric) = -3.1269771832222462874736214624435
absolute error = 1.2e-30
relative error = 3.8375719734655684169680295510759e-29 %
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) = -3.1244146744829012959671071951678
y[1] (numeric) = -3.124414674482901295967107195169
absolute error = 1.2e-30
relative error = 3.8407193827387944320701420993094e-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) = -3.1218398105282523773717624002295
y[1] (numeric) = -3.1218398105282523773717624002306
absolute error = 1.1e-30
relative error = 3.5235632407861021354695934480438e-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) = -3.1192526514770300344596872778642
y[1] (numeric) = -3.1192526514770300344596872778655
absolute error = 1.3e-30
relative error = 4.1676649673902605066630726653915e-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) = -3.1166532576486204886719441558311
y[1] (numeric) = -3.1166532576486204886719441558324
absolute error = 1.3e-30
relative error = 4.1711409403970512093832554157503e-29 %
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) = -3.1140416895625228060497202546981
y[1] (numeric) = -3.1140416895625228060497202546993
absolute error = 1.2e-30
relative error = 3.8535129572031593563438396347974e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=679.0MB, alloc=44.3MB, time=8.17
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (closed_form) = -3.1114180079378042221512398133014
y[1] (numeric) = -3.1114180079378042221512398133027
absolute error = 1.3e-30
relative error = 4.1781592723428962894655125005640e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (closed_form) = -3.1087822736925536708564976456109
y[1] (numeric) = -3.1087822736925536708564976456124
absolute error = 1.5e-30
relative error = 4.8250403789723361477466460218191e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (closed_form) = -3.1061345479433335219780511977215
y[1] (numeric) = -3.106134547943333521978051197723
absolute error = 1.5e-30
relative error = 4.8291533314073460771148845987340e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (closed_form) = -3.1034748920046295326122289070712
y[1] (numeric) = -3.1034748920046295326122289070727
absolute error = 1.5e-30
relative error = 4.8332918815112566786669277885919e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (closed_form) = -3.100803367388299017181188990184
y[1] (numeric) = -3.1008033673882990171811889901857
absolute error = 1.7e-30
relative error = 5.4824501865523064561406976732563e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (closed_form) = -3.0981200358030172411322945555567
y[1] (numeric) = -3.0981200358030172411322945555584
absolute error = 1.7e-30
relative error = 5.4871986248246462467192275714508e-29 %
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) = -3.0954249591537220432772580104725
y[1] (numeric) = -3.0954249591537220432772580104741
absolute error = 1.6e-30
relative error = 5.1689187142738365616789511915533e-29 %
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) = -3.0927181995410566917694499606439
y[1] (numeric) = -3.0927181995410566917694499606457
absolute error = 1.8e-30
relative error = 5.8201228946986202802445272954003e-29 %
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) = -3.0899998192608109787336650461838
y[1] (numeric) = -3.0899998192608109787336650461855
absolute error = 1.7e-30
relative error = 5.5016184447760699072062855244241e-29 %
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) = -3.0872698808033605585784892734012
y[1] (numeric) = -3.0872698808033605585784892734029
absolute error = 1.7e-30
relative error = 5.5064832866429897314449789232784e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (closed_form) = -3.0845284468531045350372202466516
y[1] (numeric) = -3.0845284468531045350372202466533
absolute error = 1.7e-30
relative error = 5.5113772795137383695069130772531e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (closed_form) = -3.0817755802879013019990531356729
y[1] (numeric) = -3.0817755802879013019990531356745
absolute error = 1.6e-30
relative error = 5.1918121820230889470092457672867e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=719.5MB, alloc=44.3MB, time=8.66
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (closed_form) = -3.07901134417850264320796108966
y[1] (numeric) = -3.0790113441785026432079610896616
absolute error = 1.6e-30
relative error = 5.1964732219162670920411381783327e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (closed_form) = -3.0762358017879860959223689883283
y[1] (numeric) = -3.0762358017879860959223689883301
absolute error = 1.8e-30
relative error = 5.8513069737820307818744373585864e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (closed_form) = -3.0734490165711855836443437613588
y[1] (numeric) = -3.0734490165711855836443437613605
absolute error = 1.7e-30
relative error = 5.5312451608407069487972429471351e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (closed_form) = -3.0706510521741203230426028702832
y[1] (numeric) = -3.0706510521741203230426028702849
absolute error = 1.7e-30
relative error = 5.5362852082992138798957729821547e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (closed_form) = -3.0678419724334220102091747908561
y[1] (numeric) = -3.0678419724334220102091747908577
absolute error = 1.6e-30
relative error = 5.2153924953666205661483645001979e-29 %
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) = -3.0650218413757602914050313194782
y[1] (numeric) = -3.0650218413757602914050313194798
absolute error = 1.6e-30
relative error = 5.2201911855930750083394169860509e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (closed_form) = -3.0621907232172665234654511149086
y[1] (numeric) = -3.0621907232172665234654511149103
absolute error = 1.7e-30
relative error = 5.5515810531027551822596571915609e-29 %
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) = -3.0593486823629558290512669373775
y[1] (numeric) = -3.0593486823629558290512669373792
absolute error = 1.7e-30
relative error = 5.5567383011960810039724814123497e-29 %
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) = -3.0564957834061474519474954227494
y[1] (numeric) = -3.056495783406147451947495422751
absolute error = 1.6e-30
relative error = 5.2347528456818808148675935502338e-29 %
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) = -3.0536320911278834176261477914676
y[1] (numeric) = -3.053632091127883417626147791469
absolute error = 1.4e-30
relative error = 4.5847042414428478551115649677542e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (closed_form) = -3.0507576704963455043052725029433
y[1] (numeric) = -3.0507576704963455043052725029447
absolute error = 1.4e-30
relative error = 4.5890239449016147506068015459482e-29 %
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) = -3.0478725866662705297514863885618
y[1] (numeric) = -3.0478725866662705297514863885632
absolute error = 1.4e-30
relative error = 4.5933678662443845211362451792082e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (closed_form) = -3.0449769049783639590884090937133
y[1] (numeric) = -3.0449769049783639590884090937146
absolute error = 1.3e-30
relative error = 4.2693263054789478998069030582560e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=760.1MB, alloc=44.3MB, time=9.14
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (closed_form) = -3.0420706909587118388885265947898
y[1] (numeric) = -3.0420706909587118388885265947911
absolute error = 1.3e-30
relative error = 4.2734049667672371104549247763780e-29 %
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) = -3.0391540103181910628410729949361
y[1] (numeric) = -3.0391540103181910628410729949375
absolute error = 1.4e-30
relative error = 4.6065450952695347348030101596926e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (closed_form) = -3.0362269289518779743035356069107
y[1] (numeric) = -3.0362269289518779743035356069121
absolute error = 1.4e-30
relative error = 4.6109860453786555520540113075916e-29 %
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) = -3.0332895129384553110593563675796
y[1] (numeric) = -3.0332895129384553110593563675811
absolute error = 1.5e-30
relative error = 4.9451263837552278726585190986961e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (closed_form) = -3.0303418285396174976193227616103
y[1] (numeric) = -3.0303418285396174976193227616118
absolute error = 1.5e-30
relative error = 4.9499366238919656246916242913996e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (closed_form) = -3.0273839421994742904190135275694
y[1] (numeric) = -3.0273839421994742904190135275708
absolute error = 1.4e-30
