|\^/| 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_y1 := proc(x)
> return(neg(cos(c(x))));
> end;
exact_soln_y1 := proc(x) return neg(cos(c(x))) end proc
> exact_soln_y2 := proc(x)
> return(neg(sin(c(x))));
> end;
exact_soln_y2 := proc(x) return neg(sin(c(x))) end proc
> exact_soln_y2p := proc(x)
> return(neg(cos(c(x))));
> end;
exact_soln_y2p := proc(x) return neg(cos(c(x))) end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]);
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if (rad_given < glob_least_given_sing) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 3
> rad_given := sqrt((array_x[1] - array_given_rad_poles[2,1]) * (array_x[1] - array_given_rad_poles[2,1]) + array_given_rad_poles[2,2] * array_given_rad_poles[2,2]);
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 2 ",4,rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[2,1],4," ");
> if (rad_given < glob_least_given_sing) then # if number 4
> glob_least_given_sing := rad_given;
> fi;# end if 4;
> elif
> (glob_type_given_pole = 3) then # if number 4
> omniout_str(ALWAYS,"NO POLE (given) for Equation 2");
> elif
> (glob_type_given_pole = 5) then # if number 5
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 2");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 2");
> fi;# end if 5;
> if (array_rad_test_poles[2,1] < glob_large_float) then # if number 5
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 2 ",4,array_rad_test_poles[2,1],4," ");
> if (array_rad_test_poles[2,1]< glob_least_ratio_sing) then # if number 6
> glob_least_ratio_sing := array_rad_test_poles[2,1];
> fi;# end if 6;
> omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[2,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 2");
> fi;# end if 5;
> if ((array_rad_test_poles[2,2] > glob__small) and (array_rad_test_poles[2,2] < glob_large_float)) then # if number 5
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 2 ",4,array_rad_test_poles[2,2],4," ");
> if (array_rad_test_poles[2,2]< glob_least_3_sing) then # if number 6
> glob_least_3_sing := array_rad_test_poles[2,2];
> fi;# end if 6;
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[2,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 2");
> fi;# end if 5;
> if ((array_rad_test_poles[2,3] > glob__small) and (array_rad_test_poles[2,3] < glob_large_float)) then # if number 5
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 2 ",4,array_rad_test_poles[2,3],4," ");
> if (array_rad_test_poles[2,3]< glob_least_6_sing) then # if number 6
> glob_least_6_sing := array_rad_test_poles[2,3];
> fi;# end if 6;
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[2,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 2");
> fi;# end if 5
> ;
> 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;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := sqrt((array_x[1] - array_given_rad_poles[2, 1])*
(array_x[1] - array_given_rad_poles[2, 1])
+ array_given_rad_poles[2, 2]*array_given_rad_poles[2, 2]);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 2 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[2, 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 2")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 2")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 2")
end if;
if array_rad_test_poles[2, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 2 ", 4,
array_rad_test_poles[2, 1], 4, " ");
if array_rad_test_poles[2, 1] < glob_least_ratio_sing then
glob_least_ratio_sing := array_rad_test_poles[2, 1]
end if;
omniout_float(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[2, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 2")
end if;
if glob__small < array_rad_test_poles[2, 2] and
array_rad_test_poles[2, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 2 ", 4,
array_rad_test_poles[2, 2], 4, " ");
if array_rad_test_poles[2, 2] < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[2, 2]
end if;
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[2, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 2")
end if;
if glob__small < array_rad_test_poles[2, 3] and
array_rad_test_poles[2, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 2 ", 4,
array_rad_test_poles[2, 3], 4, " ");
if array_rad_test_poles[2, 3] < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[2, 3]
end if;
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[2, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 2")
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 5
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 5;
> 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_2,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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_y1[1]) < min_size) then # if number 5
> min_size := float_abs(array_y1[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 5;
> if (float_abs(array_y2[1]) < min_size) then # if number 5
> min_size := float_abs(array_y2[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 5;
> if (min_size < glob__1) then # if number 5
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 5;
> 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_2,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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_y1[1]) < min_size then
min_size := float_abs(array_y1[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if float_abs(array_y2[1]) < min_size then
min_size := float_abs(array_y2[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_2,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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_y1[no_terms-3] + array_y1[no_terms - 2] * hn_div_ho + array_y1[no_terms - 1] * hn_div_ho_2 + array_y1[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 5
> max_estimated_step_error := est_tmp;
> fi;# end if 5;
> est_tmp := float_abs(array_y2[no_terms-3] + array_y2[no_terms - 2] * hn_div_ho + array_y2[no_terms - 1] * hn_div_ho_2 + array_y2[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 5
> max_estimated_step_error := est_tmp;
> fi;# end if 5;
> 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_2,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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_y1[no_terms - 3]
+ array_y1[no_terms - 2]*hn_div_ho
+ array_y1[no_terms - 1]*hn_div_ho_2
+ array_y1[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
est_tmp := float_abs(array_y2[no_terms - 3]
+ array_y2[no_terms - 2]*hn_div_ho
+ array_y2[no_terms - 1]*hn_div_ho_2
+ array_y2[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_2,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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_y1[no_terms-3])) + c(float_abs(array_y1[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y1[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y1[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y1[1])) > c(est_tmp)) then # if number 5
> est_tmp := c(glob_prec) * c(float_abs(array_y1[1]));
> fi;# end if 5;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 5
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 5
> ;
> est_tmp := c(float_abs(array_y2[no_terms-3])) + c(float_abs(array_y2[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y2[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y2[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y2[1])) > c(est_tmp)) then # if number 5
> est_tmp := c(glob_prec) * c(float_abs(array_y2[1]));
> fi;# end if 5;
> if (c(est_tmp) >= c(array_max_est_error[2])) then # if number 5
> array_max_est_error[2] := c(est_tmp);
> fi;# end if 5
> ;
> 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_2,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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_y1[no_terms - 3]))
+ c(float_abs(array_y1[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y1[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y1[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y1[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y1[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if;
est_tmp := c(float_abs(array_y2[no_terms - 3]))
+ c(float_abs(array_y2[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y2[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y2[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y2[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y2[1]))
end if;
if c(array_max_est_error[2]) <= c(est_tmp) then
array_max_est_error[2] := 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_2,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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 5
> ret := true;
> else
> ret := false;
> fi;# end if 5;
> 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_2,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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_2,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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 5
> if (iter >= 0) then # if number 6
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> closed_form_val_y := evalf(exact_soln_y1(ind_var));
> omniout_float(ALWAYS,"y1[1] (closed_form) ",33,closed_form_val_y,20," ");
> term_no := 1;
> numeric_val := array_y1[term_no];
> abserr := float_abs(numeric_val - closed_form_val_y);
> omniout_float(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," ");
> if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 7
> relerr := abserr*glob__100/float_abs(closed_form_val_y);
> if (c(relerr) > c(glob_prec)) then # if number 8
> glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 8;
> else
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 7;
> if (glob_good_digits < glob_min_good_digits) then # if number 7
> glob_min_good_digits := glob_good_digits;
> fi;# end if 7;
> if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 7
> glob_min_apfp_est_good_digits := glob_apfp_est_good_digits;
> fi;# end if 7;
> if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 7
> est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*36*ATS_MAX_TERMS/float_abs(numeric_val));
> if (evalf(est_rel_err) > glob_prec) then # if number 8
> glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
> else
> glob_est_digits := Digits;
> fi;# end if 8;
> else
> relerr := glob__m1 ;
> glob_est_digits := -16;
> fi;# end if 7;
> array_est_digits[1] := glob_est_digits;
> if (glob_iter = 1) then # if number 7
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 7;
> 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," ");
> ;
> closed_form_val_y := evalf(exact_soln_y2(ind_var));
> omniout_float(ALWAYS,"y2[1] (closed_form) ",33,closed_form_val_y,20," ");
> term_no := 1;
> numeric_val := array_y2[term_no];
> abserr := float_abs(numeric_val - closed_form_val_y);
> omniout_float(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," ");
> if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 7
> relerr := abserr*glob__100/float_abs(closed_form_val_y);
> if (c(relerr) > c(glob_prec)) then # if number 8
> glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 8;
> else
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 7;
> if (glob_good_digits < glob_min_good_digits) then # if number 7
> glob_min_good_digits := glob_good_digits;
> fi;# end if 7;
> if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 7
> glob_min_apfp_est_good_digits := glob_apfp_est_good_digits;
> fi;# end if 7;
> if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 7
> est_rel_err := evalf(array_max_est_error[2]*100.0 * sqrt(glob_iter)*36*ATS_MAX_TERMS/float_abs(numeric_val));
> if (evalf(est_rel_err) > glob_prec) then # if number 8
> glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
> else
> glob_est_digits := Digits;
> fi;# end if 8;
> else
> relerr := glob__m1 ;
> glob_est_digits := -16;
> fi;# end if 7;
> array_est_digits[2] := glob_est_digits;
> if (glob_iter = 1) then # if number 7
> array_1st_rel_error[2] := relerr;
> else
> array_last_rel_error[2] := relerr;
> fi;# end if 7;
> array_est_rel_error[2] := 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 6;
> #BOTTOM DISPLAY ALOT
> fi;# end if 5;
> 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_2,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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_y1(ind_var));
omniout_float(ALWAYS, "y1[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
term_no := 1;
numeric_val := array_y1[term_no];
abserr := float_abs(numeric_val - closed_form_val_y);
omniout_float(ALWAYS, "y1[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)*36*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, " ");
closed_form_val_y := evalf(exact_soln_y2(ind_var));
omniout_float(ALWAYS, "y2[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
term_no := 1;
numeric_val := array_y2[term_no];
abserr := float_abs(numeric_val - closed_form_val_y);
omniout_float(ALWAYS, "y2[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[2]*100.0*
sqrt(glob_iter)*36*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[2] := glob_est_digits;
if glob_iter = 1 then array_1st_rel_error[2] := relerr
else array_last_rel_error[2] := relerr
end if;
array_est_rel_error[2] := 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_2,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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 5
> 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 5;
> 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_2,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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_2,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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_y1_higher[1,last_no-1],array_y1_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[1,1]) then # if number 8
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y1_higher[1,last_no-1],array_y1_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 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[2,1] := glob_larger_float;
> array_ord_test_poles[2,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 2 - 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_y2_higher[1,last_no-1],array_y2_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[2,1]) then # if number 10
> array_rad_test_poles[2,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> array_rad_test_poles[2,1] := rad_c;
> array_ord_test_poles[2,1] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test2
> 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_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 9
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 9;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 9
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 10
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 11
> found_sing := 0;
> fi;# end if 11;
> 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 11
> if (rad_c < array_rad_test_poles[1,2]) then # if number 12
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 13
> glob_min_pole_est := rad_c;
> fi;# end if 13;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 12;
> fi;# end if 11;
> #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[2,2] := glob_larger_float;
> array_ord_test_poles[2,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 2 - 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_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 11
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 11;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 11
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 12
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 13
> found_sing := 0;
> fi;# end if 13;
> 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 13
> if (rad_c < array_rad_test_poles[2,2]) then # if number 14
> array_rad_test_poles[2,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> array_rad_test_poles[2,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 15
> glob_min_pole_est := rad_c;
> fi;# end if 15;
> array_ord_test_poles[2,2] := tmp_ord;
> fi;# end if 14;
> fi;# end if 13;
> #BOTTOM general radius test2
> 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_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 13
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 13;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 13
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 14
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 15
> found_sing := 0;
> fi;# end if 15;
> 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 15
> if (rad_c < array_rad_test_poles[1,3]) then # if number 16
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 17
> glob_min_pole_est := rad_c;
> fi;# end if 17;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 16;
> fi;# end if 15;
> #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[2,3] := glob_larger_float;
> array_ord_test_poles[2,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 2 - 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_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 15
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 15;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 15
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 16
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 17
> found_sing := 0;
> fi;# end if 17;
> 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 17
> if (rad_c < array_rad_test_poles[2,3]) then # if number 18
> array_rad_test_poles[2,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> array_rad_test_poles[2,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 19
> glob_min_pole_est := rad_c;
> fi;# end if 19;
> array_ord_test_poles[2,3] := tmp_ord;
> fi;# end if 18;
> fi;# end if 17;
> #BOTTOM general radius test2
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 17
> 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 18
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 18;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y1[term] := array_y1[term]* ratio;
> array_y1_higher[1,term] := array_y1_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> array_y2[term] := array_y2[term]* ratio;
> array_y2_higher[1,term] := array_y2_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 17;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 17
> display_poles();
> fi;# end if 17
> 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_2,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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_y1_higher[1, last_no - 1],
array_y1_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_y1_higher[1, last_no - 1],
array_y1_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[2, 1] := glob_larger_float;