relative error = 4.6244547329628202716969398324046e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (closed_form) = -3.0244159205439527812794883440211
y[1] (numeric) = -3.0244159205439527812794883440226
absolute error = 1.5e-30
relative error = 4.9596353127588987752361890649621e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (closed_form) = -3.0214378303801977645131863129418
y[1] (numeric) = -3.0214378303801977645131863129432
absolute error = 1.4e-30
relative error = 4.6335555407533679227342835502052e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (closed_form) = -3.018449738695970473071725239846
y[1] (numeric) = -3.0184497386959704730717252398474
absolute error = 1.4e-30
relative error = 4.6381424943150700805399559653604e-29 %
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) = -3.0154517126590456891469723218978
y[1] (numeric) = -3.0154517126590456891469723218991
absolute error = 1.3e-30
relative error = 4.3111285600844565297147576653710e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (closed_form) = -3.0124438196166072346513867648716
y[1] (numeric) = -3.0124438196166072346513867648728
absolute error = 1.2e-30
relative error = 3.9834767778431918367059488536065e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (closed_form) = -3.0094261270946418470182159254384
y[1] (numeric) = -3.0094261270946418470182159254399
absolute error = 1.5e-30
relative error = 4.9843389957145384187995576113993e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=800.5MB, alloc=44.3MB, time=9.62
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (closed_form) = -3.0063987027973314457766586856783
y[1] (numeric) = -3.0063987027973314457766586856798
absolute error = 1.5e-30
relative error = 4.9893581932573053041028538630336e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (closed_form) = -3.0033616146064437953715927811452
y[1] (numeric) = -3.0033616146064437953715927811468
absolute error = 1.6e-30
relative error = 5.3273638186577865966185549551674e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (closed_form) = -3.0003149305807215697118965919177
y[1] (numeric) = -3.0003149305807215697118965919192
absolute error = 1.5e-30
relative error = 4.9994751707937196216535238287476e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (closed_form) = -2.9972587189552698239457803379228
y[1] (numeric) = -2.9972587189552698239457803379243
absolute error = 1.5e-30
relative error = 5.0045729803493334772370100773255e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (closed_form) = -2.9941930481409418789758765659908
y[1] (numeric) = -2.9941930481409418789758765659924
absolute error = 1.6e-30
relative error = 5.3436768246904473300641644516961e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (closed_form) = -2.9911179867237236242411251475458
y[1] (numeric) = -2.9911179867237236242411251475475
absolute error = 1.7e-30
relative error = 5.6834936219352202436262316246458e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (closed_form) = -2.9880336034641162443067235940147
y[1] (numeric) = -2.9880336034641162443067235940165
absolute error = 1.8e-30
relative error = 6.0240286384771792851600758775054e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (closed_form) = -2.9849399672965173748175992138048
y[1] (numeric) = -2.9849399672965173748175992138066
absolute error = 1.8e-30
relative error = 6.0302720313342635369097769154443e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (closed_form) = -2.981837147328600693384995352407
y[1] (numeric) = -2.9818371473286006933849953524089
absolute error = 1.9e-30
relative error = 6.3719106917096119094383782487424e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (closed_form) = -2.978725212840693950989849548586
y[1] (numeric) = -2.9787252128406939509898495485879
absolute error = 1.9e-30
relative error = 6.3785675557096593440102722765973e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (closed_form) = -2.9756042332851554495006767779696
y[1] (numeric) = -2.9756042332851554495006767779714
absolute error = 1.8e-30
relative error = 6.0491915553324325651083593247427e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (closed_form) = -2.9724742782857489709176559143099
y[1] (numeric) = -2.9724742782857489709176559143118
absolute error = 1.9e-30
relative error = 6.3919812994840986548471380361493e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=841.0MB, alloc=44.3MB, time=10.11
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (closed_form) = -2.9693354176370171639685519924143
y[1] (numeric) = -2.9693354176370171639685519924161
absolute error = 1.8e-30
relative error = 6.0619625162873358977588937438962e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (closed_form) = -2.9661877213036533936959906798049
y[1] (numeric) = -2.9661877213036533936959906798068
absolute error = 1.9e-30
relative error = 6.4055285050028495924177818103398e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (closed_form) = -2.963031259419872059689434431623
y[1] (numeric) = -2.9630312594198720596894344316249
absolute error = 1.9e-30
relative error = 6.4123521949343135419344774494380e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (closed_form) = -2.9598661022887773886289919906428
y[1] (numeric) = -2.9598661022887773886289919906447
absolute error = 1.9e-30
relative error = 6.4192092964299496215231192203473e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (closed_form) = -2.9566923203817307068219240774588
y[1] (numeric) = -2.9566923203817307068219240774608
absolute error = 2.0e-30
relative error = 6.7643156043432524028024261013409e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (closed_form) = -2.9535099843377161984263881713874
y[1] (numeric) = -2.9535099843377161984263881713894
absolute error = 2.0e-30
relative error = 6.7716039918804349782801292149251e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (closed_form) = -2.9503191649627051550705940872489
y[1] (numeric) = -2.950319164962705155070594087251
absolute error = 2.1e-30
relative error = 7.1178739742435493436170209566651e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (closed_form) = -2.9471199332290187225891194843154
y[1] (numeric) = -2.9471199332290187225891194843174
absolute error = 2.0e-30
relative error = 6.7862864264526059080778996045676e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (closed_form) = -2.9439123602746891506116603791272
y[1] (numeric) = -2.9439123602746891506116603791293
absolute error = 2.1e-30
relative error = 7.1333645265311302124509626851297e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (closed_form) = -2.9406965174028195507529660518597
y[1] (numeric) = -2.9406965174028195507529660518618
absolute error = 2.1e-30
relative error = 7.1411653245153277379578290745517e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (closed_form) = -2.937472476080942169166130315194
y[1] (numeric) = -2.9374724760809421691661303151961
absolute error = 2.1e-30
relative error = 7.1490031552627028520411324251831e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (closed_form) = -2.9342403079403751792347818344126
y[1] (numeric) = -2.9342403079403751792347818344146
absolute error = 2.0e-30
relative error = 6.8160743160257913031898288565215e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (closed_form) = -2.9310000847755780001930349273582
y[1] (numeric) = -2.9310000847755780001930349273602
absolute error = 2.0e-30
relative error = 6.8236094921612286777305270189624e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=881.7MB, alloc=44.3MB, time=10.59
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (closed_form) = -2.9277518785435051474753289131013
y[1] (numeric) = -2.9277518785435051474753289131032
absolute error = 1.9e-30
relative error = 6.4896209747979393474522632328325e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (closed_form) = -2.9244957613629586206114984992521
y[1] (numeric) = -2.924495761362958620611498499254
absolute error = 1.9e-30
relative error = 6.4968464823984108221191593800887e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (closed_form) = -2.9212318055139388344955797809049
y[1] (numeric) = -2.9212318055139388344955797809069
absolute error = 2.0e-30
relative error = 6.8464268950684505302684562013550e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (closed_form) = -2.9179600834369940998699660507467
y[1] (numeric) = -2.9179600834369940998699660507487
absolute error = 2.0e-30
relative error = 6.8541033558082423136467777052562e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (closed_form) = -2.9146806677325686588795846719229
y[1] (numeric) = -2.914680667732568658879584671925
absolute error = 2.1e-30
relative error = 7.2049059207356082319988628428863e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (closed_form) = -2.9113936311603492815637706253097