array_ord_test_poles[2, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 12;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y2_higher[1, last_no - 1],
array_y2_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[2, 1] then
array_rad_test_poles[2, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y2_higher[1, last_no - 1],
array_y2_higher[1, last_no], last_no);
array_rad_test_poles[2, 1] := rad_c;
array_ord_test_poles[2, 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_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1], array_y1_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_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1],
array_y1_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[2, 2] := glob_larger_float;
array_ord_test_poles[2, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 12;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1], array_y2_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[2, 2] then
array_rad_test_poles[2, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1],
array_y2_higher[1, last_no], last_no);
array_rad_test_poles[2, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[2, 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_y1_higher[1, last_no - 5],
array_y1_higher[1, last_no - 4],
array_y1_higher[1, last_no - 3],
array_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1], array_y1_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_y1_higher[1, last_no - 5],
array_y1_higher[1, last_no - 4],
array_y1_higher[1, last_no - 3],
array_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1],
array_y1_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;
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[2, 3] := glob_larger_float;
array_ord_test_poles[2, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 12;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y2_higher[1, last_no - 5],
array_y2_higher[1, last_no - 4],
array_y2_higher[1, last_no - 3],
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1], array_y2_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[2, 3] then
array_rad_test_poles[2, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y2_higher[1, last_no - 5],
array_y2_higher[1, last_no - 4],
array_y2_higher[1, last_no - 3],
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1],
array_y2_higher[1, last_no], last_no);
array_rad_test_poles[2, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[2, 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_y1[term] := array_y1[term]*ratio;
array_y1_higher[1, term] := array_y1_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
array_y2[term] := array_y2[term]*ratio;
array_y2_higher[1, term] := array_y2_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_2,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre neg FULL $eq_no = 1
> array_tmp1[1] := neg(array_y2[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y1_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y1[2] := temporary;
> array_y1_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y1_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #emit pre diff $eq_no = 2 i = 1 order_d = 1
> array_tmp4[1] := array_y1_higher[2,1];
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if ( not array_y2_set_initial[2,3]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[1]) * (expt((glob_h) , c(2))) * c(factorial_3(0,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y2[3] := temporary;
> array_y2_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y2_higher[2,2] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y2_higher[3,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre neg FULL $eq_no = 1
> array_tmp1[2] := neg(array_y2[2]);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y1_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y1[3] := temporary;
> array_y1_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y1_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #emit pre diff $eq_no = 2 i = 2 order_d = 1
> array_tmp4[2] := array_y1_higher[2,2];
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if ( not array_y2_set_initial[2,4]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[2]) * (expt((glob_h) , c(2))) * c(factorial_3(1,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y2[4] := temporary;
> array_y2_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y2_higher[2,3] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y2_higher[3,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre neg FULL $eq_no = 1
> array_tmp1[3] := neg(array_y2[3]);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y1_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y1[4] := temporary;
> array_y1_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y1_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #emit pre diff $eq_no = 2 i = 3 order_d = 1
> array_tmp4[3] := array_y1_higher[2,3];
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if ( not array_y2_set_initial[2,5]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[3]) * (expt((glob_h) , c(2))) * c(factorial_3(2,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y2[5] := temporary;
> array_y2_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y2_higher[2,4] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y2_higher[3,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre neg FULL $eq_no = 1
> array_tmp1[4] := neg(array_y2[4]);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y1_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y1[5] := temporary;
> array_y1_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y1_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #emit pre diff $eq_no = 2 i = 4 order_d = 1
> array_tmp4[4] := array_y1_higher[2,4];
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if ( not array_y2_set_initial[2,6]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[4]) * (expt((glob_h) , c(2))) * c(factorial_3(3,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y2[6] := temporary;
> array_y2_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y2_higher[2,5] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y2_higher[3,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre neg FULL $eq_no = 1
> array_tmp1[5] := neg(array_y2[5]);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y1_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y1[6] := temporary;
> array_y1_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y1_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #emit pre diff $eq_no = 2 i = 5 order_d = 1
> array_tmp4[5] := array_y1_higher[2,5];
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if ( not array_y2_set_initial[2,7]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[5]) * (expt((glob_h) , c(2))) * c(factorial_3(4,6));
> if (7 <= ATS_MAX_TERMS) then # if number 3
> array_y2[7] := temporary;
> array_y2_higher[1,7] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(6);
> array_y2_higher[2,6] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y2_higher[3,5] := 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 neg FULL $eq_no = 1
> array_tmp1[kkk] := neg(array_y2[kkk]);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y1_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp2[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y1[kkk + order_d] := c(temporary);
> array_y1_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_y1_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;
> #emit diff $eq_no = 2
> if (kkk <= ATS_MAX_TERMS) then # if number 1
> array_tmp4[kkk] := array_y1_higher[2,kkk];
> fi;# end if 1;
> #emit assign $eq_no = 2
> order_d := 2;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y2_set_initial[2,kkk + order_d]) then # if number 2
> temporary := c(array_tmp4[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y2[kkk + order_d] := c(temporary);
> array_y2_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_y2_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_2,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
array_tmp1[1] := neg(array_y2[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y1_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y1[2] := temporary;
array_y1_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y1_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp4[1] := array_y1_higher[2, 1];
if not array_y2_set_initial[2, 3] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[1])*expt(glob_h, c(2))*c(factorial_3(0, 2));
if 3 <= ATS_MAX_TERMS then
array_y2[3] := temporary;
array_y2_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y2_higher[2, 2] := c(temporary);
temporary := c(temporary)*c(1)/c(glob_h);
array_y2_higher[3, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := neg(array_y2[2]);
array_tmp2[2] := array_tmp1[2];
if not array_y1_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y1[3] := temporary;
array_y1_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y1_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp4[2] := array_y1_higher[2, 2];
if not array_y2_set_initial[2, 4] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[2])*expt(glob_h, c(2))*c(factorial_3(1, 3));
if 4 <= ATS_MAX_TERMS then
array_y2[4] := temporary;
array_y2_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y2_higher[2, 3] := c(temporary);
temporary := c(temporary)*c(2)/c(glob_h);
array_y2_higher[3, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp1[3] := neg(array_y2[3]);
array_tmp2[3] := array_tmp1[3];
if not array_y1_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y1[4] := temporary;
array_y1_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y1_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp4[3] := array_y1_higher[2, 3];
if not array_y2_set_initial[2, 5] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[3])*expt(glob_h, c(2))*c(factorial_3(2, 4));
if 5 <= ATS_MAX_TERMS then
array_y2[5] := temporary;
array_y2_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y2_higher[2, 4] := c(temporary);
temporary := c(temporary)*c(3)/c(glob_h);
array_y2_higher[3, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp1[4] := neg(array_y2[4]);
array_tmp2[4] := array_tmp1[4];
if not array_y1_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y1[5] := temporary;
array_y1_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y1_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp4[4] := array_y1_higher[2, 4];
if not array_y2_set_initial[2, 6] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[4])*expt(glob_h, c(2))*c(factorial_3(3, 5));
if 6 <= ATS_MAX_TERMS then
array_y2[6] := temporary;
array_y2_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y2_higher[2, 5] := c(temporary);
temporary := c(temporary)*c(4)/c(glob_h);
array_y2_higher[3, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp1[5] := neg(array_y2[5]);
array_tmp2[5] := array_tmp1[5];
if not array_y1_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y1[6] := temporary;
array_y1_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y1_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
array_tmp4[5] := array_y1_higher[2, 5];
if not array_y2_set_initial[2, 7] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[5])*expt(glob_h, c(2))*c(factorial_3(4, 6));
if 7 <= ATS_MAX_TERMS then
array_y2[7] := temporary;
array_y2_higher[1, 7] := temporary
end if;
temporary := c(temporary)*c(6)/c(glob_h);
array_y2_higher[2, 6] := c(temporary);
temporary := c(temporary)*c(5)/c(glob_h);
array_y2_higher[3, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp1[kkk] := neg(array_y2[kkk]);
array_tmp2[kkk] := array_tmp1[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y1_set_initial[1, kkk + order_d] then
temporary := c(array_tmp2[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y1[kkk + order_d] := c(temporary);
array_y1_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_y1_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
if kkk <= ATS_MAX_TERMS then
array_tmp4[kkk] := array_y1_higher[2, kkk]
end if;
order_d := 2;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y2_set_initial[2, kkk + order_d] then
temporary := c(array_tmp4[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y2[kkk + order_d] := c(temporary);
array_y2_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_y2_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_2,
> #END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 30;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y1_init:= Array(0..(30),[]);
> array_y2_init:= Array(0..(30),[]);
> array_norms:= Array(0..(30),[]);
> array_fact_1:= Array(0..(30),[]);
> array_1st_rel_error:= Array(0..(3),[]);
> array_last_rel_error:= Array(0..(3),[]);
> array_est_rel_error:= Array(0..(3),[]);
> array_max_est_error:= Array(0..(3),[]);
> array_type_pole:= Array(0..(3),[]);
> array_type_real_pole:= Array(0..(3),[]);
> array_type_complex_pole:= Array(0..(3),[]);
> array_est_digits:= Array(0..(3),[]);
> array_y1:= Array(0..(30),[]);
> array_x:= Array(0..(30),[]);
> array_y2:= Array(0..(30),[]);
> array_tmp0:= Array(0..(30),[]);
> array_tmp1:= Array(0..(30),[]);
> array_tmp2:= Array(0..(30),[]);
> array_tmp3:= Array(0..(30),[]);
> array_tmp4:= Array(0..(30),[]);
> array_m1:= Array(0..(30),[]);
> array_y1_higher := Array(0..(2) ,(0..30+ 1),[]);
> array_y1_higher_work := Array(0..(2) ,(0..30+ 1),[]);
> array_y1_higher_work2 := Array(0..(2) ,(0..30+ 1),[]);
> array_y1_set_initial := Array(0..(3) ,(0..30+ 1),[]);
> array_y2_higher := Array(0..(3) ,(0..30+ 1),[]);
> array_y2_higher_work := Array(0..(3) ,(0..30+ 1),[]);
> array_y2_higher_work2 := Array(0..(3) ,(0..30+ 1),[]);
> array_y2_set_initial := Array(0..(3) ,(0..30+ 1),[]);
> array_given_rad_poles := Array(0..(3) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(3) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(3) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(3) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(30) ,(0..30+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 30) do # do number 1
> array_y1_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_y2_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_y1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_y2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y1_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y1_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y1_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 <=3) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y1_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 <=3) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y2_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 <=3) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y2_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 <=3) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y2_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 <=3) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y2_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 <=3) 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 <=3) 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 <=3) 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 <=3) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=30) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y1);
> zero_ats_ar(array_x);
> zero_ats_ar(array_y2);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_2);
> array_const_2[1] := c(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_y1_set_initial[1,1] := true;
> array_y1_set_initial[1,2] := false;
> array_y1_set_initial[1,3] := false;
> array_y1_set_initial[1,4] := false;
> array_y1_set_initial[1,5] := false;
> array_y1_set_initial[1,6] := false;
> array_y1_set_initial[1,7] := false;
> array_y1_set_initial[1,8] := false;
> array_y1_set_initial[1,9] := false;
> array_y1_set_initial[1,10] := false;
> array_y1_set_initial[1,11] := false;
> array_y1_set_initial[1,12] := false;
> array_y1_set_initial[1,13] := false;
> array_y1_set_initial[1,14] := false;
> array_y1_set_initial[1,15] := false;
> array_y1_set_initial[1,16] := false;
> array_y1_set_initial[1,17] := false;
> array_y1_set_initial[1,18] := false;
> array_y1_set_initial[1,19] := false;
> array_y1_set_initial[1,20] := false;
> array_y1_set_initial[1,21] := false;
> array_y1_set_initial[1,22] := false;
> array_y1_set_initial[1,23] := false;
> array_y1_set_initial[1,24] := false;
> array_y1_set_initial[1,25] := false;
> array_y1_set_initial[1,26] := false;
> array_y1_set_initial[1,27] := false;
> array_y1_set_initial[1,28] := false;
> array_y1_set_initial[1,29] := false;
> array_y1_set_initial[1,30] := false;
> array_y2_set_initial[2,1] := true;
> array_y2_set_initial[2,2] := true;
> array_y2_set_initial[2,3] := false;
> array_y2_set_initial[2,4] := false;
> array_y2_set_initial[2,5] := false;
> array_y2_set_initial[2,6] := false;
> array_y2_set_initial[2,7] := false;
> array_y2_set_initial[2,8] := false;
> array_y2_set_initial[2,9] := false;
> array_y2_set_initial[2,10] := false;
> array_y2_set_initial[2,11] := false;
> array_y2_set_initial[2,12] := false;
> array_y2_set_initial[2,13] := false;
> array_y2_set_initial[2,14] := false;
> array_y2_set_initial[2,15] := false;
> array_y2_set_initial[2,16] := false;
> array_y2_set_initial[2,17] := false;
> array_y2_set_initial[2,18] := false;
> array_y2_set_initial[2,19] := false;
> array_y2_set_initial[2,20] := false;
> array_y2_set_initial[2,21] := false;
> array_y2_set_initial[2,22] := false;
> array_y2_set_initial[2,23] := false;
> array_y2_set_initial[2,24] := false;
> array_y2_set_initial[2,25] := false;
> array_y2_set_initial[2,26] := false;
> array_y2_set_initial[2,27] := false;
> array_y2_set_initial[2,28] := false;
> array_y2_set_initial[2,29] := false;
> array_y2_set_initial[2,30] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 30;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 2;
> 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/mtest5postode.ode#################");
> omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = neg ( y2 ) ; ");
> omniout_str(ALWAYS,"diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := c(0.5);");
> omniout_str(ALWAYS,"x_end := c(5.0);");
> omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);");
> omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);");
> omniout_str(ALWAYS,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 3;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=100000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=false;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y1 := proc(x)");
> omniout_str(ALWAYS,"return(neg(cos(c(x))));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
> omniout_str(ALWAYS,"return(neg(sin(c(x))));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2p := proc(x)");