y[1] (numeric) = -2.9113936311603492815637706253117
absolute error = 2.0e-30
relative error = 6.8695623243597288121674026058229e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (closed_form) = -2.9080990466386104291664638938584
y[1] (numeric) = -2.9080990466386104291664638938606
absolute error = 2.2e-30
relative error = 7.5650793343607669680469073000140e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (closed_form) = -2.9047969872435579901582564720901
y[1] (numeric) = -2.9047969872435579901582564720922
absolute error = 2.1e-30
relative error = 7.2294208828436852064823709150808e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (closed_form) = -2.9014875262086715948766603725351
y[1] (numeric) = -2.9014875262086715948766603725371
absolute error = 2.0e-30
relative error = 6.8930160200046379084778675447793e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (closed_form) = -2.8981707369240455147037604273318
y[1] (numeric) = -2.8981707369240455147037604273338
absolute error = 2.0e-30
relative error = 6.9009046793519379403624789388133e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (closed_form) = -2.8948466929357281517131548371806
y[1] (numeric) = -2.8948466929357281517131548371826
absolute error = 2.0e-30
relative error = 6.9088287296200673767251335993377e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (closed_form) = -2.8915154679450601247307721867428
y[1] (numeric) = -2.8915154679450601247307721867447
absolute error = 1.9e-30
relative error = 6.5709487673959789122183666370105e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=922.2MB, alloc=44.3MB, time=11.07
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (closed_form) = -2.8881771358080109577667859112155
y[1] (numeric) = -2.8881771358080109577667859112173
absolute error = 1.8e-30
relative error = 6.2323047214914778739473709741442e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (closed_form) = -2.8848317705345143767884258494995
y[1] (numeric) = -2.8848317705345143767884258495014
absolute error = 1.9e-30
relative error = 6.5861726129283428025959408291104e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (closed_form) = -2.8814794462878022208160114419108
y[1] (numeric) = -2.8814794462878022208160114419127
absolute error = 1.9e-30
relative error = 6.5938349914234577003378711987846e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (closed_form) = -2.8781202373837369733370022120385
y[1] (numeric) = -2.8781202373837369733370022120407
absolute error = 2.2e-30
relative error = 7.6438780125455757277691873395153e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (closed_form) = -2.8747542182901429200452783008831
y[1] (numeric) = -2.8747542182901429200452783008853
absolute error = 2.2e-30
relative error = 7.6528281478912803858232742354156e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (closed_form) = -2.8713814636261359389252268850663
y[1] (numeric) = -2.8713814636261359389252268850686
absolute error = 2.3e-30
relative error = 8.0100816597716539619142674940185e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (closed_form) = -2.8680020481614519287125191984192
y[1] (numeric) = -2.8680020481614519287125191984213
absolute error = 2.1e-30
relative error = 7.3221705031424794330919981195352e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (closed_form) = -2.8646160468157738817757174768489
y[1] (numeric) = -2.8646160468157738817757174768509
absolute error = 2.0e-30
relative error = 6.9817384505094265336964960066672e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (closed_form) = -2.8612235346580576074750513497645
y[1] (numeric) = -2.8612235346580576074750513497664
absolute error = 1.9e-30
relative error = 6.6405157688145025864216791465746e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (closed_form) = -2.857824586905856112066848897709
y[1] (numeric) = -2.8578245869058561120668488977109
absolute error = 1.9e-30
relative error = 6.6484136524877296500889250055885e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (closed_form) = -2.8544192789246426412341986758835
y[1] (numeric) = -2.8544192789246426412341986758854
absolute error = 1.9e-30
relative error = 6.6563451768578124824112377502437e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (closed_form) = -2.8510076862271323913364553581433
y[1] (numeric) = -2.8510076862271323913364553581452
absolute error = 1.9e-30
relative error = 6.6643103390379001791600424927051e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=962.8MB, alloc=44.3MB, time=11.65
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (closed_form) = -2.8475898844726028954821831774678
y[1] (numeric) = -2.8475898844726028954821831774697
absolute error = 1.9e-30
relative error = 6.6723091353862413788039149254333e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (closed_form) = -2.8441659494662130905420579190215
y[1] (numeric) = -2.8441659494662130905420579190234
absolute error = 1.9e-30
relative error = 6.6803415614921762480956329933811e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (closed_form) = -2.8407359571583210712301197533899
y[1] (numeric) = -2.840735957158321071230119753392
absolute error = 2.1e-30
relative error = 7.3924505187053607301746534218442e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (closed_form) = -2.8372999836438005373935855735579
y[1] (numeric) = -2.8372999836438005373935855735599
absolute error = 2.0e-30
relative error = 7.0489550330575245915596743252063e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (closed_form) = -2.8338581051613559406631906133399
y[1] (numeric) = -2.8338581051613559406631906133418
absolute error = 1.9e-30
relative error = 6.7046405624173502558776015676129e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (closed_form) = -2.8304103980928363366277348714274
y[1] (numeric) = -2.8304103980928363366277348714292
absolute error = 1.8e-30
relative error = 6.3595017924356873249491069856835e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (closed_form) = -2.8269569389625479487081601386415
y[1] (numeric) = -2.8269569389625479487081601386432
absolute error = 1.7e-30
relative error = 6.0135334096170395051433678772965e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (closed_form) = -2.8234978044365654499180781215028
y[1] (numeric) = -2.8234978044365654499180781215045
absolute error = 1.7e-30
relative error = 6.0209007328739125743767761265766e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (closed_form) = -2.8200330713220419687092091685204
y[1] (numeric) = -2.8200330713220419687092091685221
absolute error = 1.7e-30
relative error = 6.0282980979476020522778376993598e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (closed_form) = -2.8165628165665178251116743327912
y[1] (numeric) = -2.8165628165665178251116743327927
absolute error = 1.5e-30
relative error = 5.3256401425782828800574224370314e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (closed_form) = -2.8130871172572280033905108422517
y[1] (numeric) = -2.8130871172572280033905108422531
absolute error = 1.4e-30
relative error = 4.9767388695910917988037323702881e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (closed_form) = -2.8096060506204083674511523943855
y[1] (numeric) = -2.8096060506204083674511523943868
absolute error = 1.3e-30
relative error = 4.6269832018369197722664537448188e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1003.5MB, alloc=44.3MB, time=12.14
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (closed_form) = -2.8061196940206006252379309430181
y[1] (numeric) = -2.8061196940206006252379309430194
absolute error = 1.3e-30
relative error = 4.6327318209914401562686577125788e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (closed_form) = -2.8026281249599560483809156991947
y[1] (numeric) = -2.802628124959956048380915699196
absolute error = 1.3e-30
relative error = 4.6385033691138541630448223324587e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (closed_form) = -2.7991314210775379533576078246989
y[1] (numeric) = -2.7991314210775379533576078247003
absolute error = 1.4e-30
relative error = 5.0015515150805739649149577058275e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (closed_form) = -2.7956296601486229504471556547098
y[1] (numeric) = -2.7956296601486229504471556547111
absolute error = 1.3e-30
relative error = 4.6501152085032915832610855937375e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (closed_form) = -2.7921229200840009667658451450909
y[1] (numeric) = -2.7921229200840009667658451450921
absolute error = 1.2e-30
relative error = 4.2978050549576020171821179010367e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (closed_form) = -2.7886112789292740496836535000557