> omniout_str(ALWAYS,"return(neg(cos(c(x))));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := c(0.5);
> x_end := c(5.0);
> array_y1_init[0 + 1] := exact_soln_y1(x_start);
> array_y2_init[0 + 1] := exact_soln_y2(x_start);
> array_y2_init[1 + 1] := exact_soln_y2p(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 17
> #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 18
> glob_display_interval := c(display_max);
> fi;# end if 18;
> 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_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y1[term_no] := array_y1_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 18
> array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 18;
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> order_diff := 2;
> #Start Series array_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y2[term_no] := array_y2_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 18
> array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 18;
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> if (glob_subiter_method = 1 ) then # if number 18
> atomall();
> elif
> (glob_subiter_method = 2 ) then # if number 19
> subiter := 1;
> while (subiter <= 3) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> else
> subiter := 1;
> while (subiter <= 3 + ATS_MAX_TERMS) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> fi;# end if 19;
> if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 19
> 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 19;
> if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 19
> omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
> glob_h_reason := 2;
> glob_h := glob_display_interval;
> found_h := true;
> fi;# end if 19;
> if (glob_look_poles) then # if number 19
> check_for_pole();
> fi;# end if 19;
> if ( not found_h) then # if number 19
> 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 20
> 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 20;
> fi;# end if 19;
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 19
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 19;
> if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 19
> 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 19;
> else
> found_h := true;
> glob_h := glob_h * glob_check_sign;
> fi;# end if 18;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 18
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 18;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 18
> 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_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y1[term_no] := array_y1_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 19
> array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 19;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> order_diff := 2;
> #Start Series array_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y2[term_no] := array_y2_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 19
> array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 19;
> 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 19
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 19;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> track_estimated_error();
> if (glob_subiter_method = 1 ) then # if number 19
> atomall();
> elif
> (glob_subiter_method = 2 ) then # if number 20
> subiter := 1;
> while (subiter <= 3) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> else
> subiter := 1;
> while (subiter <= 3 + ATS_MAX_TERMS) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> fi;# end if 20;
> track_estimated_error();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 20
> check_for_pole();
> fi;# end if 20;
> if (reached_interval()) then # if number 20
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 20;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y1;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[2,iii] := array_y1_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_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_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_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[1,iii] := array_y1_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_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_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_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[1,iii] := array_y1_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_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_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_y1[term_no] := array_y1_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y1_higher[ord,term_no] := array_y1_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
> #Jump Series array_y2;
> order_diff := 3;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_y2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[3,iii] := array_y2_higher[3,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 =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[2,iii] := array_y2_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 =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 2;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[2,iii] := array_y2_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 =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_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 =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 1;
> calc_term := 3;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_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 =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_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 =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #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_y2[term_no] := array_y2_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y2_higher[ord,term_no] := array_y2_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 20
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 20;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 20
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 20;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y1 , x , 1 ) = neg ( y2 ) ; ");
> omniout_str(INFO,"diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 20
> logstart(html_log_file);
> logitem_str(html_log_file,"2016-08-26T16:46:27-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest5")
> ;
> logitem_str(html_log_file,"diff ( y1 , x , 1 ) = neg ( y2 ) ; ")
> ;
> 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 21
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 21;
> if (glob_min_good_digits <> -16) then # if number 21
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 21;
> if (glob_good_digits <> -16) then # if number 21
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 21;
> 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 21
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 22
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 23
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 24
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 25
> 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 26
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 26;
> if (glob_least_ratio_sing < glob_large_float) then # if number 26
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 26;
> if (glob_least_3_sing < glob_large_float) then # if number 26
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 26;
> if (glob_least_6_sing < glob_large_float) then # if number 26
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 26;
> 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 26
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 26;
> log_revs(html_log_file," 308.maple.seems.ok | ")
> ;
> logitem_str(html_log_file,"mtest5 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest5 maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; ")
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> ;
> logditto(html_log_file)
> ;
> if (array_est_digits[2] <> -16) then # if number 26
> logitem_integer(html_log_file,array_est_digits[2])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 26;
> if (glob_min_good_digits <> -16) then # if number 26
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 26;
> if (glob_good_digits <> -16) then # if number 26
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 26;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logditto(html_log_file)
> ;
> if (glob_type_given_pole = 0) then # if number 26
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 4) then # if number 27
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 5) then # if number 28
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 3) then # if number 29
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 1) then # if number 30
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 31
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> fi;# end if 31;
> if (glob_least_ratio_sing < glob_large_float) then # if number 31
> logditto(html_log_file)
> ;
> else
> logditto(html_log_file)
> ;
> fi;# end if 31;
> if (glob_least_3_sing < glob_large_float) then # if number 31
> logditto(html_log_file)
> ;
> else
> logditto(html_log_file)
> ;
> fi;# end if 31;
> if (glob_least_6_sing < glob_large_float) then # if number 31
> logditto(html_log_file)
> ;
> else
> logditto(html_log_file)
> ;
> fi;# end if 31;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> if (c(glob_percent_done) < glob__100) then # if number 31
> logditto(html_log_file)
> ;
> 0;
> else
> logditto(html_log_file)
> ;
> 0;
> fi;# end if 31;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 30;
> if (glob_html_log) then # if number 30
> fclose(html_log_file);
> fi;# end if 30
> ;
> ;;
> fi;# end if 29
> #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_2,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
ATS_MAX_TERMS := 30;
Digits := 32;
max_terms := 30;
glob_html_log := true;
array_y1_init := Array(0 .. 30, []);
array_y2_init := Array(0 .. 30, []);
array_norms := Array(0 .. 30, []);
array_fact_1 := Array(0 .. 30, []);
array_1st_rel_error := Array(0 .. 3, []);
array_last_rel_error := Array(0 .. 3, []);
array_est_rel_error := Array(0 .. 3, []);
array_max_est_error := Array(0 .. 3, []);
array_type_pole := Array(0 .. 3, []);
array_type_real_pole := Array(0 .. 3, []);
array_type_complex_pole := Array(0 .. 3, []);
array_est_digits := Array(0 .. 3, []);
array_y1 := Array(0 .. 30, []);
array_x := Array(0 .. 30, []);
array_y2 := Array(0 .. 30, []);
array_tmp0 := Array(0 .. 30, []);
array_tmp1 := Array(0 .. 30, []);
array_tmp2 := Array(0 .. 30, []);
array_tmp3 := Array(0 .. 30, []);
array_tmp4 := Array(0 .. 30, []);
array_m1 := Array(0 .. 30, []);
array_y1_higher := Array(0 .. 2, 0 .. 31, []);
array_y1_higher_work := Array(0 .. 2, 0 .. 31, []);
array_y1_higher_work2 := Array(0 .. 2, 0 .. 31, []);
array_y1_set_initial := Array(0 .. 3, 0 .. 31, []);
array_y2_higher := Array(0 .. 3, 0 .. 31, []);
array_y2_higher_work := Array(0 .. 3, 0 .. 31, []);
array_y2_higher_work2 := Array(0 .. 3, 0 .. 31, []);
array_y2_set_initial := Array(0 .. 3, 0 .. 31, []);
array_given_rad_poles := Array(0 .. 3, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 3, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 3, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 3, 0 .. 5, []);
array_fact_2 := Array(0 .. 30, 0 .. 31, []);
term := 1;
while term <= 30 do array_y1_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_y2_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 30 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 3 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 3 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 3 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 30 do array_y1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_y2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y1_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y1_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y1_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 30 do
array_y1_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 30 do
array_y2_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 30 do
array_y2_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 30 do
array_y2_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 30 do
array_y2_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 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 <= 3 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 <= 3 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 <= 3 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 30 do
term := 1;
while term <= 30 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y1);
zero_ats_ar(array_x);
zero_ats_ar(array_y2);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_2);
array_const_2[1] := c(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_y1_set_initial[1, 1] := true;
array_y1_set_initial[1, 2] := false;
array_y1_set_initial[1, 3] := false;
array_y1_set_initial[1, 4] := false;
array_y1_set_initial[1, 5] := false;
array_y1_set_initial[1, 6] := false;
array_y1_set_initial[1, 7] := false;
array_y1_set_initial[1, 8] := false;
array_y1_set_initial[1, 9] := false;
array_y1_set_initial[1, 10] := false;
array_y1_set_initial[1, 11] := false;
array_y1_set_initial[1, 12] := false;
array_y1_set_initial[1, 13] := false;
array_y1_set_initial[1, 14] := false;
array_y1_set_initial[1, 15] := false;
array_y1_set_initial[1, 16] := false;
array_y1_set_initial[1, 17] := false;
array_y1_set_initial[1, 18] := false;
array_y1_set_initial[1, 19] := false;
array_y1_set_initial[1, 20] := false;
array_y1_set_initial[1, 21] := false;
array_y1_set_initial[1, 22] := false;
array_y1_set_initial[1, 23] := false;
array_y1_set_initial[1, 24] := false;
array_y1_set_initial[1, 25] := false;
array_y1_set_initial[1, 26] := false;
array_y1_set_initial[1, 27] := false;
array_y1_set_initial[1, 28] := false;
array_y1_set_initial[1, 29] := false;
array_y1_set_initial[1, 30] := false;
array_y2_set_initial[2, 1] := true;
array_y2_set_initial[2, 2] := true;
array_y2_set_initial[2, 3] := false;
array_y2_set_initial[2, 4] := false;
array_y2_set_initial[2, 5] := false;
array_y2_set_initial[2, 6] := false;
array_y2_set_initial[2, 7] := false;
array_y2_set_initial[2, 8] := false;
array_y2_set_initial[2, 9] := false;
array_y2_set_initial[2, 10] := false;
array_y2_set_initial[2, 11] := false;
array_y2_set_initial[2, 12] := false;
array_y2_set_initial[2, 13] := false;
array_y2_set_initial[2, 14] := false;
array_y2_set_initial[2, 15] := false;
array_y2_set_initial[2, 16] := false;
array_y2_set_initial[2, 17] := false;
array_y2_set_initial[2, 18] := false;
array_y2_set_initial[2, 19] := false;
array_y2_set_initial[2, 20] := false;
array_y2_set_initial[2, 21] := false;
array_y2_set_initial[2, 22] := false;
array_y2_set_initial[2, 23] := false;
array_y2_set_initial[2, 24] := false;
array_y2_set_initial[2, 25] := false;
array_y2_set_initial[2, 26] := false;
array_y2_set_initial[2, 27] := false;
array_y2_set_initial[2, 28] := false;
array_y2_set_initial[2, 29] := false;
array_y2_set_initial[2, 30] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 30;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 2;
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/mtest5postode.ode#################");
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = neg ( y2 ) ; ")
;
omniout_str(ALWAYS,
"diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := c(0.5);");
omniout_str(ALWAYS, "x_end := c(5.0);");
omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);");
omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);");
omniout_str(ALWAYS, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);")
;
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 3;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=100000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=false;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y1 := proc(x)");
omniout_str(ALWAYS, "return(neg(cos(c(x))));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
omniout_str(ALWAYS, "return(neg(sin(c(x))));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2p := proc(x)");
omniout_str(ALWAYS, "return(neg(cos(c(x))));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := c(0.5);
x_end := c(5.0);
array_y1_init[1] := exact_soln_y1(x_start);
array_y2_init[1] := exact_soln_y2(x_start);
array_y2_init[2] := exact_soln_y2p(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_y1[term_no] := array_y1_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_y1_higher[r_order, term_no] :=
array_y1_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;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_y2[term_no] := array_y2_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_y2_higher[r_order, term_no] :=
array_y2_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;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 3 do atomall(); subiter := subiter + 1
end do
else
subiter := 1;
while subiter <= 3 + ATS_MAX_TERMS do
atomall(); subiter := subiter + 1
end do
end if;
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_y1[term_no] := array_y1_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_y1_higher[r_order, term_no] := array_y1_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;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_y2[term_no] := array_y2_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_y2_higher[r_order, term_no] := array_y2_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();
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 3 do atomall(); subiter := subiter + 1
end do
else
subiter := 1;
while subiter <= 3 + ATS_MAX_TERMS do
atomall(); subiter := subiter + 1
end do
end if;
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_y1_higher_work[2, iii] := array_y1_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_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_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_y1[term_no] := array_y1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y1_higher[ord, term_no] :=
array_y1_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 3;
ord := 3;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, 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 := 3;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 2;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_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 := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_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_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 3;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_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 := 3;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_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_y2[term_no] := array_y2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y2_higher[ord, term_no] :=
array_y2_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 ( y1 , x , 1 ) = neg ( y2 ) ; ");
omniout_str(INFO,
"diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; ")
;
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2016-08-26T16:46:27-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"mtest5");
logitem_str(html_log_file,
"diff ( y1 , x , 1 ) = neg ( y2 ) ; ");
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,
"mtest5 diffeq.mxt");
logitem_str(html_log_file, "mtest5 maple results");
logitem_str(html_log_file, "OK");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file, "diff ( y2 , x , 2 ) = d\
iff ( y1 , x , 1 ) ; ");
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
if array_est_digits[2] <> -16 then
logitem_integer(html_log_file, array_est_digits[2])
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");
logditto(html_log_file);
if glob_type_given_pole = 0 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 4 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 5 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 3 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 1 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 2 then
logditto(html_log_file); logditto(html_log_file)
end if;
if glob_least_ratio_sing < glob_large_float then
logditto(html_log_file)
else logditto(html_log_file)
end if;
if glob_least_3_sing < glob_large_float then
logditto(html_log_file)
else logditto(html_log_file)
end if;
if glob_least_6_sing < glob_large_float then
logditto(html_log_file)
else logditto(html_log_file)
end if;
logditto(html_log_file);
logditto(html_log_file);
if c(glob_percent_done) < glob__100 then
logditto(html_log_file); 0
else logditto(html_log_file); 0
end if;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
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/mtest5postode.ode#################
diff ( y1 , x , 1 ) = neg ( y2 ) ;
diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(0.5);
x_end := c(5.0);
array_y1_init[0 + 1] := exact_soln_y1(x_start);
array_y2_init[0 + 1] := exact_soln_y2(x_start);
array_y2_init[1 + 1] := exact_soln_y2p(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_y1 := proc(x)
return(neg(cos(c(x))));
end;
exact_soln_y2 := proc(x)
return(neg(sin(c(x))));
end;
exact_soln_y2p := proc(x)
return(neg(cos(c(x))));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
memory used=4.0MB, alloc=40.3MB, time=0.08
x[1] = 0.5
y1[1] (closed_form) = -0.87758256189037271611628158260383
y1[1] (numeric) = -0.87758256189037271611628158260383
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.47942553860420300027328793521557
y2[1] (numeric) = -0.47942553860420300027328793521557
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=46.5MB, alloc=40.3MB, time=0.64
x[1] = 0.51
y1[1] (closed_form) = -0.87274450764575126310580847357551
y1[1] (numeric) = -0.87274450764575126310580829204146
absolute error = 1.8153405e-25
relative error = 2.0800365789719186990226439353236e-23 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.48817724688290749450013023767457
y2[1] (numeric) = -0.48817724688290749450018673842341
absolute error = 5.650074884e-23
relative error = 1.1573818567081245829182316538780e-20 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=88.8MB, alloc=40.3MB, time=1.19
x[1] = 0.52
y1[1] (closed_form) = -0.86781917967764990038784757198851
y1[1] (numeric) = -0.86781917967764990038784603706466
absolute error = 1.53492385e-24
relative error = 1.7687139048599330374525699087152e-22 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.49688013784373671433445894254775
y2[1] (numeric) = -0.49688013784373671433469319928928
absolute error = 2.3425674153e-22
relative error = 4.7145523374426196900849765901770e-20 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=131.2MB, alloc=40.3MB, time=1.73
x[1] = 0.53
y1[1] (closed_form) = -0.8628070705147610118066950185642
y1[1] (numeric) = -0.86280707051476101180668974932709
absolute error = 5.26923711e-24
relative error = 6.1070861494636456264914944366958e-22 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.50553334120484696181366102246608
y2[1] (numeric) = -0.50553334120484696181419358947032
absolute error = 5.3256700424e-22
relative error = 1.0534755293700771725430103145241e-19 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=173.5MB, alloc=40.3MB, time=2.28
x[1] = 0.54
y1[1] (closed_form) = -0.8577086813638241425379687789178
y1[1] (numeric) = -0.85770868136382414253795619250672
absolute error = 1.258641108e-23
relative error = 1.4674459234791255950566383318281e-21 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.51413599165311310467728068295824
y2[1] (numeric) = -0.51413599165311310467823138940838
absolute error = 9.5070645014e-22
relative error = 1.8491342087978941274450486348949e-19 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=215.9MB, alloc=40.3MB, time=2.82
x[1] = 0.55
y1[1] (closed_form) = -0.85252452205950574280498179761777
y1[1] (numeric) = -0.85252452205950574280495711660561
absolute error = 2.468101216e-23
relative error = 2.8950501154355392165755907014611e-21 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.52268722893065916778837810775729
y2[1] (numeric) = -0.52268722893065916778986603377868
absolute error = 1.48792602139e-21
relative error = 2.8466852431693744784529787335485e-19 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=258.2MB, alloc=40.3MB, time=3.37
x[1] = 0.56
y1[1] (closed_form) = -0.84725511101341612609452550386632
y1[1] (numeric) = -0.84725511101341612609448276386934
absolute error = 4.273999698e-23
relative error = 5.0445251287865314686607979484335e-21 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.53118619792088340385186944111203
y2[1] (numeric) = -0.53118619792088340385401289394696
absolute error = 2.14345283493e-21
relative error = 4.0352193700056431459950137616647e-19 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.57
y1[1] (closed_form) = -0.84190097516226874013375636391601
y1[1] (numeric) = -0.84190097516226874013368842144124
absolute error = 6.794247477e-23
relative error = 8.0701266270542930770546015305649e-21 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.53963204873396924099446349307883
y2[1] (numeric) = -0.53963204873396924099737998341027
absolute error = 2.91649033144e-21
relative error = 5.4045906618822548026512249782746e-19 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
memory used=300.7MB, alloc=40.3MB, time=3.92
TOP MAIN SOLVE Loop
x[1] = 0.58
y1[1] (closed_form) = -0.83646264991518693465788732805002
y1[1] (numeric) = -0.83646264991518693465778586857855
absolute error = 1.0145947147e-22
relative error = 1.2129587792149174290075522317684e-20 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.54802393679187355618269605957646
y2[1] (numeric) = -0.54802393679187355618650227800479
absolute error = 3.80621842833e-21
relative error = 6.9453506914525727011739579310416e-19 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.001
memory used=343.1MB, alloc=40.3MB, time=4.46
TOP MAIN SOLVE Loop
x[1] = 0.59
y1[1] (closed_form) = -0.83094067910016349524799652249068
y1[1] (numeric) = -0.83094067910016349524785206879549
absolute error = 1.4445369519e-22
relative error = 1.7384357129612524394486386009507e-20 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.55636102291278377572254337887577
y2[1] (numeric) = -0.5563610229127837757273551725516
absolute error = 4.81179367583e-21
relative error = 8.6486893899185062673543756131147e-19 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=385.5MB, alloc=40.3MB, time=5.01
TOP MAIN SOLVE Loop
x[1] = 0.6
y1[1] (closed_form) = -0.82533561490967829724095249895538
y1[1] (numeric) = -0.82533561490967829724075441965198
absolute error = 1.9807930340e-22
relative error = 2.3999849251831580357023464394235e-20 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.56464247339503535720094544565866
y2[1] (numeric) = -0.5646424733950353572068777950756
absolute error = 5.93234941694e-21
relative error = 1.0506381819402395017993723933786e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=427.8MB, alloc=40.3MB, time=5.55
TOP MAIN SOLVE Loop
x[1] = 0.61
y1[1] (closed_form) = -0.81964801784547951790074657865482
y1[1] (numeric) = -0.81964801784547951790048309698317
absolute error = 2.6348167165e-22
relative error = 3.2145709611131116706408706742149e-20 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.57286746010048126119097603216272
y2[1] (numeric) = -0.5728674601004812611981430281133
absolute error = 7.16699595058e-21
relative error = 1.2510740179452512538128791137238e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=470.1MB, alloc=40.3MB, time=6.10
TOP MAIN SOLVE Loop
x[1] = 0.62
y1[1] (closed_form) = -0.8138784566625339286839996543607
y1[1] (numeric) = -0.81387845666253392868365785719681
absolute error = 3.4179716389e-22
relative error = 4.1996094268375820817880658201422e-20 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.58103516053730507584296322758221
y2[1] (numeric) = -0.58103516053730507585147804828066
absolute error = 8.51482069845e-21
relative error = 1.4654570457622607397495594928893e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=512.5MB, alloc=40.3MB, time=6.64
TOP MAIN SOLVE Loop
x[1] = 0.63
y1[1] (closed_form) = -0.80802750831215187252370896577706
y1[1] (numeric) = -0.80802750831215187252327481287238
absolute error = 4.3415290468e-22
relative error = 5.3729965900156075544932130025539e-20 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.58914475794226951311811209079462
y2[1] (numeric) = -0.58914475794226951312808697916968
absolute error = 9.97488837506e-21
relative error = 1.6931133207226877445144488600830e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=554.8MB, alloc=40.3MB, time=7.19
TOP MAIN SOLVE Loop
x[1] = 0.64
y1[1] (closed_form) = -0.80209575788429261358611077926032
y1[1] (numeric) = -0.80209575788429261358556911270744
absolute error = 5.4166655288e-22
relative error = 6.7531407260994244823099519940650e-20 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.59719544136239205188354623920793
y2[1] (numeric) = -0.59719544136239205189509248036934
absolute error = 1.154624116141e-20
relative error = 1.9334108001677583017473120388829e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=597.2MB, alloc=40.3MB, time=7.74
TOP MAIN SOLVE Loop
x[1] = 0.65
y1[1] (closed_form) = -0.79608379854905582891760457067991
y1[1] (numeric) = -0.79608379854905582891693912460266
absolute error = 6.6544607725e-22
relative error = 8.3589953527862714744730042433820e-20 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.60518640573603956037252167860594
y2[1] (numeric) = -0.60518640573603956038574957748786
absolute error = 1.322789888192e-20
relative error = 2.1857561168830238819523201165992e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=639.6MB, alloc=40.3MB, time=8.28
TOP MAIN SOLVE Loop
x[1] = 0.66
y1[1] (closed_form) = -0.78999223149736509278381709123024
y1[1] (numeric) = -0.78999223149736509278301050169653
absolute error = 8.0658953371e-22
relative error = 1.0210094499045593021978273281274e-19 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.6131168519734337886151454793963
y2[1] (numeric) = -0.61311685197343378863016433858099
absolute error = 1.501885918469e-20
relative error = 2.4495916457603360239523195502497e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=682.0MB, alloc=40.3MB, time=8.83
TOP MAIN SOLVE Loop
x[1] = 0.67
y1[1] (closed_form) = -0.78382166588084928530294214483812
y1[1] (numeric) = -0.78382166588084928530197595999353
absolute error = 9.6618484459e-22
relative error = 1.2326590175384003775642935319370e-19 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.62098598703655968035744391412659
y2[1] (numeric) = -0.62098598703655968037436201185186
absolute error = 1.691809772527e-20
relative error = 2.7243928330823946094203839120938e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=724.4MB, alloc=40.3MB, time=9.37
TOP MAIN SOLVE Loop
x[1] = 0.68
y1[1] (closed_form) = -0.77757271875092793718239408404432
y1[1] (numeric) = -0.77757271875092793718124877446474
absolute error = 1.14530957958e-21
relative error = 1.4729292218736721390509672302087e-19 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.62879302401846851370417818742025
y2[1] (numeric) = -0.62879302401846851372310275577381
absolute error = 1.892456835356e-20
relative error = 3.0096657613370977007559007734351e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=766.8MB, alloc=40.3MB, time=9.92
TOP MAIN SOLVE Loop
x[1] = 0.69
y1[1] (closed_form) = -0.77124601499710660197353931549777
y1[1] (numeric) = -0.77124601499710660197219428475914
absolute error = 1.34503073863e-21
relative error = 1.7439710708068242044070425334062e-19 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.63653718222196794023742920700872
y2[1] (numeric) = -0.63653718222196794025846641031275
absolute error = 2.103720330403e-20
relative error = 3.3049449256986344942918520470230e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=809.1MB, alloc=40.3MB, time=10.46
TOP MAIN SOLVE Loop
x[1] = 0.7
y1[1] (closed_form) = -0.76484218728448842625585999019186
y1[1] (numeric) = -0.7648421872844884262542935856551
absolute error = 1.56640453676e-21
relative error = 2.0480101160755726267510126218430e-19 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.64421768723769105367261435139872
y2[1] (numeric) = -0.6442176872376910536958692647879
absolute error = 2.325491338918e-20
relative error = 3.6097912009981572050452194360958e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=851.5MB, alloc=40.3MB, time=11.01
TOP MAIN SOLVE Loop
x[1] = 0.71
y1[1] (closed_form) = -0.75836187599050816654145794413955
y1[1] (numeric) = -0.75836187599050816653964746794872
absolute error = 1.81047619083e-21
relative error = 2.3873512740409175588624059286114e-19 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.65183377102153668121012797285284
y2[1] (numeric) = -0.65183377102153668123570456104919
absolute error = 2.557658819635e-20
relative error = 3.9237899804220094421222568150426e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=893.8MB, alloc=40.3MB, time=11.55
TOP MAIN SOLVE Loop
x[1] = 0.72
y1[1] (closed_form) = -0.75180572914089497944548696225195
y1[1] (numeric) = -0.75180572914089497944340868254367
absolute error = 2.07827970828e-21
relative error = 2.7643839727783082336367333950381e-19 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.65938467197147315361800383264817
y2[1] (numeric) = -0.6593846719714731536460049289357
absolute error = 2.800109628753e-20
relative error = 4.2465494691907862006855278010871e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=936.2MB, alloc=40.3MB, time=12.10
TOP MAIN SOLVE Loop
x[1] = 0.73
y1[1] (closed_form) = -0.74517440234487038879013215855033
y1[1] (numeric) = -0.74517440234487038878776132087246
absolute error = 2.37083767787e-21
relative error = 3.1815876530508687939638360998966e-19 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.66686963500369787373259413076153
y2[1] (numeric) = -0.66686963500369787376312141616399
absolute error = 3.052728540246e-20
relative error = 4.5776991184027628528540501226854e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=978.5MB, alloc=40.3MB, time=12.68
TOP MAIN SOLVE Loop
x[1] = 0.74
y1[1] (closed_form) = -0.73846855872958790979142456069883
y1[1] (numeric) = -0.7384685587295879097887353996363
absolute error = 2.68916106253e-21
relative error = 3.6415376534869046583913195309296e-19 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.67428791162814506748388115760817
y2[1] (numeric) = -0.67428791162814506751703514027299
absolute error = 3.315398266482e-20
relative error = 4.9168881857552402993445875220710e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1020.9MB, alloc=40.3MB, time=13.22
TOP MAIN SOLVE Loop
x[1] = 0.75
y1[1] (closed_form) = -0.73168886887382088631183875300008
y1[1] (numeric) = -0.73168886887382088630880450400587
absolute error = 3.03424899421e-21
relative error = 4.1469115129223779666979975441169e-19 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.68163876002333416673324195277989
y2[1] (numeric) = -0.68163876002333416676912194757152
absolute error = 3.587999479163e-20
relative error = 5.2637844113209964423067667527599e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1063.3MB, alloc=40.3MB, time=13.76
TOP MAIN SOLVE Loop
x[1] = 0.76
y1[1] (closed_form) = -0.72483601074090517233968836666701
y1[1] (numeric) = -0.72483601074090517233628127809615
absolute error = 3.40708857086e-21
relative error = 4.7004957264435281074368658138712e-19 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.68892144511055133914775563876973
y2[1] (numeric) = -0.68892144511055133918645974707522
absolute error = 3.870410830549e-20
relative error = 5.6180727977308276835267900582254e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1105.6MB, alloc=40.3MB, time=14.31
TOP MAIN SOLVE Loop
x[1] = 0.77
y1[1] (closed_form) = -0.71791066961094336337129056532434
y1[1] (numeric) = -0.71791066961094336336748191066874
absolute error = 3.80865465560e-21
relative error = 5.3051929952009496437475577584881e-19 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.69613523862735674701988373445221
y2[1] (numeric) = -0.69613523862735674706150882420237
absolute error = 4.162508975016e-20
relative error = 5.9794544853434770172077730615608e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1148.0MB, alloc=40.3MB, time=14.86
TOP MAIN SOLVE Loop
x[1] = 0.78
y1[1] (closed_form) = -0.71091353801227735721626502376456
y1[1] (numeric) = -0.71091353801227735721202511408656
absolute error = 4.23990967800e-21
relative error = 5.9640300139097610954072220869090e-19 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.70327941920041018436789732511792
y2[1] (numeric) = -0.70327941920041018441253901102682
absolute error = 4.464168590890e-20
relative error = 6.3476457137982409125434698963347e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1190.4MB, alloc=40.3MB, time=15.40
TOP MAIN SOLVE Loop
x[1] = 0.79
y1[1] (closed_form) = -0.70384531565223609691278086108495
y1[1] (numeric) = -0.70384531565223609690807905764735
absolute error = 4.70180343760e-21
relative error = 6.6801658447395571606482904113928e-19 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.7103532724176078098140288749692
y2[1] (numeric) = -0.71035327241760780986178149899514
absolute error = 4.775262402594e-20
relative error = 6.7223768623489678552081675583500e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1232.8MB, alloc=40.3MB, time=15.95