y[1] (numeric) = -2.7886112789292740496836535000569
absolute error = 1.2e-30
relative error = 4.3032171929705334615016745754788e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (closed_form) = -2.78509481486415395693263049815
y[1] (numeric) = -2.7850948148641539569326304981511
absolute error = 1.1e-30
relative error = 3.9495962368292072025874713339992e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (closed_form) = -2.7815736062017585397287917998547
y[1] (numeric) = -2.7815736062017585397287917998558
absolute error = 1.1e-30
relative error = 3.9545960514848681935023965850111e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (closed_form) = -2.7780477313879069252400713903567
y[1] (numeric) = -2.7780477313879069252400713903578
absolute error = 1.1e-30
relative error = 3.9596151915303566992310914201279e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (closed_form) = -2.7745172690004135047436861883984
y[1] (numeric) = -2.7745172690004135047436861883995
absolute error = 1.1e-30
relative error = 3.9646536436815959125721574050056e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (closed_form) = -2.7709822977483807338270146393469
y[1] (numeric) = -2.770982297748380733827014639348
absolute error = 1.1e-30
relative error = 3.9697113940201922819652381367722e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (closed_form) = -2.7674428964714907509967827109768
y[1] (numeric) = -2.7674428964714907509967827109777
absolute error = 9e-31
relative error = 3.2520996228955848007078831057294e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1044.3MB, alloc=44.3MB, time=12.62
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (closed_form) = -2.7638991441392958210719850277215
y[1] (numeric) = -2.7638991441392958210719850277225
absolute error = 1.0e-30
relative error = 3.6180770275950477987989350403743e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (closed_form) = -2.7603511198505076097465458175956
y[1] (numeric) = -2.7603511198505076097465458175965
absolute error = 9e-31
relative error = 3.2604547788425601371330150379046e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (closed_form) = -2.7567989028322852957182438104454
y[1] (numeric) = -2.7567989028322852957182438104463
absolute error = 9e-31
relative error = 3.2646559713708398885053277724814e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (closed_form) = -2.7532425724395225267908871219617
y[1] (numeric) = -2.7532425724395225267908871219625
absolute error = 8e-31
relative error = 2.9056647896126222145536942031323e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (closed_form) = -2.7496822081541332263671283908357
y[1] (numeric) = -2.7496822081541332263671283908363
absolute error = 6e-31
relative error = 2.1820703433317158292578423947396e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (closed_form) = -2.7461178895843362567596569129171
y[1] (numeric) = -2.7461178895843362567596569129178
absolute error = 7e-31
relative error = 2.5490529836865630356885814517806e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (closed_form) = -2.7425496964639389457587931431252
y[1] (numeric) = -2.7425496964639389457587931431261
absolute error = 9e-31
relative error = 3.2816178359881686099402579103956e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (closed_form) = -2.7389777086516194829047416205657
y[1] (numeric) = -2.7389777086516194829047416205665
absolute error = 8e-31
relative error = 2.9207977760207281188723182586398e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (closed_form) = -2.7354020061302081919229310227556
y[1] (numeric) = -2.7354020061302081919229310227564
absolute error = 8e-31
relative error = 2.9246158268771815257318833515869e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (closed_form) = -2.7318226690059676857909845794854
y[1] (numeric) = -2.7318226690059676857909845794861
absolute error = 7e-31
relative error = 2.5623917977615656321642314011309e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (closed_form) = -2.7282397775078719109159203846322
y[1] (numeric) = -2.7282397775078719109159203846329
absolute error = 7e-31
relative error = 2.5657568875394796894274737401193e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (closed_form) = -2.7246534119868840869101791446714
y[1] (numeric) = -2.724653411986884086910179144672
absolute error = 6e-31
relative error = 2.2021149455572967194844542261472e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1084.9MB, alloc=44.3MB, time=13.10
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (closed_form) = -2.7210636529152335484650165057321
y[1] (numeric) = -2.7210636529152335484650165057328
absolute error = 7e-31
relative error = 2.5725234293951533968766124279261e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (closed_form) = -2.7174705808856914958296782173495
y[1] (numeric) = -2.7174705808856914958296782173502
absolute error = 7e-31
relative error = 2.5759248505713446457818231167268e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (closed_form) = -2.713874276610845660414598931654
y[1] (numeric) = -2.7138742766108456604145989316547
absolute error = 7e-31
relative error = 2.5793383504639631883515219168241e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (closed_form) = -2.7102748209223738920466293132038
y[1] (numeric) = -2.7102748209223738920466293132044
absolute error = 6e-31
relative error = 2.2137976391479189019567744850377e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (closed_form) = -2.7066722947703166744140012591308
y[1] (numeric) = -2.7066722947703166744140012591314
absolute error = 6e-31
relative error = 2.2167441590889558244186666973609e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (closed_form) = -2.7030667792223485752483873143951
y[1] (numeric) = -2.7030667792223485752483873143956
absolute error = 5e-31
relative error = 1.8497508231884901353003190539165e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (closed_form) = -2.6994583554630486378009977259016
y[1] (numeric) = -2.699458355463048637800997725902
absolute error = 4e-31
relative error = 1.4817787397627270945731593309265e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (closed_form) = -2.6958471047931697201791869257517
y[1] (numeric) = -2.695847104793169720179186925752
absolute error = 3e-31
relative error = 1.1128227541784738721811531046484e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (closed_form) = -2.6922331086289067891195104822109
y[1] (numeric) = -2.6922331086289067891195104822113
absolute error = 4e-31
relative error = 1.4857554448682600161200724360088e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (closed_form) = -2.6886164485011641747825836218671
y[1] (numeric) = -2.6886164485011641747825836218676
absolute error = 5e-31
relative error = 1.8596925577790665639531719079773e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (closed_form) = -2.6849972060548217931644432232215
y[1] (numeric) = -2.6849972060548217931644432232221
absolute error = 6e-31
relative error = 2.2346391968191467355124030646634e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (closed_form) = -2.6813754630480003427284066264593
y[1] (numeric) = -2.6813754630480003427284066264599
absolute error = 6e-31
relative error = 2.2376575316235716861161074069334e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1125.6MB, alloc=44.3MB, time=13.59
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (closed_form) = -2.6777513013513254818706526127476
y[1] (numeric) = -2.6777513013513254818706526127483
absolute error = 7e-31
relative error = 2.6141337309657750801309841703250e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (closed_form) = -2.6741248029471909938419223960331
y[1] (numeric) = -2.6741248029471909938419223960338
absolute error = 7e-31
relative error = 2.6176788728354040922881468430457e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (closed_form) = -2.6704960499290209457568513583932
y[1] (numeric) = -2.670496049929020945756851358394
absolute error = 8e-31
relative error = 2.9956981214080551886438928955368e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (closed_form) = -2.666865124500530848331495464532
y[1] (numeric) = -2.6668651245005308483314954645329
absolute error = 9e-31
relative error = 3.3747488454953577537798546977514e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (closed_form) = -2.6632321089749878229986097305112
y[1] (numeric) = -2.6632321089749878229986097305121
absolute error = 9e-31
relative error = 3.3793524678792932659391731253833e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (closed_form) = -2.6595970857744697830591697153401
y[1] (numeric) = -2.6595970857744697830591697153409