TOP MAIN SOLVE Loop
x[1] = 0.8
y1[1] (closed_form) = -0.69670670934716542092074998164232
y1[1] (numeric) = -0.69670670934716542091555470873273
absolute error = 5.19527290959e-21
relative error = 7.4569009310361353926800030654840e-19 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.71735609089952276162717461058139
y2[1] (numeric) = -0.71735609089952276167813122261229
absolute error = 5.095661203090e-20
relative error = 7.1033915620627652372396137624754e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1275.2MB, alloc=40.3MB, time=16.56
TOP MAIN SOLVE Loop
x[1] = 0.81
y1[1] (closed_form) = -0.6894984329517470175496392406801
y1[1] (numeric) = -0.68949843295174701754391799862726
absolute error = 5.72124205284e-21
relative error = 8.2976868103199708592187032578866e-19 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.72428717437014251092817685251454
y2[1] (numeric) = -0.72428717437014251098242919128058
absolute error = 5.425233876604e-20
relative error = 7.4904458736576599330374893491031e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1317.6MB, alloc=40.3MB, time=17.11
TOP MAIN SOLVE Loop
x[1] = 0.82
y1[1] (closed_form) = -0.68222120728761355166655797843693
y1[1] (numeric) = -0.68222120728761355166027735681676
absolute error = 6.28062162017e-21
relative error = 9.2061365918843246361889887926750e-19 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.73114582972689587938131336468772
y2[1] (numeric) = -0.73114582972689587943895183890414
absolute error = 5.763847421642e-20
relative error = 7.8833075253878747681399348270061e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1360.1MB, alloc=40.3MB, time=17.66
TOP MAIN SOLVE Loop
x[1] = 0.83
y1[1] (closed_form) = -0.67487576007126710211246291786445
y1[1] (numeric) = -0.67487576007126710210558860889351
absolute error = 6.87430897094e-21
relative error = 1.0186036271645125782718015761090e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.73793137110996271872858022613808
y2[1] (numeric) = -0.73793137110996271878969389588113
absolute error = 6.111366974305e-20
relative error = 8.2817552059245841192350663005985e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1402.5MB, alloc=40.3MB, time=18.20
TOP MAIN SOLVE Loop
x[1] = 0.84
y1[1] (closed_form) = -0.66746282584130811792267103687086
y1[1] (numeric) = -0.6674628258413081179151678489849
absolute error = 7.50318788596e-21
relative error = 1.1241356964715683048143001474169e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.74464311997085932125657267062965
y2[1] (numeric) = -0.74464311997085932132124922894836
absolute error = 6.467655831871e-20
relative error = 8.6855779076077458897446162682196e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1444.8MB, alloc=40.3MB, time=18.74
TOP MAIN SOLVE Loop
x[1] = 0.85
y1[1] (closed_form) = -0.65998314588498217039541602946147
y1[1] (numeric) = -0.65998314588498217038724790107665
absolute error = 8.16812838482e-21
relative error = 1.2376268145252744833989019323840e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.75128040514029270271207152423547
y2[1] (numeric) = -0.75128040514029270278039727900203
absolute error = 6.832575476656e-20
relative error = 9.0945743159374662369922236999596e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1487.2MB, alloc=40.3MB, time=19.29
TOP MAIN SOLVE Loop
x[1] = 0.86
y1[1] (closed_form) = -0.65243746816405184627203066422386
y1[1] (numeric) = -0.65243746816405184626316067767822
absolute error = 8.86998654564e-21
relative error = 1.3595151993033131897314697668766e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.75784256289527697229458872952865
y2[1] (numeric) = -0.75784256289527697236664858553024
absolute error = 7.205985600159e-20
relative error = 9.5085522415488352292903204363697e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1529.6MB, alloc=40.3MB, time=19.84
TOP MAIN SOLVE Loop
x[1] = 0.87
y1[1] (closed_form) = -0.64482654724000119477766380548283
y1[1] (numeric) = -0.6448265472400011947680542011557
absolute error = 9.60960432713e-21
relative error = 1.4902618957394372978426845050826e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.76432893702550507814480282372285
y2[1] (numeric) = -0.76432893702550507822068026499755
absolute error = 7.587744127470e-20
relative error = 9.9273280912257319406764674822370e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1572.1MB, alloc=40.3MB, time=20.38
TOP MAIN SOLVE Loop
x[1] = 0.88
y1[1] (closed_form) = -0.63715114419858020801549860572209
y1[1] (numeric) = -0.63715114419858020800511079632888
absolute error = 1.038780939321e-20
relative error = 1.6303524662544500871407210887900e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.77073887889896929120964513075599
y2[1] (numeric) = -0.77073887889896929128942220317556
absolute error = 7.977707241957e-20
relative error = 1.0350726374869615500670879809491e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1614.5MB, alloc=40.3MB, time=20.93
TOP MAIN SOLVE Loop
x[1] = 0.89
y1[1] (closed_form) = -0.62941202657369688020355305738025
y1[1] (numeric) = -0.62941202657369688019234764244013
absolute error = 1.120541494012e-20
relative error = 1.7802988292293101432432857527398e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.77707174752682386549033371297318
y2[1] (numeric) = -0.77707174752682386557409100707524
absolute error = 8.375729410206e-20
relative error = 1.0778579245563006188357292311617e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1656.9MB, alloc=40.3MB, time=21.47
TOP MAIN SOLVE Loop
x[1] = 0.9
y1[1] (closed_form) = -0.62160996827066445648471615140713
y1[1] (numeric) = -0.62160996827066445647265293188121
absolute error = 1.206321952592e-20
relative error = 1.9406412608665525580756779306408e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.78332690962748338846138231571355
y2[1] (numeric) = -0.78332690962748338854919894978583
absolute error = 8.781663407228e-20
relative error = 1.1210726070171879692666337896776e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1699.3MB, alloc=40.3MB, time=22.02
TOP MAIN SOLVE Loop
x[1] = 0.91
y1[1] (closed_form) = -0.61374574948881154652117822617468
y1[1] (numeric) = -0.61374574948881154650821621927195
absolute error = 1.296200690273e-20
relative error = 2.1119505778290191821354695101850e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.78950373968995041187895751787155
y2[1] (numeric) = -0.78950373968995041197091112129087
absolute error = 9.195360341932e-20
relative error = 1.1647013028137335476351760712582e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1741.7MB, alloc=40.3MB, time=22.57
TOP MAIN SOLVE Loop
x[1] = 0.92
y1[1] (closed_form) = -0.60582015664346284179740470667438
y1[1] (numeric) = -0.60582015664346284178350216082315
absolute error = 1.390254585123e-20
relative error = 2.2948305200435784644467043776568e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.79560162003636603026827610248162
y2[1] (numeric) = -0.79560162003636603036444279930995
absolute error = 9.616669682833e-20
relative error = 1.2087292736273504755421644130158e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1784.1MB, alloc=40.3MB, time=23.11
TOP MAIN SOLVE Loop
x[1] = 0.93
y1[1] (closed_form) = -0.59783398228729823849490708443298
y1[1] (numeric) = -0.59783398228729823848002149441488
absolute error = 1.488559001810e-20
relative error = 2.4899203556726727986878279804612e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.80161994088377715208431921591065
y2[1] (numeric) = -0.80161994088377715218477360875087
absolute error = 1.0045439284022e-19
relative error = 1.2531423897647822827580147027215e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1826.4MB, alloc=40.3MB, time=23.66
TOP MAIN SOLVE Loop
x[1] = 0.94
y1[1] (closed_form) = -0.58978802503109822996098981522402
y1[1] (numeric) = -0.58978802503109822994507793746825
absolute error = 1.591187775577e-20
relative error = 2.6978977328220595117940323276191e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.80755810040511428687021979863415
y2[1] (numeric) = -0.80755810040511428697503495274804
absolute error = 1.0481515411389e-19
relative error = 1.2979270972739808932364331765446e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1868.8MB, alloc=40.3MB, time=24.20
TOP MAIN SOLVE Loop
x[1] = 0.95
y1[1] (closed_form) = -0.58168308946388349416618097376046
y1[1] (numeric) = -0.58168308946388349414919884179554
absolute error = 1.698213196492e-20
relative error = 2.9194818059042809455348116473205e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.81341550478937375068542210210256
y2[1] (numeric) = -0.81341550478937375079466952979339
absolute error = 1.0924742769083e-19
relative error = 1.3430703871217525884325661005400e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1911.2MB, alloc=40.3MB, time=24.75
TOP MAIN SOLVE Loop
x[1] = 0.96
y1[1] (closed_form) = -0.57351998607245666212505080035186
y1[1] (numeric) = -0.57351998607245666210695374041217
absolute error = 1.809705993969e-20
relative error = 3.1554366681484184432222628737010e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.81919156830099827163322214643043
y2[1] (numeric) = -0.8191915683009982717469717916924
absolute error = 1.1374964526197e-19
relative error = 1.3885597662813662045528743494832e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1953.6MB, alloc=40.3MB, time=25.30
TOP MAIN SOLVE Loop
x[1] = 0.97
y1[1] (closed_form) = -0.56529953116035431303652775484986
y1[1] (numeric) = -0.56529953116035431301727040163434
absolute error = 1.925735321552e-20
relative error = 3.4065751259322042244429499905884e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.82488571333845005747662003785634
y2[1] (numeric) = -0.82488571333845005759494026129349
absolute error = 1.1832022343715e-19
relative error = 1.4343832305967371181285502379502e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=1996.0MB, alloc=40.3MB, time=25.84
TOP MAIN SOLVE Loop
x[1] = 0.98
y1[1] (closed_form) = -0.55702254676621730087665826735994
y1[1] (numeric) = -0.55702254676621730085619457994029
absolute error = 2.046368741965e-20
relative error = 3.6737628554627649503192558558850e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.83049737049197046808453328771915
y2[1] (numeric) = -0.83049737049197046820749085173582
absolute error = 1.2295756401667e-19
relative error = 1.4805292392898527025241912254660e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2038.4MB, alloc=40.3MB, time=26.39
TOP MAIN SOLVE Loop
x[1] = 0.99
y1[1] (closed_form) = -0.54868986058158757534312640865361
y1[1] (numeric) = -0.54868986058158757532140968652919
absolute error = 2.171672212442e-20
relative error = 3.9579229879336956692671881604403e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.83602597860052051678925941154711
y2[1] (numeric) = -0.83602597860052051691691946581248
absolute error = 1.2766005426537e-19
relative error = 1.5269866910005434821428867783864e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2080.8MB, alloc=40.3MB, time=26.93
TOP MAIN SOLVE Loop
x[1] = 1
y1[1] (closed_form) = -0.54030230586813971740093660744298
y1[1] (numeric) = -0.54030230586813971737791950673968
absolute error = 2.301710070330e-20
relative error = 4.2600411757112327285031602609933e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.8414709848078965066525023216303
y2[1] (numeric) = -0.84147098480789650678492838881895
absolute error = 1.3242606718865e-19
relative error = 1.5737449012443630402382262605507e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2123.2MB, alloc=40.3MB, time=27.48
TOP MAIN SOLVE Loop
x[1] = 1.01
y1[1] (closed_form) = -0.53186072137435546620673135577918
y1[1] (numeric) = -0.53186072137435546618236590558952
absolute error = 2.436545018966e-20
relative error = 4.5811711996137679055937224635412e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.84683184461801519012309878478201
y2[1] (numeric) = -0.8468318446180151902603527465929
absolute error = 1.3725396181089e-19
relative error = 1.6207935811955896958063724948403e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2165.6MB, alloc=40.3MB, time=28.03
TOP MAIN SOLVE Loop
x[1] = 1.02
y1[1] (closed_form) = -0.52336595125164956988961380803381
y1[1] (numeric) = -0.52336595125164956986385142689543
absolute error = 2.576238113838e-20
relative error = 4.9224411860894439285250159339416e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.85210802194936292361654998545538
y2[1] (numeric) = -0.85210802194936292375869206891141
absolute error = 1.4214208345603e-19
relative error = 1.6681228177015904945170570192116e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2208.1MB, alloc=40.3MB, time=28.57
TOP MAIN SOLVE Loop
x[1] = 1.03
y1[1] (closed_form) = -0.51481884496995534753350229983735
y1[1] (numeric) = -0.51481884496995534750629381234707
absolute error = 2.720848749028e-20
relative error = 5.2850605132506130508587435888279e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.85729898918860337214627438529442
y2[1] (numeric) = -0.85729898918860337229336314932461
absolute error = 1.4708876403019e-19
relative error = 1.7157230544433884154071608576507e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2250.5MB, alloc=40.3MB, time=29.12
TOP MAIN SOLVE Loop
x[1] = 1.04
y1[1] (closed_form) = -0.50622025723277840373447342099217
y1[1] (numeric) = -0.50622025723277840370576907455287
absolute error = 2.870434643930e-20
relative error = 5.6703274966139298860308481471767e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.86240422724333840328079169211617
y2[1] (numeric) = -0.86240422724333840343288401442255
absolute error = 1.5209232230638e-19
relative error = 1.7635850741657508411106959890427e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2293.0MB, alloc=40.3MB, time=29.67
TOP MAIN SOLVE Loop
x[1] = 1.05
y1[1] (closed_form) = -0.4975710478917269902908495728121
y1[1] (numeric) = -0.49757104789172699026059905450942
absolute error = 3.025051830268e-20
relative error = 6.0796379594141110473287897896759e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.86742322559401689438140948500027
y2[1] (numeric) = -0.86742322559401689453856054921157
absolute error = 1.5715106421130e-19
relative error = 1.8116999819053952621544129711989e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2335.4MB, alloc=40.3MB, time=30.22
TOP MAIN SOLVE Loop
x[1] = 1.06
y1[1] (closed_form) = -0.48887208186052756191863753995641
y1[1] (numeric) = -0.48887208186052756188678999356256
absolute error = 3.184754639385e-20
relative error = 6.5144948086718367236070558296969e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.87235548234498626228294592199742
y2[1] (numeric) = -0.87235548234498626244520920511156
absolute error = 1.6226328311414e-19
relative error = 1.8600591891502610316719535765069e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2377.8MB, alloc=40.3MB, time=30.76
TOP MAIN SOLVE Loop
x[1] = 1.07
y1[1] (closed_form) = -0.48012422902853412436509306817592
y1[1] (numeric) = -0.48012422902853412433159711127754
absolute error = 3.349595689838e-20
relative error = 6.9765187576878798718835942020486e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.87720050427468161030706325777682
y2[1] (numeric) = -0.87720050427468161047449051789411
absolute error = 1.6742726011729e-19
relative error = 1.9086543988677732636133326083330e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2420.2MB, alloc=40.3MB, time=31.31
TOP MAIN SOLVE Loop
x[1] = 1.08
y1[1] (closed_form) = -0.47132836417374002391352478852603
y1[1] (numeric) = -0.47132836417374002387832852977324
absolute error = 3.519625875279e-20
relative error = 7.4674603584468412317959871715545e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.88195780688494747373533498762476
y2[1] (numeric) = -0.88195780688494747390797625197372
absolute error = 1.7264126434896e-19
relative error = 1.9574775913456058811107995856314e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2462.6MB, alloc=40.3MB, time=31.86
TOP MAIN SOLVE Loop
x[1] = 1.09
y1[1] (closed_form) = -0.46248536687530087702789707387514
y1[1] (numeric) = -0.46248536687530087699094813034898
absolute error = 3.694894352616e-20
relative error = 7.9892135346462711349032680758575e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.88662691444948723160860062863605
y2[1] (numeric) = -0.8866269144494872317865041818939
absolute error = 1.7790355325785e-19
relative error = 2.0065210107941686346029848592488e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2505.1MB, alloc=40.3MB, time=32.40
TOP MAIN SOLVE Loop
x[1] = 1.1
y1[1] (closed_form) = -0.45359612142557738777137005178472
y1[1] (numeric) = -0.45359612142557738773261556647975
absolute error = 3.875448530497e-20
relative error = 8.5438308385819260349358893574575e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.8912073600614353399518025778717
y2[1] (numeric) = -0.891207360061435340135014950781
absolute error = 1.8321237290930e-19
relative error = 2.0557771526558113610747576021867e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2547.4MB, alloc=40.3MB, time=32.95
TOP MAIN SOLVE Loop
x[1] = 1.11
y1[1] (closed_form) = -0.44466151674170684864373751193357
y1[1] (numeric) = -0.44466151674170684860312417135298
absolute error = 4.061334058059e-20
relative error = 9.1335406936466035778010554732413e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.89569868568004762924062595933937
y2[1] (numeric) = -0.89569868568004762942919191762304
absolute error = 1.8856595828367e-19
relative error = 2.1052387515842310050948088831442e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2589.8MB, alloc=40.3MB, time=33.50
TOP MAIN SOLVE Loop
x[1] = 1.12
y1[1] (closed_form) = -0.43568244627671216761398879396113
y1[1] (numeric) = -0.43568244627671216757146284582102
absolute error = 4.252594814011e-20
relative error = 9.7607669309451063469360864463821e-18 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.90010044217650499711910324733915
y2[1] (numeric) = -0.90010044217650499731306578091525
absolute error = 1.9396253357610e-19
relative error = 2.1548987700426544161186648447526e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2632.2MB, alloc=40.3MB, time=34.05
TOP MAIN SOLVE Loop
x[1] = 1.13
y1[1] (closed_form) = -0.42665980793015731037121583565354
y1[1] (numeric) = -0.4266598079301573103267231066937
absolute error = 4.449272895984e-20
relative error = 1.0428150984196594661645145816240e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.9044121893788259160370815224114
y2[1] (numeric) = -0.90441218937882591623648183490962
absolute error = 1.9940031249822e-19
relative error = 2.2047503874884015023227377805737e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2674.5MB, alloc=40.3MB, time=34.60
TOP MAIN SOLVE Loop
x[1] = 1.14
y1[1] (closed_form) = -0.41759450395835809217518674082258
y1[1] (numeric) = -0.4175945039583580921286726547205
absolute error = 4.651408610208e-20
relative error = 1.1138577175028701057861896654935e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.9086334961158832645942155781022
y2[1] (numeric) = -0.9086334961158832647990930766836
absolute error = 2.0487749858140e-19
relative error = 2.2547869901031118520665742078300e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2717.0MB, alloc=40.3MB, time=35.14
TOP MAIN SOLVE Loop
x[1] = 1.15
y1[1] (closed_form) = -0.40848744088415729815257671880992
y1[1] (numeric) = -0.40848744088415729810398631419511
absolute error = 4.859040461481e-20
relative error = 1.1895201602682742681125828127559e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.91276394026052108094403304975368
y2[1] (numeric) = -0.91276394026052108115442533523533
absolute error = 2.1039228548165e-19
relative error = 2.3050021610362897831267234842066e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2759.3MB, alloc=40.3MB, time=35.69
TOP MAIN SOLVE Loop
x[1] = 1.16
y1[1] (closed_form) = -0.39933952940627315445163962339401
y1[1] (numeric) = -0.39933952940627315440091757195955
absolute error = 5.072205143446e-20
relative error = 1.2701485252379629867031640017383e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.91680310877176692661866166687433
y2[1] (numeric) = -0.91680310877176692683460452416053
absolute error = 2.1594285728620e-19
relative error = 2.3553896711312066718274349306988e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2801.7MB, alloc=40.3MB, time=36.24
TOP MAIN SOLVE Loop
x[1] = 1.17
y1[1] (closed_form) = -0.3901516843082302153326619350505
y1[1] (numeric) = -0.39015168430823021527975255975873
absolute error = 5.290937529177e-20
relative error = 1.3561232059162452627599471820293e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.92075059773613563957301300896203
y2[1] (numeric) = -0.92075059773613563979454039778343
absolute error = 2.2152738882140e-19
relative error = 2.4059434701000788651797791269158e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2844.2MB, alloc=40.3MB, time=36.79
TOP MAIN SOLVE Loop
x[1] = 1.18
y1[1] (closed_form) = -0.38092482436688177302959946671276
y1[1] (numeric) = -0.38092482436688177297444676009201
absolute error = 5.515270662075e-20
relative error = 1.4478632814864944380305885867278e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.92460601240802034610753802587476
y2[1] (numeric) = -0.92460601240802034633468207183713
absolute error = 2.2714404596237e-19
relative error = 2.4566576781260791584635039483007e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2886.6MB, alloc=40.3MB, time=37.34
TOP MAIN SOLVE Loop
x[1] = 1.19
y1[1] (closed_form) = -0.37165987226053293806567955835047
y1[1] (numeric) = -0.37165987226053293800822720087977
absolute error = 5.745235747070e-20
relative error = 1.5458315992323754330336236756573e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.92836896724916669260202111160267
y2[1] (numeric) = -0.92836896724916669283481209754656
absolute error = 2.3279098594389e-19
relative error = 2.5075265778612652570307686331719e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2928.7MB, alloc=40.3MB, time=37.88
TOP MAIN SOLVE Loop
x[1] = 1.2
y1[1] (closed_form) = -0.36235775447667357763837335562308
y1[1] (numeric) = -0.36235775447667357757856473420177
absolute error = 5.980862142131e-20
relative error = 1.6505406792711571707505024619135e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.93203908596722634967013443549483
y2[1] (numeric) = -0.93203908596722634990860079316766
absolute error = 2.3846635767283e-19
relative error = 2.5585446068000552138825521214185e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=2970.8MB, alloc=40.3MB, time=38.42
TOP MAIN SOLVE Loop
x[1] = 1.21
y1[1] (closed_form) = -0.35301940121933033870301071366479
y1[1] (numeric) = -0.35301940121933033864078894016371
absolute error = 6.222177350108e-20
relative error = 1.7625596011484286828073555814313e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.93561600155338593341646488854361
y2[1] (numeric) = -0.93561600155338593366063319058551
absolute error = 2.4416830204190e-19
relative error = 2.6097063500037610147288332803635e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3013.0MB, alloc=40.3MB, time=38.96
TOP MAIN SOLVE Loop
x[1] = 1.22
y1[1] (closed_form) = -0.3436457463160470204755229744352
y1[1] (numeric) = -0.34364574631604702041083090432657
absolute error = 6.469207010863e-20
relative error = 1.8825220682095523724683376229908e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.93909935631906758093524527188837
y2[1] (numeric) = -0.93909935631906758118514022413307
absolute error = 2.4989495224470e-19
relative error = 2.6610065331553257742977801195357e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3055.1MB, alloc=40.3MB, time=39.51
TOP MAIN SOLVE Loop
x[1] = 1.23
y1[1] (closed_form) = -0.33423772712450259823954724549766
y1[1] (numeric) = -0.33423772712450259817232749656031
absolute error = 6.721974893735e-20
relative error = 2.0111358916796019142180227754503e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.94248880193169751002382356538924
y2[1] (numeric) = -0.9424888019316975102794679994813
absolute error = 2.5564443409206e-19
relative error = 2.7124400159248432184541609573376e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3097.2MB, alloc=40.3MB, time=40.06
TOP MAIN SOLVE Loop
x[1] = 1.24
y1[1] (closed_form) = -0.32479628443877623657769341569738
y1[1] (numeric) = -0.32479628443877623650788838679418
absolute error = 6.980502890320e-20
relative error = 2.1491941948725763731311196403407e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.94578399944953898628470596308179
y2[1] (numeric) = -0.94578399944953898654612082941139
absolute error = 2.6141486632960e-19
relative error = 2.7640017856270302995473997595232e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3139.4MB, alloc=40.3MB, time=40.60
TOP MAIN SOLVE Loop
x[1] = 1.25
y1[1] (closed_form) = -0.31532236239526866544753855243804
y1[1] (numeric) = -0.31532236239526866537509044236252
absolute error = 7.244811007552e-20
relative error = 2.2975887128710369603159872843841e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.94898461935558621434849084703605
y2[1] (numeric) = -0.94898461935558621461569520799256
absolute error = 2.6720436095651e-19
relative error = 2.8156869511537157339836781480276e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3181.6MB, alloc=40.3MB, time=41.15
TOP MAIN SOLVE Loop
x[1] = 1.26
y1[1] (closed_form) = -0.30581690837828932688634248917648
y1[1] (numeric) = -0.30581690837828932681119331556521
absolute error = 7.514917361127e-20
relative error = 2.4573256596496617847911532262705e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.95209034159051576385681622142542
y2[1] (numeric) = -0.95209034159051576412982724497083
absolute error = 2.7301102354541e-19
relative error = 2.8674907371639867492272598638504e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3223.7MB, alloc=40.3MB, time=41.69
TOP MAIN SOLVE Loop
x[1] = 1.27
y1[1] (closed_form) = -0.29628087292531873355113701608796
y1[1] (numeric) = -0.2962808729253187334732286343956
absolute error = 7.790838169236e-20
relative error = 2.6295447601167886827088341745080e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.95510085558469223509018174218289
y2[1] (numeric) = -0.95510085558469223536901469574626
absolute error = 2.7883295356337e-19
relative error = 2.9194084785179514173444145387507e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3265.8MB, alloc=40.3MB, time=42.24
TOP MAIN SOLVE Loop
x[1] = 1.28
y1[1] (closed_form) = -0.28671520963195551277938689359259
y1[1] (numeric) = -0.28671520963195551269866101612642
absolute error = 8.072587746617e-20
relative error = 2.8155422089324971233111533717092e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.95801586028922496370075385916029
y2[1] (numeric) = -0.95801586028922496398542210385422
absolute error = 2.8466824469393e-19
relative error = 2.9714356149384485577621856846810e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3308.0MB, alloc=40.3MB, time=42.78
TOP MAIN SOLVE Loop
x[1] = 1.29
y1[1] (closed_form) = -0.27712087505655764138660609006118
y1[1] (numeric) = -0.27712087505655764130300430507184
absolute error = 8.360178498934e-20
relative error = 3.0167985350175333789662714233328e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.96083506420607265890556129128537
y2[1] (numeric) = -0.96083506420607265919607627644554
absolute error = 2.9051498516017e-19
relative error = 3.0235676858881009442304283869563e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3350.2MB, alloc=40.3MB, time=43.32
TOP MAIN SOLVE Loop
x[1] = 1.3
y1[1] (closed_form) = -0.26749882862458740699798410929287
y1[1] (numeric) = -0.26749882862458740691144790011807
absolute error = 8.653620917480e-20
relative error = 3.2350126398589374143530934143459e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.96355818541719296470134863003955
y2[1] (numeric) = -0.96355818541719296499771988808819
absolute error = 2.9637125804864e-19
relative error = 3.0758003256473792948100962564061e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3392.4MB, alloc=40.3MB, time=43.87
TOP MAIN SOLVE Loop
x[1] = 1.31
y1[1] (closed_form) = -0.2578500325326696613381769786162
y1[1] (numeric) = -0.25785003253266966124864774287419
absolute error = 8.952923574201e-20
relative error = 3.4721436667131940047011004860305e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.9661849516127340291692578059375
y2[1] (numeric) = -0.96618495161273402947149294757186
absolute error = 3.0223514163436e-19
relative error = 3.1281292585842487994055188944927e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3434.5MB, alloc=40.3MB, time=44.42
TOP MAIN SOLVE Loop
x[1] = 1.32
y1[1] (closed_form) = -0.24817545165237295957398272942735
y1[1] (numeric) = -0.2481754516523729594814017982569
absolute error = 9.258093117045e-20
relative error = 3.7304628863990535720591771860363e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.96871510011826526273589984597277
y2[1] (numeric) = -0.96871510011826526304400455567933
absolute error = 3.0810470970656e-19
relative error = 3.1805502946010146675366858047040e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3476.6MB, alloc=40.3MB, time=44.96
TOP MAIN SOLVE Loop
x[1] = 1.33
y1[1] (closed_form) = -0.23847605343372320751578498601058
y1[1] (numeric) = -0.23847605343372320742009364335408
absolute error = 9.569134265650e-20
relative error = 4.0126185115309428097654091162737e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.9711483779210445623376830377638
y2[1] (numeric) = -0.97114837792104456265166106965904
absolute error = 3.1397803189524e-19
relative error = 3.2330593247488980658872955382290e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3518.8MB, alloc=40.3MB, time=45.50
TOP MAIN SOLVE Loop
x[1] = 1.34
y1[1] (closed_form) = -0.22875280780845946523263949230014
y1[1] (numeric) = -0.2287528078084594651337789942268
absolute error = 9.886049807334e-20
relative error = 4.3217173603446391543914854826124e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.97348454169531937478787034808955
y2[1] (numeric) = -0.9734845416953193751077235220882
absolute error = 3.1985317399865e-19
relative error = 3.2856523170016341175489772607611e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3560.9MB, alloc=40.3MB, time=46.05
TOP MAIN SOLVE Loop
x[1] = 1.35
y1[1] (closed_form) = -0.21900668709304158142002217301063
y1[1] (numeric) = -0.21900668709304158131793376707625
absolute error = 1.0208840593438e-19
relative error = 4.6614287120378808385668078615602e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.97572335782665906926111353926522
y2[1] (numeric) = -0.97572335782665906958684173757648
absolute error = 3.2572819831126e-19
relative error = 3.3383253121744661735580851631842e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3603.1MB, alloc=40.3MB, time=46.59
TOP MAIN SOLVE Loop
x[1] = 1.36
y1[1] (closed_form) = -0.20923866589141935767597525239186
y1[1] (numeric) = -0.20923866589141935757060019703207
absolute error = 1.0537505535979e-19
relative error = 5.0361177228339091837103888465964e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.97786460243531618567849243942663
y2[1] (numeric) = -0.97786460243531618601009360337933
absolute error = 3.3160116395270e-19
relative error = 3.3910744199847929643538869129142e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3645.2MB, alloc=40.3MB, time=47.14
TOP MAIN SOLVE Loop
x[1] = 1.37
y1[1] (closed_form) = -0.19944972099757296568819838964531
y1[1] (numeric) = -0.19944972099757296557947797359886
absolute error = 1.0872041604645e-19
relative error = 5.4510187080067653212641240189791e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.97990806139861422288768850489193
y2[1] (numeric) = -0.97990806139861422322515863208897
absolute error = 3.3747012719704e-19
relative error = 3.4438958152397668110437535036469e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3687.3MB, alloc=40.3MB, time=47.68
TOP MAIN SOLVE Loop
x[1] = 1.38
y1[1] (closed_form) = -0.1896408312978343632091500735982
y1[1] (numeric) = -0.18964083129783436309702563535707
absolute error = 1.1212443824113e-19
relative error = 5.9124629160181510299858337865781e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.98185353037235972787813108520605
y2[1] (numeric) = -0.98185353037235972822146422700892
absolute error = 3.4333314180287e-19
relative error = 3.4967857341477784528458153897778e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3729.5MB, alloc=40.3MB, time=48.22
TOP MAIN SOLVE Loop
x[1] = 1.39
y1[1] (closed_form) = -0.17981297767299947659616321780405
y1[1] (numeric) = -0.17981297767299947648057616508703
absolute error = 1.1558705271702e-19
relative error = 6.4281818928120908129591175978668e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.98370081481127654484003822444291
y2[1] (numeric) = -0.98370081481127654518922648378679
absolute error = 3.4918825934388e-19
relative error = 3.5497404707433522727739476841513e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3771.6MB, alloc=40.3MB, time=48.77
TOP MAIN SOLVE Loop
x[1] = 1.4
y1[1] (closed_form) = -0.16996714290024093861674803520365
y1[1] (numeric) = -0.16996714290024093849763986445022
absolute error = 1.1910817075343e-19
relative error = 7.0077174164972774291372055009326e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.9854497299884601806594745788061
y2[1] (numeric) = -0.98544972998846018101450810834598
absolute error = 3.5503352953988e-19
relative error = 3.6027563734178253391750061642463e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3813.7MB, alloc=40.3MB, time=49.31
TOP MAIN SOLVE Loop
x[1] = 1.41
y1[1] (closed_form) = -0.16010431155483119016356254936092
y1[1] (numeric) = -0.16010431155483119004087486524186
absolute error = 1.2268768411906e-19
relative error = 7.6629843960849826668025226523224e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.98710010101385034142908886194224
y2[1] (numeric) = -0.98710010101385034178995586253057
absolute error = 3.6086700058833e-19
relative error = 3.6558298415498445060820460993233e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3855.9MB, alloc=40.3MB, time=49.86
TOP MAIN SOLVE Loop
x[1] = 1.42
y1[1] (closed_form) = -0.15022546991168577348698210297591
y1[1] (numeric) = -0.15022546991168577336065663791765
absolute error = 1.2632546505826e-19
relative error = 8.4090577405099110693841647452462e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.9886517628517197927362734733357
y2[1] (numeric) = -0.98865176285171979310296019283185
absolute error = 3.6668671949615e-19
relative error = 3.7089573222269821213803196769100e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=3898.0MB, alloc=40.3MB, time=50.40
TOP MAIN SOLVE Loop
x[1] = 1.43
y1[1] (closed_form) = -0.14033160584673666253389762457492
y1[1] (numeric) = -0.14033160584673666240387625829392
absolute error = 1.3002136628100e-19
relative error = 9.2652945497540302168407521744264e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.99010456033717779485729149548183
y2[1] (numeric) = -0.99010456033717779522978222789396
absolute error = 3.7249073241213e-19
relative error = 3.7621353070556421972364406897508e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=3940.2MB, alloc=40.3MB, time=50.94
x[1] = 1.44
y1[1] (closed_form) = -0.13042370873814549297752015612917
y1[1] (numeric) = -0.13042370873814549284374493517343
absolute error = 1.3377522095574e-19
relative error = 1.0256971086777129666446264124422e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.99145834819168646252760446395798
y2[1] (numeric) = -0.99145834819168646290588154891735
absolute error = 3.7827708495937e-19
relative error = 3.8153603290476778306946018735873e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=3982.3MB, alloc=40.3MB, time=51.48
x[1] = 1.45
y1[1] (closed_form) = -0.12050276936736657053286662724802
y1[1] (numeric) = -0.12050276936736657039527978454206
absolute error = 1.3758684270596e-19
relative error = 1.1417732839525925279632965238565e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.99271299103758849766535413432301
y2[1] (numeric) = -0.99271299103758849804939795689122
absolute error = 3.8404382256821e-19
relative error = 3.8686289595828247294334033742750e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=4024.5MB, alloc=40.3MB, time=52.03
x[1] = 1.46
y1[1] (closed_form) = -0.11056977982006955117464810912337
y1[1] (numeric) = -0.11056977982006955103319208351351
absolute error = 1.4145602560986e-19
relative error = 1.2793371375076599171192542648593e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.99386836341164484228683230125003
y2[1] (numeric) = -0.99386836341164484267662129205929
absolute error = 3.8978899080926e-19
relative error = 3.9219378054376749797214775575184e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=4066.7MB, alloc=40.3MB, time=52.58
x[1] = 1.47
y1[1] (closed_form) = -0.10062573338693170090697460146241
y1[1] (numeric) = -0.10062573338693170076159205725894
absolute error = 1.4538254420347e-19
relative error = 1.4447849402939197034946508567679e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.99492434977758089785992846273557
y2[1] (numeric) = -0.99492434977758089825543909846207
absolute error = 3.9551063572650e-19
relative error = 3.9752835058757773775756178845178e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=4108.8MB, alloc=40.3MB, time=53.12
x[1] = 1.48
y1[1] (closed_form) = -0.090671624464309655776226540647838
y1[1] (numeric) = -0.09067162446430965562686038716087
absolute error = 1.49366153486968e-19
relative error = 1.6473307318516367915100668634830e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.99588084453764005648407513256269