absolute error = 8e-31
relative error = 3.0079744194299320733149955807411e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (closed_form) = -2.6559601374291236355375006712059
y[1] (numeric) = -2.6559601374291236355375006712068
absolute error = 9e-31
relative error = 3.3886050747401972286930684391073e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (closed_form) = -2.6523213465764225104161926490453
y[1] (numeric) = -2.6523213465764225104161926490462
absolute error = 9e-31
relative error = 3.3932539930039276676970597384378e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (closed_form) = -2.6486807959604220239357334315207
y[1] (numeric) = -2.6486807959604220239357334315216
absolute error = 9e-31
relative error = 3.3979179422926894339850840876936e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (closed_form) = -2.6450385684310155826524845764828
y[1] (numeric) = -2.6450385684310155826524845764836
absolute error = 8e-31
relative error = 3.0245305665790126186151315058664e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (closed_form) = -2.6413947469431887349572590224398
y[1] (numeric) = -2.6413947469431887349572590224404
absolute error = 6e-31
relative error = 2.2715271948441746232934741015037e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (closed_form) = -2.6377494145562725767653315557092
y[1] (numeric) = -2.63774941455627257676533155571
absolute error = 8e-31
relative error = 3.0328885510702599555782039970676e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1166.3MB, alloc=44.3MB, time=14.07
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (closed_form) = -2.6341026544331962180972258896467
y[1] (numeric) = -2.6341026544331962180972258896474
absolute error = 7e-31
relative error = 2.6574514809508263259489620130787e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (closed_form) = -2.6304545498397383172780740830206
y[1] (numeric) = -2.6304545498397383172780740830214
absolute error = 8e-31
relative error = 3.0412994592464651286220177630489e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (closed_form) = -2.6268051841437776894917354511536
y[1] (numeric) = -2.6268051841437776894917354511544
absolute error = 8e-31
relative error = 3.0455246732001734542020784961189e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (closed_form) = -2.623154640814542996434192924372
y[1] (numeric) = -2.6231546408145429964341929243728
absolute error = 8e-31
relative error = 3.0497630126433708449865911493820e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (closed_form) = -2.6195030034218615238190149086001
y[1] (numeric) = -2.6195030034218615238190149086008
absolute error = 7e-31
relative error = 2.6722626356434359134356919469117e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (closed_form) = -2.6158503556354070534958800281944
y[1] (numeric) = -2.6158503556354070534958800281949
absolute error = 5e-31
relative error = 1.9114243248771268116938872511928e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (closed_form) = -2.6121967812239468369513106074327
y[1] (numeric) = -2.6121967812239468369513106074331
absolute error = 4e-31
relative error = 1.5312782056663422131935259396835e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (closed_form) = -2.6085423640545876769688483011286
y[1] (numeric) = -2.6085423640545876769688483011288
absolute error = 2e-31
relative error = 7.6671171898902960977772966607996e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (closed_form) = -2.6048871880920211242339318438447
y[1] (numeric) = -2.604887188092021124233931843845
absolute error = 3e-31
relative error = 1.1516813525415600405570693935299e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (closed_form) = -2.6012313373977677956767023788826
y[1] (numeric) = -2.6012313373977677956767023788829
absolute error = 3e-31
relative error = 1.1532999610104475751034854878449e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (closed_form) = -2.5975748961294208213538661809524
y[1] (numeric) = -2.5975748961294208213538661809527
absolute error = 3e-31
relative error = 1.1549233881456979042599254396848e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (closed_form) = -2.593917948539888426678587729025
y[1] (numeric) = -2.5939179485398884266785877290253
absolute error = 3e-31
relative error = 1.1565516178677488246659087749289e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1206.9MB, alloc=44.3MB, time=14.55
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (closed_form) = -2.5902605789766356568151679477611
y[1] (numeric) = -2.5902605789766356568151679477613
absolute error = 2e-31
relative error = 7.7212308917204123069671603587218e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (closed_form) = -2.5866028718809252500629829470542
y[1] (numeric) = -2.5866028718809252500629829470544
absolute error = 2e-31
relative error = 7.7321494603678394753862091256095e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (closed_form) = -2.5829449117870576670618176801359
y[1] (numeric) = -2.5829449117870576670618176801362
absolute error = 3e-31
relative error = 1.1614649566507383017292755219874e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (closed_form) = -2.5792867833216102826583265424381
y[1] (numeric) = -2.5792867833216102826583265424384
absolute error = 3e-31
relative error = 1.1631122290855127245617541701247e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (closed_form) = -2.5756285712026757472808889776155
y[1] (numeric) = -2.5756285712026757472808889776158
absolute error = 3e-31
relative error = 1.1647642185453651506338556741368e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (closed_form) = -2.5719703602390995246776025759664
y[1] (numeric) = -2.5719703602390995246776025759668
absolute error = 4e-31
relative error = 1.5552278758096363731534442775237e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (closed_form) = -2.5683122353297166128795688766971
y[1] (numeric) = -2.5683122353297166128795688766975
absolute error = 4e-31
relative error = 1.5574430339800507776201978658944e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (closed_form) = -2.5646542814625874552589780523246
y[1] (numeric) = -2.564654281462587455258978052325
absolute error = 4e-31
relative error = 1.5596644073675514671592659263088e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (closed_form) = -2.5609965837142330485587877948568
y[1] (numeric) = -2.5609965837142330485587877948572
absolute error = 4e-31
relative error = 1.5618919702730603512688796676742e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (closed_form) = -2.5573392272488692547780189736216
y[1] (numeric) = -2.5573392272488692547780189736221
absolute error = 5e-31
relative error = 1.9551571206213783637461172114997e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (closed_form) = -2.55368229731764032380385592869
y[1] (numeric) = -2.5536822973176403238038559286906
absolute error = 6e-31
relative error = 2.3495483390014230516501779713611e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (closed_form) = -2.5500258792578516336888425372703
y[1] (numeric) = -2.5500258792578516336888425372708
absolute error = 5e-31
relative error = 1.9607644144596595650677433906456e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1247.6MB, alloc=44.3MB, time=15.03
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (closed_form) = -2.5463700584922016554785063793067
y[1] (numeric) = -2.5463700584922016554785063793073
absolute error = 6e-31
relative error = 2.3562953781952723204915778508895e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (closed_form) = -2.5427149205280131495017223694303
y[1] (numeric) = -2.5427149205280131495017223694308
absolute error = 5e-31
relative error = 1.9664021159563234975500322917543e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (closed_form) = -2.5390605509564636000430440525642
y[1] (numeric) = -2.5390605509564636000430440525649
absolute error = 7e-31
relative error = 2.7569251932030929331951555739976e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (closed_form) = -2.5354070354518148953230853176387
y[1] (numeric) = -2.5354070354518148953230853176395
absolute error = 8e-31
relative error = 3.1553119038239093165812389429389e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (closed_form) = -2.5317544597706422597198275063216
y[1] (numeric) = -2.5317544597706422597198275063223
absolute error = 7e-31
relative error = 2.7648810780150247572574369596332e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (closed_form) = -2.5281029097510624451704567202932
y[1] (numeric) = -2.5281029097510624451704567202939
absolute error = 7e-31
relative error = 2.7688746265037434252039236800217e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (closed_form) = -2.5244524713119611887000035008251
y[1] (numeric) = -2.5244524713119611887000035008257
absolute error = 6e-31
relative error = 2.3767530061208846213069472113048e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (closed_form) = -2.5208032304522199430296619082445
y[1] (numeric) = -2.5208032304522199430296619082453
absolute error = 8e-31
relative error = 3.1735916168930165087932021786364e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (closed_form) = -2.5171552732499418872242073068458
y[1] (numeric) = -2.5171552732499418872242073068465
absolute error = 7e-31
relative error = 2.7809170432947432822055190101204e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (closed_form) = -2.5135086858616772243444118040629
y[1] (numeric) = -2.5135086858616772243444118040636
absolute error = 7e-31
relative error = 2.7849515855562960379523344016159e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (closed_form) = -2.5098635545216477730767732429238
y[1] (numeric) = -2.5098635545216477730767732429244
absolute error = 6e-31
relative error = 2.3905682000882847283401750192991e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (closed_form) = -2.506219965540970860319227846222
y[1] (numeric) = -2.5062199655409708603192278462226
absolute error = 6e-31
relative error = 2.3940436523914181434286148428378e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=1288.3MB, alloc=44.3MB, time=15.52
x[1] = 3.97
y[1] (closed_form) = -2.5025780053068825217078080022669
y[1] (numeric) = -2.5025780053068825217078080022676
absolute error = 7e-31
relative error = 2.7971156084469838967403215373490e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (closed_form) = -2.498937760281960017075435208899
y[1] (numeric) = -2.4989377602819600170754352088999
absolute error = 9e-31
relative error = 3.6015302754017020664212298007942e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (closed_form) = -2.4952993170033436678402037986135
y[1] (numeric) = -2.4952993170033436678402037986142
absolute error = 7e-31
relative error = 2.8052746828009571780202513185202e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (closed_form) = -2.4916627620819580233266136976429
y[1] (numeric) = -2.4916627620819580233266136976437
absolute error = 8e-31
relative error = 3.2107073724998972273719451479124e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (closed_form) = -2.488028182201732363029250070779
y[1] (numeric) = -2.4880281822017323630292500707797
absolute error = 7e-31
relative error = 2.8134729542353839192257231677596e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (closed_form) = -2.4843956641188205418343842172076
y[1] (numeric) = -2.4843956641188205418343842172084
absolute error = 8e-31
relative error = 3.2200990025626554513883361484104e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (closed_form) = -2.4807652946608201852208834569065
y[1] (numeric) = -2.4807652946608201852208834569073
absolute error = 8e-31
relative error = 3.2248113181919496764009447148839e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (closed_form) = -2.4771371607259912414676679289857
y[1] (numeric) = -2.4771371607259912414676679289865
absolute error = 8e-31
relative error = 3.2295345315700589692266977596512e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (closed_form) = -2.4735113492824738979007391600876
y[1] (numeric) = -2.4735113492824738979007391600885
absolute error = 9e-31
relative error = 3.6385521346448465378809204298431e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (closed_form) = -2.4698879473675058682185289005279
y[1] (numeric) = -2.4698879473675058682185289005287
absolute error = 8e-31
relative error = 3.2390133360206415840994994035666e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (closed_form) = -2.4662670420866390579399770167267
y[1] (numeric) = -2.4662670420866390579399770167276
absolute error = 9e-31
relative error = 3.6492398618704945967365883054824e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (closed_form) = -2.462648720612955615025344119723
y[1] (numeric) = -2.4626487206129556150253441197239
absolute error = 9e-31
relative error = 3.6546016184394709032219650520369e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=1328.9MB, alloc=44.3MB, time=16.00
x[1] = 4.09
y[1] (closed_form) = -2.4590330701862833727252980508027
y[1] (numeric) = -2.4590330701862833727252980508035
absolute error = 8e-31
relative error = 3.2533112697805085655639697606448e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (closed_form) = -2.4554201781124106917192832867019
y[1] (numeric) = -2.4554201781124106917192832867027
absolute error = 8e-31
relative error = 3.2580981745250425039523747906402e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (closed_form) = -2.451810131762300708609588719247
y[1] (numeric) = -2.4518101317623007086095887192478
absolute error = 8e-31
relative error = 3.2628953997550361393166821434672e-29 %
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) = -2.4482030185713049978428720590002
y[1] (numeric) = -2.4482030185713049978428720590011
absolute error = 9e-31
relative error = 3.6761657149055063186658768721372e-29 %
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) = -2.4445989260383766541361782614116
y[1] (numeric) = -2.4445989260383766541361782614124
absolute error = 8e-31
relative error = 3.2725204592004355704211323951538e-29 %
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) = -2.4409979417252828024897048296182
y[1] (numeric) = -2.440997941725282802489704829619
absolute error = 8e-31
relative error = 3.2773481137577886122925669138471e-29 %
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) = -2.4374001532558165428737185634477
y[1] (numeric) = -2.4374001532558165428737185634485
absolute error = 8e-31
relative error = 3.2821857294600582531513748411781e-29 %
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) = -2.4338056483150083366821162530041
y[1] (numeric) = -2.4338056483150083366821162530049
absolute error = 8e-31
relative error = 3.2870332130006451258567358017838e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (closed_form) = -2.4302145146483368420501459116485
y[1] (numeric) = -2.4302145146483368420501459116495
absolute error = 1.0e-30
relative error = 4.1148630870748649724578047949927e-29 %
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) = -2.4266268400609392051387653620253
y[1] (numeric) = -2.4266268400609392051387653620262
absolute error = 9e-31
relative error = 3.7088520787044395760274759925043e-29 %
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) = -2.4230427124168208144930112853723
y[1] (numeric) = -2.4230427124168208144930112853732
absolute error = 9e-31
relative error = 3.7143381558565718525284478042058e-29 %
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) = -2.4194622196380645255865841746395
y[1] (numeric) = -2.4194622196380645255865841746404
absolute error = 9e-31
relative error = 3.7198348984124001773817623489944e-29 %
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) = -2.4158854497040393626696229524164
y[1] (numeric) = -2.4158854497040393626696229524171
absolute error = 7e-31
relative error = 2.8974883725788995936896793308010e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1369.7MB, alloc=44.3MB, time=16.50
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (closed_form) = -2.4123124906506087050413472824371
y[1] (numeric) = -2.4123124906506087050413472824376
absolute error = 5e-31
relative error = 2.0726999588065323012366561860100e-29 %
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) = -2.4087434305693379648738857761415
y[1] (numeric) = -2.4087434305693379648738857761421
absolute error = 6e-31
relative error = 2.4909253197555464210638424103803e-29 %
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) = -2.4051783576067017637181843316641
y[1] (numeric) = -2.4051783576067017637181843316647
absolute error = 6e-31
relative error = 2.4946174910580700724195136918540e-29 %
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) = -2.4016173599632906148274007005201
y[1] (numeric) = -2.4016173599632906148274007005207
absolute error = 6e-31
relative error = 2.4983163846266133163054226454043e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (closed_form) = -2.3980605258930171184376390165437
y[1] (numeric) = -2.3980605258930171184376390165444
absolute error = 7e-31
relative error = 2.9190255727149589747774645595933e-29 %
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) = -2.3945079437023216771502614022885
y[1] (numeric) = -2.3945079437023216771502614022893
absolute error = 8e-31
relative error = 3.3409786845938051861842600434693e-29 %