y2[1] (numeric) = -0.99588084453764005688528193673351
absolute error = 4.0120680417082e-19
relative error = 4.0286627297976519190847114120990e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=4150.9MB, alloc=40.3MB, time=53.66
x[1] = 1.49
y1[1] (closed_form) = -0.080708448454800614868318484563714
y1[1] (numeric) = -0.080708448454800614714911895629214
absolute error = 1.53406588934500e-19
relative error = 1.9007500685682581841266190359047e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.9967377520431433885532007170437
y2[1] (numeric) = -0.99673775204314338896007626117695
absolute error = 4.0687554413325e-19
relative error = 4.0820721729384095548341484344412e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=4193.1MB, alloc=40.3MB, time=54.21
x[1] = 1.5
y1[1] (closed_form) = -0.070737201667702910088189851434269
y1[1] (numeric) = -0.070737201667702909930686284927074
absolute error = 1.57503566507195e-19
relative error = 2.2266016013340226902991186102529e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.99749498660405443094172337114149
y2[1] (numeric) = -0.99749498660405443135423827621999
absolute error = 4.1251490507850e-19
relative error = 4.1355085551146096017425152796105e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=4235.2MB, alloc=40.3MB, time=54.75
x[1] = 1.51
y1[1] (closed_form) = -0.060758881219385906581595514916193
y1[1] (numeric) = -0.060758881219385906419938732246601
absolute error = 1.61656782669592e-19
relative error = 2.6606280337172059957217264019352e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.99815247249754811924273786483671
y2[1] (numeric) = -0.99815247249754811966086080311503
absolute error = 4.1812293827832e-19
relative error = 4.1889686175109593304604573730508e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=4277.3MB, alloc=40.3MB, time=55.30
x[1] = 1.52
y1[1] (closed_form) = -0.050774484933579196726129270152727
y1[1] (numeric) = -0.050774484933579196560263355743354
absolute error = 1.65865914409373e-19
relative error = 3.2667178136095525390165788964774e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.99871014397558300717231239411685
y2[1] (numeric) = -0.99871014397558300759601009126173
absolute error = 4.2369769714488e-19
relative error = 4.2424491200045204004005590332705e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=4319.4MB, alloc=40.3MB, time=55.84
x[1] = 1.53
y1[1] (closed_form) = -0.040785011241591058688989007076121
y1[1] (numeric) = -0.04078501124159105851885838781569
absolute error = 1.70130619260431e-19
relative error = 4.1714005729373940678402577977152e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.99916794527147601592426506870898
y2[1] (numeric) = -0.99916794527147601635350230627304
absolute error = 4.2923723756406e-19
relative error = 4.2959468385210791241464970596121e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=4361.6MB, alloc=40.3MB, time=56.38
x[1] = 1.54
y1[1] (closed_form) = -0.030791459082466157622476807076397
y1[1] (numeric) = -0.030791459082466157448026271747123
absolute error = 1.74450535329274e-19
relative error = 5.6655494909175269240750168151452e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.99952583060547905600596353844003
y2[1] (numeric) = -0.99952583060547905644070315666842
absolute error = 4.3473961822839e-19
relative error = 4.3494585624169351736420246881661e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=4403.7MB, alloc=40.3MB, time=56.93
x[1] = 1.55
y1[1] (closed_form) = -0.020794827803092473643912774695556
y1[1] (numeric) = -0.020794827803092473465087493370795
absolute error = 1.78825281324761e-19
relative error = 8.5995076765274896462337214209917e-16 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.99978376418935696389761134763447
y2[1] (numeric) = -0.99978376418935696433781424860448
absolute error = 4.4020290097001e-19
relative error = 4.4029810918857498753519712779903e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=4445.9MB, alloc=40.3MB, time=57.47
x[1] = 1.56
y1[1] (closed_form) = -0.010796117058267445823920663760906
y1[1] (numeric) = -0.010796117058267445640666207169755
absolute error = 1.83254456591151e-19
relative error = 1.6974107968829263661820343440822e-15 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 17
h = 0.001
y2[1] (closed_form) = -0.99994172022996629574517002341348
y2[1] (numeric) = -0.99994172022996629619079517450676
absolute error = 4.4562515109328e-19
relative error = 4.4565112353827507259646065442982e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=4488.1MB, alloc=40.3MB, time=58.02
x[1] = 1.57
y1[1] (closed_form) = -0.00079632671073332548540853364535419
y1[1] (numeric) = -0.00079632671073332529767089250085802
absolute error = 1.8773764114449617e-19
relative error = 2.3575454472902378729619752932501e-14 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 16
h = 0.001
y2[1] (closed_form) = -0.99999968293183462021052992382333
y2[1] (numeric) = -0.99999968293183462066153436153037
absolute error = 4.5100443770704e-19
relative error = 4.5100458070623498240712063898226e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=4530.2MB, alloc=40.3MB, time=58.56
x[1] = 1.58
y1[1] (closed_form) = 0.0092035432688082648053890569827275
y1[1] (numeric) = 0.0092035432688082649976634526950694
absolute error = 1.922743957123419e-19
relative error = 2.0891344789346424276464130894318e-15 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 17
h = 0.001
y2[1] (closed_form) = -0.99995764649874005255179423225172
y2[1] (numeric) = -0.99995764649874005300813306630831
absolute error = 4.5633883405659e-19
relative error = 4.5635816242259715277072209935009e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.59
y1[1] (closed_form) = 0.019202492901692568095027346243403
y1[1] (numeric) = 0.019202492901692568291891608020156
absolute error = 1.96864261776753e-19
relative error = 1.0252015859847070431459891485622e-15 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 17
h = 0.001
y2[1] (closed_form) = -0.99981561513429087198158434374551
y2[1] (numeric) = -0.99981561513429087244321076160073
absolute error = 4.6162641785522e-19
relative error = 4.6171155047745113811051429870703e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=4572.4MB, alloc=40.3MB, time=59.10
TOP MAIN SOLVE Loop
x[1] = 1.6
y1[1] (closed_form) = 0.029199522301288726205770462946499
y1[1] (numeric) = 0.02919952230128872640727722456714
absolute error = 2.01506761620641e-19
relative error = 6.9010293915578017033623617785620e-16 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.99957360304150516434211382554623
y2[1] (numeric) = -0.99957360304150516480897909716158
absolute error = 4.6686527161535e-19
relative error = 4.6706442646621632946539961106911e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=4614.6MB, alloc=40.3MB, time=59.65
TOP MAIN SOLVE Loop
x[1] = 1.61
y1[1] (closed_form) = 0.039193631772987609585327609601018
y1[1] (numeric) = 0.039193631772987609791529007978446
absolute error = 2.06201398377428e-19
relative error = 5.2610944444179510085891459802533e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.9992316344213905321324131478443
y2[1] (numeric) = -0.99923163442139053260446663082347
absolute error = 4.7205348297917e-19
relative error = 4.7241647153466537636846908363663e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=4656.8MB, alloc=40.3MB, time=60.20
TOP MAIN SOLVE Loop
x[1] = 1.62
y1[1] (closed_form) = 0.049183821914170445143744274712327
y1[1] (numeric) = 0.049183821914170445354691930796295
absolute error = 2.10947656083968e-19
relative error = 4.2889642950498620509504995521792e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.9987897434705240139155188912468
y2[1] (numeric) = -0.99878974347052401439270803629543
absolute error = 4.7718914504863e-19
relative error = 4.7776736612305096646746076781379e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=4699.0MB, alloc=40.3MB, time=60.74
TOP MAIN SOLVE Loop
x[1] = 1.63
y1[1] (closed_form) = 0.059169093714148245297971697419802
y1[1] (numeric) = 0.059169093714148245513716697156619
absolute error = 2.15744999736817e-19
relative error = 3.6462447908886769763393465812656e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.9982479743776324551116699849331
y2[1] (numeric) = -0.99824797437763245559394034164815
absolute error = 4.8227035671505e-19
relative error = 4.8311678970921650034467306839791e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=4741.2MB, alloc=40.3MB, time=61.28
TOP MAIN SOLVE Loop
x[1] = 1.64
y1[1] (closed_form) = 0.069148448654062044364492707456605
y1[1] (numeric) = 0.069148448654062044585085582808364
absolute error = 2.20592875351759e-19
relative error = 3.1901348424365631916647305323939e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.99760638131917367213758197436794
y2[1] (numeric) = -0.99760638131917367262487719735585
absolute error = 4.8729522298791e-19
relative error = 4.8846442054985714569576909747643e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=4783.4MB, alloc=40.3MB, time=61.82
TOP MAIN SOLVE Loop
x[1] = 1.65
y1[1] (closed_form) = 0.079120888806733952359614597341276
y1[1] (numeric) = 0.079120888806733952585105307367907
absolute error = 2.25490710026631e-19
relative error = 2.8499516806166055247286886130949e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.99686502845391885177170304020219
y2[1] (numeric) = -0.99686502845391885226396489552525
absolute error = 4.9226185532306e-19
relative error = 4.9380993541977315821816324857118e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=4825.5MB, alloc=40.3MB, time=62.37
TOP MAIN SOLVE Loop
x[1] = 1.66
y1[1] (closed_form) = 0.089085416936459041185257931650621
y1[1] (numeric) = 0.089085416936459041415695843658047
absolute error = 2.30437912007426e-19
relative error = 2.5867074537214982311044695885466e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.99602398991653672750100059061296
y2[1] (numeric) = -0.99602398991653672799816896256308
absolute error = 4.9716837195012e-19
relative error = 4.9915300934848059597233981846865e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=4867.7MB, alloc=40.3MB, time=62.91
TOP MAIN SOLVE Loop
x[1] = 1.67
y1[1] (closed_form) = 0.099041036598728084094782342448611
y1[1] (numeric) = 0.099041036598728084330216213206277
absolute error = 2.35433870757666e-19
relative error = 2.3771345579867397637187682703614e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.99508334981018017442629724653424
y2[1] (numeric) = -0.99508334981018017492831014473352
absolute error = 5.0201289819928e-19
relative error = 5.0449331535397796890440495787105e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=4909.9MB, alloc=40.3MB, time=63.46
TOP MAIN SOLVE Loop
x[1] = 1.68
y1[1] (closed_form) = 0.10898675223987117624800473417282
y1[1] (numeric) = 0.10898675223987117648848269120384
absolute error = 2.4047795703102e-19
relative error = 2.2064879638008400942715275695268e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.99404320219807596406048786919357
y2[1] (numeric) = -0.99404320219807596456728143602065
absolute error = 5.0679356682708e-19
relative error = 5.0983052417282647179856025204901e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=4952.0MB, alloc=40.3MB, time=64.00
TOP MAIN SOLVE Loop
x[1] = 1.69
y1[1] (closed_form) = 0.11892156929661227207639046983309
y1[1] (numeric) = 0.11892156929661227232195999278033
absolute error = 2.4556952294724e-19
relative error = 2.0649704204183887939551356628875e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.99290365109411852003714929394559
y2[1] (numeric) = -0.99290365109411852054865781228699
absolute error = 5.1150851834140e-19
relative error = 5.1516430398634267700244093157094e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=4994.2MB, alloc=40.3MB, time=64.54
TOP MAIN SOLVE Loop
x[1] = 1.7
y1[1] (closed_form) = 0.12884449429552468408764285733487
y1[1] (numeric) = 0.12884449429552468433835075940614
absolute error = 2.5070790207127e-19
relative error = 1.9458177351081283189333464770177e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.99166481045246861534613339864788
y2[1] (numeric) = -0.99166481045246861586228929997351
absolute error = 5.1615590132563e-19
relative error = 5.2049432014243064213363317451228e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5036.4MB, alloc=40.3MB, time=65.09
TOP MAIN SOLVE Loop
x[1] = 1.71
y1[1] (closed_form) = 0.13875453495237759764268978305111
y1[1] (numeric) = 0.13875453495237759789858219254665
absolute error = 2.5589240949554e-19
relative error = 1.8442093412180414807962534764067e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.99032680415615805121775222386113
y2[1] (numeric) = -0.99032680415615805173848609662287
absolute error = 5.2073387276174e-19
relative error = 5.2582023487231487357730706235558e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5078.6MB, alloc=40.3MB, time=65.64
TOP MAIN SOLVE Loop
x[1] = 1.72
y1[1] (closed_form) = 0.14865070027136366713637828033119
y1[1] (numeric) = 0.14865070027136366739750062225691
absolute error = 2.6112234192572e-19
relative error = 1.7566169647975958315604977407045e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.98888976600470145717817065708548
y2[1] (numeric) = -0.98888976600470145770341125543786
absolute error = 5.2524059835238e-19
relative error = 5.3114170700183265928246082980413e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5120.7MB, alloc=40.3MB, time=66.18
TOP MAIN SOLVE Loop
x[1] = 1.73
y1[1] (closed_form) = 0.15853200064419777090494835134257
y1[1] (numeric) = 0.158532000644197771171345329112
absolute error = 2.6639697776943e-19
relative error = 1.6803987629432598004221186253490e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.98735383970071645108567767622206
y2[1] (numeric) = -0.98735383970071645161535192906413
absolute error = 5.2967425284207e-19
relative error = 5.3645839165685846859109200839657e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5162.9MB, alloc=40.3MB, time=66.72
TOP MAIN SOLVE Loop
x[1] = 1.74
y1[1] (closed_form) = 0.16839744794907701506737731534509
y1[1] (numeric) = 0.16839744794907701533909289257331
absolute error = 2.7171557722822e-19
relative error = 1.6135373815782893560853409620905e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.98571917883555349712068269566555
y2[1] (numeric) = -0.98571917883555349765471571600258
absolute error = 5.3403302033703e-19
relative error = 5.4176993996189879551067551398072e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5205.0MB, alloc=40.3MB, time=67.26
TOP MAIN SOLVE Loop
x[1] = 1.75
y1[1] (closed_form) = 0.17824605564949209038267694394263
y1[1] (numeric) = 0.17824605564949209065975432633552
absolute error = 2.7707738239289e-19
relative error = 1.5544657152904551696686870596358e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.98398594687393689873166293696799
y2[1] (numeric) = -0.98398594687393689926997803159215
absolute error = 5.3831509462416e-19
relative error = 5.4707599873184580859629829331344e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5247.1MB, alloc=40.3MB, time=67.80
TOP MAIN SOLVE Loop
x[1] = 1.76
y1[1] (closed_form) = 0.1880768388928801010698001765041
y1[1] (numeric) = 0.18807683889288010135228179384595
absolute error = 2.8248161734185e-19
relative error = 1.5019479219487440960105306783123e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.98215431713761846242496809945596
y2[1] (numeric) = -0.98215431713761846296748677894458
absolute error = 5.4251867948862e-19
relative error = 5.5237621015578434328485460402336e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5289.3MB, alloc=40.3MB, time=68.35
TOP MAIN SOLVE Loop
x[1] = 1.77
y1[1] (closed_form) = 0.19788881460910900038948584173039
y1[1] (numeric) = 0.19788881460910900067741332997306
absolute error = 2.8792748824267e-19
relative error = 1.4549962756177753078455058651772e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.98022447278804546701848144889842
y2[1] (numeric) = -0.98022447278804546756512343792868
absolute error = 5.4664198903026e-19
relative error = 5.5767021147253148537780396735264e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5331.4MB, alloc=40.3MB, time=68.89
TOP MAIN SOLVE Loop
x[1] = 1.78
y1[1] (closed_form) = 0.20768100160878378462655329031263
y1[1] (numeric) = 0.20768100160878378491996747376937
absolute error = 2.9341418345674e-19
relative error = 1.4128118661978282988475314228977e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.9781966068080446715477686473056
y2[1] (numeric) = -0.97819660680804467209845189528435
absolute error = 5.5068324797875e-19
relative error = 5.6295763463715706556470067384888e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5373.5MB, alloc=40.3MB, time=69.44
TOP MAIN SOLVE Loop
x[1] = 1.79
y1[1] (closed_form) = 0.21745242068136461493517026446461
y1[1] (numeric) = 0.21745242068136461523411113811191
absolute error = 2.9894087364730e-19
relative error = 1.3747415306327690735518911386493e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.97607092198252419340866043310862
y2[1] (numeric) = -0.97607092198252419396330112511605
absolute error = 5.5464069200743e-19
relative error = 5.6823810597787731170409612885822e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5415.7MB, alloc=40.3MB, time=69.98
TOP MAIN SOLVE Loop
x[1] = 1.8
y1[1] (closed_form) = 0.22720209469308705531667430653058
y1[1] (numeric) = 0.22720209469308705562118101842085
absolute error = 3.0450671189027e-19
relative error = 1.3402460584776247965829212612478e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.97384763087819518653237317884336
y2[1] (numeric) = -0.9738476308781951870908857468891
absolute error = 5.5851256804574e-19
relative error = 5.7351124584251972198044437505600e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5457.8MB, alloc=40.3MB, time=70.52
TOP MAIN SOLVE Loop
x[1] = 1.81
y1[1] (closed_form) = 0.23692904868467463478774985084198
y1[1] (numeric) = 0.23692904868467463509786068463047
absolute error = 3.1011083378849e-19
relative error = 1.3088763725262406307321226966202e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.97152695582231534740845126909038
y2[1] (numeric) = -0.97152695582231534797074840368063
absolute error = 5.6229713459025e-19
relative error = 5.7877666823388658628555047140192e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5499.9MB, alloc=40.3MB, time=71.06
TOP MAIN SOLVE Loop
x[1] = 1.82
y1[1] (closed_form) = 0.24663230996883396256417104483087
y1[1] (numeric) = 0.24663230996883396287992340241973
absolute error = 3.1575235758886e-19
relative error = 1.2802554443445000742435754776762e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.96910912888045637458721531849805
y2[1] (numeric) = -0.96910912888045637515320798051232
absolute error = 5.6599266201427e-19