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) = -2.3909597017493777385643328506655
y[1] (numeric) = -2.3909597017493777385643328506661
absolute error = 6e-31
relative error = 2.5094525832493201432382491046876e-29 %
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) = -2.3874158884432965723120103252038
y[1] (numeric) = -2.3874158884432965723120103252043
absolute error = 5e-31
relative error = 2.0943146203404999319750389135459e-29 %
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) = -2.3838765922433315886538773926802
y[1] (numeric) = -2.3838765922433315886538773926806
absolute error = 4e-31
relative error = 1.6779392075140206699806318262735e-29 %
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) = -2.3803419016580822057953516592556
y[1] (numeric) = -2.380341901658082205795351659256
absolute error = 4e-31
relative error = 1.6804308646643188044670373677795e-29 %
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) = -2.3768119052446972730893537885603
y[1] (numeric) = -2.3768119052446972730893537885606
absolute error = 3e-31
relative error = 1.2621949567738909217430455913846e-29 %
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) = -2.3732866916080780572944239008123
y[1] (numeric) = -2.3732866916080780572944239008125
absolute error = 2e-31
relative error = 8.4271319056057715878689794399368e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1410.3MB, alloc=44.3MB, time=16.98
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (closed_form) = -2.3697663494000807990614036500826
y[1] (numeric) = -2.3697663494000807990614036500828
absolute error = 2e-31
relative error = 8.4396506031335572158971817575157e-30 %
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) = -2.366250967318718846825670216824
y[1] (numeric) = -2.3662509673187188468256702168244
absolute error = 4e-31
relative error = 1.6904377664270070742896912020217e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (closed_form) = -2.3627406341073643752857117999657
y[1] (numeric) = -2.3627406341073643752857117999659
absolute error = 2e-31
relative error = 8.4647462828927619837028491722540e-30 %
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) = -2.3592354385539496956525729129928
y[1] (numeric) = -2.3592354385539496956525729129929
absolute error = 1e-31
relative error = 4.2386613207748852284671469905000e-30 %
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) = -2.3557354694901681648583718478512
y[1] (numeric) = -2.3557354694901681648583718478513
absolute error = 1e-31
relative error = 4.2449587950400114884613269526704e-30 %
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) = -2.3522408157906747009157020361581
y[1] (numeric) = -2.3522408157906747009157020361581
absolute error = 0
relative error = 0 %
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) = -2.3487515663722859116232736765864
y[1] (numeric) = -2.3487515663722859116232736765864
absolute error = 0
relative error = 0 %
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) = -2.3452678101931798438166318785189
y[1] (numeric) = -2.3452678101931798438166318785188
absolute error = 1e-31
relative error = 4.2639053657485280657119498528088e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (closed_form) = -2.3417896362520953603662026638186
y[1] (numeric) = -2.3417896362520953603662026638184
absolute error = 2e-31
relative error = 8.5404767748519429478526034225860e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (closed_form) = -2.3383171335875311521282684400961
y[1] (numeric) = -2.338317133587531152128268440096
absolute error = 1e-31
relative error = 4.2765798771946885006137599502245e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (closed_form) = -2.3348503912769443920577599800286
y[1] (numeric) = -2.3348503912769443920577599800285
absolute error = 1e-31
relative error = 4.2829296632282023795806961418806e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (closed_form) = -2.331389498435949038694972482518
y[1] (numeric) = -2.3313894984359490386949724825181
absolute error = 1e-31
relative error = 4.2892875715141825720414646358475e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1451.0MB, alloc=44.3MB, time=17.46
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (closed_form) = -2.3279345442175137962414689237959
y[1] (numeric) = -2.3279345442175137962414689237961
absolute error = 2e-31
relative error = 8.5913068516806511343282850364133e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (closed_form) = -2.3244856178111597384435246015749
y[1] (numeric) = -2.324485617811159738443524601575
absolute error = 1e-31
relative error = 4.3020270477803386060467640322838e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (closed_form) = -2.3210428084421576035044925052102
y[1] (numeric) = -2.3210428084421576035044925052104
absolute error = 2e-31
relative error = 8.6168165133600625347082258225897e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (closed_form) = -2.3176062053707247672504298823242
y[1] (numeric) = -2.3176062053707247672504298823246
absolute error = 4e-31
relative error = 1.7259187478574079732011284682352e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (closed_form) = -2.3141758978912219017762220908267
y[1] (numeric) = -2.3141758978912219017762220908271
absolute error = 4e-31
relative error = 1.7284770806078200930480464025645e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (closed_form) = -2.3107519753313493268022704986616
y[1] (numeric) = -2.3107519753313493268022704986622
absolute error = 6e-31
relative error = 2.5965573389327655875923824373779e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (closed_form) = -2.3073345270513430609745767964646
y[1] (numeric) = -2.3073345270513430609745767964651
absolute error = 5e-31
relative error = 2.1670026350230832616400843416762e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (closed_form) = -2.3039236424431705803437565957192
y[1] (numeric) = -2.3039236424431705803437565957195
absolute error = 3e-31
relative error = 1.3021264874988143590802967777504e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (closed_form) = -2.3005194109297262912611505726609
y[1] (numeric) = -2.3005194109297262912611505726613
absolute error = 4e-31
relative error = 1.7387377741722465092103566700278e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (closed_form) = -2.2971219219640267249327716623727
y[1] (numeric) = -2.297121921964026724932771662373
absolute error = 3e-31
relative error = 1.3059820514163289812391868089187e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (closed_form) = -2.2937312650284054608743318851117
y[1] (numeric) = -2.2937312650284054608743318851121
absolute error = 4e-31
relative error = 1.7438834535616203438681647949807e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (closed_form) = -2.2903475296337077865130322753616
y[1] (numeric) = -2.2903475296337077865130322753619
absolute error = 3e-31
relative error = 1.3098448865006028071211061196738e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1491.6MB, alloc=44.3MB, time=17.95
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (closed_form) = -2.2869708053184851001841740614532
y[1] (numeric) = -2.2869708053184851001841740614534
absolute error = 2e-31
relative error = 8.7451925286885271285178229209719e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (closed_form) = -2.2836011816481890647729586884774
y[1] (numeric) = -2.2836011816481890647729586884776
absolute error = 2e-31
relative error = 8.7580967117756528622162307619505e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (closed_form) = -2.2802387482143655192540884688261
y[1] (numeric) = -2.2802387482143655192540884688264
absolute error = 3e-31
relative error = 1.3156517063615698362864038800256e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (closed_form) = -2.276883594633848155383958562862
y[1] (numeric) = -2.2768835946338481553839585628624
absolute error = 4e-31
relative error = 1.7567872197890076506628052567812e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (closed_form) = -2.2735358105479519668023446173072
y[1] (numeric) = -2.2735358105479519668023446173076
absolute error = 4e-31
relative error = 1.7593740909829555341399273191336e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (closed_form) = -2.2701954856216664778025387019458
y[1] (numeric) = -2.2701954856216664778025387019461
absolute error = 3e-31
relative error = 1.3214721018522707056336081078499e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (closed_form) = -2.2668627095428487590308691677129
y[1] (numeric) = -2.2668627095428487590308691677132
absolute error = 3e-31
relative error = 1.3234149502618095415356172093745e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (closed_form) = -2.2635375720214162373784576833481
y[1] (numeric) = -2.2635375720214162373784576833484
absolute error = 3e-31
relative error = 1.3253590473079259300367234777472e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (closed_form) = -2.2602201627885393073299189762699
y[1] (numeric) = -2.2602201627885393073299189762702
absolute error = 3e-31
relative error = 1.3273043260966045510763736598226e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (closed_form) = -2.2569105715958337510354956894998
y[1] (numeric) = -2.2569105715958337510354956895001
absolute error = 3e-31
relative error = 1.3292507189944778534314776983313e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (closed_form) = -2.2536088882145529743748422542616
y[1] (numeric) = -2.2536088882145529743748422542619
absolute error = 3e-31
relative error = 1.3311981576256489612314250503677e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (closed_form) = -2.2503152024347800662823277517938
y[1] (numeric) = -2.2503152024347800662823277517942
absolute error = 4e-31
relative error = 1.7775287638247781460108177528112e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1532.2MB, alloc=44.3MB, time=18.43
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (closed_form) = -2.247029604064619688605318383054
y[1] (numeric) = -2.2470296040646196886053183830544
absolute error = 4e-31
relative error = 1.7801278598040974862126504327058e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (closed_form) = -2.2437521829293898037684253670284
y[1] (numeric) = -2.2437521829293898037684253670288
absolute error = 4e-31
relative error = 1.7827280706096938776296610840285e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (closed_form) = -2.2404830288708132475181638335818
y[1] (numeric) = -2.2404830288708132475181638335821
absolute error = 3e-31
relative error = 1.3389969758048011846320582063716e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (closed_form) = -2.2372222317462091540238625520325
y[1] (numeric) = -2.2372222317462091540238625520326
absolute error = 1e-31
relative error = 4.4698286375398407856022065640029e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (closed_form) = -2.2339698814276842406119931293884
y[1] (numeric) = -2.2339698814276842406119931293886
absolute error = 2e-31
relative error = 8.9526721762329271076057540837933e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (closed_form) = -2.2307260678013239594123506104535
y[1] (numeric) = -2.2307260678013239594123506104538
absolute error = 3e-31
relative error = 1.3448536076672549065048834333477e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (closed_form) = -2.227490880766383523195715204455
y[1] (numeric) = -2.2274908807663835231957152044553
absolute error = 3e-31
relative error = 1.3468068605371032599502335791171e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (closed_form) = -2.2242644102344788126837571386614
y[1] (numeric) = -2.2242644102344788126837571386618
absolute error = 4e-31
relative error = 1.7983473464732215219889139851711e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (closed_form) = -2.221046746128777172613013388475
y[1] (numeric) = -2.2210467461287771726130133884753
absolute error = 3e-31
relative error = 1.3507144796609601877788681031993e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (closed_form) = -2.2178379783831881038357662460808
y[1] (numeric) = -2.2178379783831881038357662460811
absolute error = 3e-31
relative error = 1.3526686932230328361370779338724e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (closed_form) = -2.2146381969415538587415893569213
y[1] (numeric) = -2.2146381969415538587415893569216
absolute error = 3e-31
relative error = 1.3546230730342507912042763972088e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (closed_form) = -2.2114474917568399472841969666007
y[1] (numeric) = -2.2114474917568399472841969666011
absolute error = 4e-31
relative error = 1.8087700544145773558263686556807e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1572.7MB, alloc=44.3MB, time=18.91
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (closed_form) = -2.2082659527903255608990366724942
y[1] (numeric) = -2.2082659527903255608990366724945
absolute error = 3e-31
relative error = 1.3585320174905805101492852519920e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (closed_form) = -2.2050936700107939215978049570901
y[1] (numeric) = -2.2050936700107939215978049570904
absolute error = 3e-31
relative error = 1.3604864232299551321158968143107e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (closed_form) = -2.2019307333937225635267381872835
y[1] (numeric) = -2.2019307333937225635267381872839
absolute error = 4e-31
relative error = 1.8165875698710130520348103602907e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (closed_form) = -2.1987772329204735542761395894042
y[1] (numeric) = -2.1987772329204735542761395894046
absolute error = 4e-31
relative error = 1.8191929314672296990831900042197e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (closed_form) = -2.1956332585774836632291449482316
y[1] (numeric) = -2.1956332585774836632291449482319
absolute error = 3e-31
relative error = 1.3663484046254850991374338561572e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (closed_form) = -2.1924989003554544842382064247431
y[1] (numeric) = -2.1924989003554544842382064247434
absolute error = 3e-31
relative error = 1.3683017124951036556975231862758e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (closed_form) = -2.1893742482485425199181849375727
y[1] (numeric) = -2.189374248248542519918184937573
absolute error = 3e-31
relative error = 1.3702545384371550734013658120955e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (closed_form) = -2.1862593922535492348452870034167
y[1] (numeric) = -2.186259392253549234845287003417
absolute error = 3e-31
relative error = 1.3722067978894601434126742412220e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (closed_form) = -2.1831544223691110849513617788178
y[1] (numeric) = -2.1831544223691110849513617788182
absolute error = 4e-31
relative error = 1.8322112073314942690764124470278e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (closed_form) = -2.1800594285948895304032882873528
y[1] (numeric) = -2.1800594285948895304032882873532
absolute error = 4e-31
relative error = 1.8348123668252998343131182992805e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (closed_form) = -2.1769745009307610392573314503282
y[1] (numeric) = -2.1769745009307610392573314503285
absolute error = 3e-31
relative error = 1.3780593198116726104664231544049e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (closed_form) = -2.1738997293760070891784285643056
y[1] (numeric) = -2.1738997293760070891784285643059
absolute error = 3e-31
relative error = 1.3800084518438739080318250329778e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=1613.2MB, alloc=44.3MB, time=19.39
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (closed_form) = -2.1708352039285041745143852843921
y[1] (numeric) = -2.1708352039285041745143852843924
absolute error = 3e-31
relative error = 1.3819565826880722202736872945665e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (closed_form) = -2.1677810145839138260149119780801
y[1] (numeric) = -2.1677810145839138260149119780803
absolute error = 2e-31
relative error = 9.2260241534769696703494023529432e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (closed_form) = -2.1647372513348726504853175109455
y[1] (numeric) = -2.1647372513348726504853175109457
absolute error = 2e-31
relative error = 9.2389965515062468599670227656823e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (closed_form) = -2.161704004170182397664498113729
y[1] (numeric) = -2.1617040041701823976644981137291
absolute error = 1e-31
relative error = 4.6259802362898984535718163721004e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (closed_form) = -2.1586813630740000616166139618532
y[1] (numeric) = -2.1586813630740000616166139618533
absolute error = 1e-31
relative error = 4.6324576526476445279190189715421e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (closed_form) = -2.1556694180250280239255354754732
y[1] (numeric) = -2.1556694180250280239255354754735
absolute error = 3e-31
relative error = 1.3916790649414728687615393810398e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
Finished!
diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ;
Iterations = 4900
Total Elapsed Time = 19 Seconds
Elapsed Time(since restart) = 19 Seconds
Time to Timeout = 2 Minutes 40 Seconds
Percent Done = 100 %
> quit
memory used=1636.8MB, alloc=44.3MB, time=19.65