relative error = 5.8403398043326814991261136477960e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5542.2MB, alloc=40.3MB, time=71.60
TOP MAIN SOLVE Loop
x[1] = 1.83
y1[1] (closed_form) = 0.25631090822752264682983758361853
y1[1] (numeric) = 0.25631090822752264715126796792121
absolute error = 3.2143038430268e-19
relative error = 1.2540643959536515290935793598705e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.96659439183329760489723892974281
y2[1] (numeric) = -0.96659439183329760546683636261869
absolute error = 5.6959743287588e-19
relative error = 5.8928278261117290990252528515097e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5584.4MB, alloc=40.3MB, time=72.15
TOP MAIN SOLVE Loop
x[1] = 1.84
y1[1] (closed_form) = 0.2659638756089802903802829832816
y1[1] (numeric) = 0.26596387560898029070742698111069
absolute error = 3.2714399782909e-19
relative error = 1.2300316991547251996979009609187e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.96398299615244814699489367172712
y2[1] (numeric) = -0.96398299615244814756800341395163
absolute error = 5.7310974222451e-19
relative error = 5.9452266742459855692792584868686e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5626.5MB, alloc=40.3MB, time=72.69
TOP MAIN SOLVE Loop
x[1] = 1.85
y1[1] (closed_form) = 0.2755902468245128601219498354748
y1[1] (numeric) = 0.27559024682451286045484210055617
absolute error = 3.3289226508137e-19
relative error = 1.2079246958741078020333961974450e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.96127520297529993001245916863613
y2[1] (numeric) = -0.96127520297529993058898706654198
absolute error = 5.7652789790585e-19
relative error = 5.9975321959976111700383375547264e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5668.7MB, alloc=40.3MB, time=73.24
TOP MAIN SOLVE Loop
x[1] = 1.86
y1[1] (closed_form) = 0.28518905924502075207093548828912
y1[1] (numeric) = 0.28518905924502075240960972440566
absolute error = 3.3867423611654e-19
relative error = 1.1875428777426112653887693195616e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.9584712830789141819789777659032
y2[1] (numeric) = -0.95847128307891418255882798676839
absolute error = 5.7985022086519e-19
relative error = 6.0497401549948051020358121620286e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5710.8MB, alloc=40.3MB, time=73.78
TOP MAIN SOLVE Loop
x[1] = 1.87
y1[1] (closed_form) = 0.29475935299726089912514806480989
y1[1] (numeric) = 0.29475935299726089946963700907774
absolute error = 3.4448894426785e-19
relative error = 1.1687125133262564240589249527071e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.95557151685294394934425049217263
y2[1] (numeric) = -0.95557151685294394992732553762163
absolute error = 5.8307504544900e-19
relative error = 6.1018462267406756618648468957959e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5753.0MB, alloc=40.3MB, time=74.32
TOP MAIN SOLVE Loop
x[1] = 1.88
y1[1] (closed_form) = 0.30430017105983329547931375952224
y1[1] (numeric) = 0.30430017105983329582964916580248
absolute error = 3.5033540628024e-19
relative error = 1.1512823179167881075294419589318e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.95257619427159536533145742581513
y2[1] (numeric) = -0.95257619427159536591765814551996
absolute error = 5.8620071970483e-19
relative error = 6.1538459939478016695851009925456e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5795.2MB, alloc=40.3MB, time=74.86
TOP MAIN SOLVE Loop
x[1] = 1.89
y1[1] (closed_form) = 0.31381055935888233911038241555123
y1[1] (numeric) = 0.31381055935888233946659503800014
absolute error = 3.5621262244891e-19
relative error = 1.1351199372534035789014607608487e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.94948561486463047096820167213832
y2[1] (numeric) = -0.94948561486463047155742727781787
absolute error = 5.8922560567955e-19
relative error = 6.2057349416879448103618416043672e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5837.3MB, alloc=40.3MB, time=75.41
TOP MAIN SOLVE Loop
x[1] = 1.9
y1[1] (closed_form) = 0.32328956686350342227883369508031
y1[1] (numeric) = 0.32328956686350342264095327184102
absolute error = 3.6211957676071e-19
relative error = 1.1201090721050118360818158440809e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.94630008768741448848970961163496
y2[1] (numeric) = -0.9463000876874144890818576913505
absolute error = 5.9214807971554e-19
relative error = 6.2575084523413956190555703661506e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5879.5MB, alloc=40.3MB, time=75.95
TOP MAIN SOLVE Loop
x[1] = 1.91
y1[1] (closed_form) = 0.33273624568084522946633893939753
y1[1] (numeric) = 0.33273624568084522983439417643619
absolute error = 3.6805523703866e-19
relative error = 1.1061471114622484727293759144055e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.94301993129001054236188657694821
y2[1] (numeric) = -0.94301993129001054295685310969348
absolute error = 5.9496653274527e-19
relative error = 6.3091618003384241986238113215386e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5921.7MB, alloc=40.3MB, time=76.50
TOP MAIN SOLVE Loop
x[1] = 1.92
y1[1] (closed_form) = 0.34214965115089823259923660315905
y1[1] (numeric) = 0.3421496511508982329732551582483
absolute error = 3.7401855508925e-19
relative error = 1.0931431723842285237616603317662e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.93964547368532491842637133968703
y2[1] (numeric) = -0.93964547368532491902405071027084
absolute error = 5.9767937058381e-19
relative error = 6.3606901466750966234841483184549e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=5963.9MB, alloc=40.3MB, time=77.04
TOP MAIN SOLVE Loop
x[1] = 1.93
y1[1] (closed_form) = 0.35152884194095990478728906471187
y1[1] (numeric) = 0.35152884194095990516729753156466
absolute error = 3.8000846685279e-19
relative error = 1.0810164672536693736019676380564e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.93617705231630604661512937274878
y2[1] (numeric) = -0.9361770523163060472154143869684
absolute error = 6.0028501421962e-19
relative error = 6.4120885331934173766944528767590e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6006.1MB, alloc=40.3MB, time=77.58
TOP MAIN SOLVE Loop
x[1] = 1.94
y1[1] (closed_form) = 0.36087288013976720613506768584073
y1[1] (numeric) = 0.36087288013976720652109157839721
absolute error = 3.8602389255648e-19
relative error = 1.0696949363636628148050965449064e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.9326150140222004873089793388657
y2[1] (numeric) = -0.93261501402220048791176123896875
absolute error = 6.0278190010305e-19
relative error = 6.4633518766051201902374265608739e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6048.2MB, alloc=40.3MB, time=78.12
TOP MAIN SOLVE Loop
x[1] = 1.95
y1[1] (closed_form) = 0.37018083135128692845582845913069
y1[1] (numeric) = 0.37018083135128692884789219600127
absolute error = 3.9206373687058e-19
relative error = 1.0591140968575087077662780585778e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.92895971500386929571329703509148
y2[1] (numeric) = -0.92895971500386929631846551552459
absolute error = 6.0516848043311e-19
relative error = 6.5144749622494594073481295173410e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6090.4MB, alloc=40.3MB, time=78.67
TOP MAIN SOLVE Loop
x[1] = 1.96
y1[1] (closed_form) = 0.37945176478815451993156521544745
y1[1] (numeric) = 0.3794517647881545203296921045147
absolute error = 3.9812688906725e-19
relative error = 1.0492160691083402441302977907076e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.92521152078816823258555628949003
y2[1] (numeric) = -0.92521152078816823319299951293198
absolute error = 6.0744322344195e-19
relative error = 6.5654524375624062227001950101381e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6132.6MB, alloc=40.3MB, time=79.21
TOP MAIN SOLVE Loop
x[1] = 1.97
y1[1] (closed_form) = 0.38868475336475204591463981387931
y1[1] (numeric) = 0.38868475336475204631885203706165
absolute error = 4.0421222318234e-19
relative error = 1.0399487494252612630801209972183e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.92137080619139538326395099715317
y2[1] (numeric) = -0.92137080619139538387355561083069
absolute error = 6.0960461367752e-19
relative error = 6.6162788052445355885185994424602e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6174.9MB, alloc=40.3MB, time=79.75
TOP MAIN SOLVE Loop
x[1] = 1.98
y1[1] (closed_form) = 0.39787887378991597815247385990719
y1[1] (numeric) = 0.39787887378991597856279245808707
absolute error = 4.1031859817988e-19
relative error = 1.0312651040540853663185188070197e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.917437955281809840204735217402
y2[1] (numeric) = -0.91743795528180984081638636968572
absolute error = 6.1165115228372e-19
relative error = 6.6669484161012156208485007236318e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6217.1MB, alloc=40.3MB, time=80.30
TOP MAIN SOLVE Loop
x[1] = 1.99
y1[1] (closed_form) = 0.40703320665926554173363571613029
y1[1] (numeric) = 0.40703320665926554215008057424979
absolute error = 4.1644485811950e-19
relative error = 1.0231225642189756588072338126162e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.91341336134122519712879327105761
y2[1] (numeric) = -0.91341336134122519774237462833631
absolute error = 6.1358135727870e-19
relative error = 6.7174554615419457784036734338125e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6259.2MB, alloc=40.3MB, time=80.84
TOP MAIN SOLVE Loop
x[1] = 2
y1[1] (closed_form) = 0.41614683654714238699756822950076
y1[1] (numeric) = 0.41614683654714238742015806182732
absolute error = 4.2258983232656e-19
relative error = 1.0154825057253264274804510408775e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.90929742682568169539601986591174
y2[1] (numeric) = -0.90929742682568169601141362974242
absolute error = 6.1539376383068e-19
relative error = 6.7677939657103531757950042321378e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6301.4MB, alloc=40.3MB, time=81.38
TOP MAIN SOLVE Loop
x[1] = 2.01
y1[1] (closed_form) = 0.42521885209815239251738234016543
y1[1] (numeric) = 0.42521885209815239294613467573038
absolute error = 4.2875233556495e-19
relative error = 1.0083097996463759343529429503263e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.90509056332520095536009971027372
y2[1] (numeric) = -0.90509056332520095597718663480536
absolute error = 6.1708692453164e-19
relative error = 6.8179577772254306636069390524309e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6343.6MB, alloc=40.3MB, time=81.93
TOP MAIN SOLVE Loop
x[1] = 2.02
y1[1] (closed_form) = 0.4342483461183004450517028740902
y1[1] (numeric) = 0.43424834611830044548663404230297
absolute error = 4.3493116821277e-19
relative error = 1.0015724230168594277284664990245e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = 0.001
y2[1] (closed_form) = -0.90079319152262731719701352455371
y2[1] (numeric) = -0.90079319152262731781567293422251
absolute error = 6.1865940966880e-19
relative error = 6.8679405605083294309592294166159e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6385.7MB, alloc=40.3MB, time=82.47
TOP MAIN SOLVE Loop
x[1] = 2.03
y1[1] (closed_form) = 0.4432344156657090830635167316961
y1[1] (numeric) = 0.44323441566570908350464184813666
absolute error = 4.4112511644056e-19
relative error = 9.9524112038551642322505754025656e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.89640574115155990703888883196757
y2[1] (numeric) = -0.896405741151559907658998639461
absolute error = 6.2010980749343e-19
relative error = 6.9177357866629823461313194453025e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6427.9MB, alloc=40.3MB, time=83.01
TOP MAIN SOLVE Loop
x[1] = 2.04
y1[1] (closed_form) = 0.45217616214091193201727020529136
y1[1] (numeric) = 0.45217616214091193246460315768373
absolute error = 4.4733295239237e-19
relative error = 9.8928910863940536603957081784751e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.8919286509533796351715256485842
y2[1] (numeric) = -0.8919286509533796357929623730718
absolute error = 6.2143672448760e-19
relative error = 6.9673367238887135827084436781220e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6470.0MB, alloc=40.3MB, time=83.56
TOP MAIN SOLVE Loop
x[1] = 2.05
y1[1] (closed_form) = 0.4610726913767129021859299941674
y1[1] (numeric) = 0.46107269137671290263948342853664
absolute error = 4.5355343436924e-19
relative error = 9.8369181877802994862598017127472e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.88736236863337542355996660468034
y2[1] (numeric) = -0.88736236863337542418260539030867
absolute error = 6.2263878562833e-19
relative error = 7.0167364273882207198743172790834e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6512.2MB, alloc=40.3MB, time=84.10
TOP MAIN SOLVE Loop
x[1] = 2.06
y1[1] (closed_form) = 0.4699231137276021631231096264879
y1[1] (numeric) = 0.46992311372760216358289493350349
absolute error = 4.5978530701559e-19
relative error = 9.7842666935108731058054878992540e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.8827073508159740500427975851999
y2[1] (numeric) = -0.88270735081597405066651221984929
absolute error = 6.2371463464939e-19
relative error = 7.0659277287407727304748121005198e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6554.3MB, alloc=40.3MB, time=84.64
TOP MAIN SOLVE Loop
x[1] = 2.07
y1[1] (closed_form) = 0.47872654415871995327732713901173
y1[1] (numeric) = 0.47872654415871995374335444051974
absolute error = 4.6602730150801e-19
relative error = 9.7347286711868734818718607241144e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.87796406299907808617345112044384
y2[1] (numeric) = -0.87796406299907808679811405474426
absolute error = 6.2466293430042e-19
relative error = 7.1149032247015323765676836733412e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6596.4MB, alloc=40.3MB, time=85.18
TOP MAIN SOLVE Loop
x[1] = 2.08
y1[1] (closed_form) = 0.48748210233435932844156884977235
y1[1] (numeric) = 0.48748210233435932891384698551913
absolute error = 4.7227813574678e-19
relative error = 9.6881123119233806732022408498160e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.87313297950751649487667680502462
y2[1] (numeric) = -0.87313297950751649550215917162832
absolute error = 6.2548236660370e-19
relative error = 7.1636552653926576620616553754591e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6638.6MB, alloc=40.3MB, time=85.73
TOP MAIN SOLVE Loop
x[1] = 2.09
y1[1] (closed_form) = 0.49618891270599899883706631187045
y1[1] (numeric) = 0.49618891270599899931560282642027
absolute error = 4.7853651454982e-19
relative error = 9.6442403749025652366346627953156e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.86821458344561254282162205872751
y2[1] (numeric) = -0.86821458344561254344779369183573
absolute error = 6.2617163310822e-19
relative error = 7.2121759418412854962137600541130e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6680.8MB, alloc=40.3MB, time=86.27
TOP MAIN SOLVE Loop
x[1] = 2.1
y1[1] (closed_form) = 0.50484610459985745162093852371917
y1[1] (numeric) = 0.50484610459985745210573965356838
absolute error = 4.8480112984921e-19
relative error = 9.6029488082009633570753303635781e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.86320936664887377068075931326902
y2[1] (numeric) = -0.86320936664887377130748876841028
absolute error = 6.2672945514126e-19
relative error = 7.2604570728226781569603132780218e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6722.9MB, alloc=40.3MB, time=86.82
TOP MAIN SOLVE Loop
x[1] = 2.11
y1[1] (closed_form) = 0.51345281230395960347841015707169
y1[1] (numeric) = 0.51345281230395960396948081796195
absolute error = 4.9107066089026e-19
relative error = 9.5640855230051877810998142859688e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.85811782963480885223737550831068
y2[1] (numeric) = -0.85811782963480885286453008236777
absolute error = 6.2715457405709e-19
relative error = 7.3084901909565215784495408506532e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6765.1MB, alloc=40.3MB, time=87.36
TOP MAIN SOLVE Loop
x[1] = 2.12
y1[1] (closed_form) = 0.52200817515470727670690188298389
y1[1] (numeric) = 0.5220081751547072772042456574168
absolute error = 4.9734377443291e-19
relative error = 9.5275093016601224341754531236837e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.85294048155287626061472733365415
y2[1] (numeric) = -0.85294048155287626124217308513737
absolute error = 6.2744575148322e-19
relative error = 7.3562665280100533414693426395775e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6807.3MB, alloc=40.3MB, time=87.90
TOP MAIN SOLVE Loop
x[1] = 2.13
y1[1] (closed_form) = 0.53051133762294484181652620960972
y1[1] (numeric) = 0.53051133762294484232014533456558
absolute error = 5.0361912495586e-19
relative error = 9.4930888228029126641054356245554e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.8476778401335697467185299963159
y2[1] (numeric) = -0.84767784013356974734613176587969
absolute error = 6.2760176956379e-19
relative error = 7.4037769993479826975736583197780e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6849.5MB, alloc=40.3MB, time=88.45
TOP MAIN SOLVE Loop
x[1] = 2.14
y1[1] (closed_form) = 0.5389614493995114201544499120086
y1[1] (numeric) = 0.53896144939951142066434526687135
absolute error = 5.0989535486275e-19
relative error = 9.4607017891697882691254095775327e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.84233043163664572130250663706891
y2[1] (numeric) = -0.84233043163664572193012806826917
absolute error = 6.2762143120026e-19
relative error = 7.4510121874712905528086903696528e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6891.7MB, alloc=40.3MB, time=88.99
TOP MAIN SOLVE Loop
x[1] = 2.15
y1[1] (closed_form) = 0.54735766548027109140415388226403
y1[1] (numeric) = 0.54735766548027109192032497695507
absolute error = 5.1617109469104e-19
relative error = 9.4302341456775455125100450395086e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.83689879079849771787564813704379
y2[1] (numeric) = -0.83689879079849771850315169733299
absolute error = 6.2750356028920e-19
relative error = 7.4979623245779745901017464252500e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6933.9MB, alloc=40.3MB, time=89.54
TOP MAIN SOLVE Loop
x[1] = 2.16
y1[1] (closed_form) = 0.55569914625061260300969874398337
y1[1] (numeric) = 0.55569914625061260353214370730651
absolute error = 5.2244496332314e-19
relative error = 9.4015793770452289302535534536182e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.83138346077868319896103812034632
y2[1] (numeric) = -0.83138346077868319958828512230367
absolute error = 6.2724700195735e-19
relative error = 7.5446172740778765145079164923749e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=6976.1MB, alloc=40.3MB, time=90.08
TOP MAIN SOLVE Loop
x[1] = 2.17
y1[1] (closed_form) = 0.56398505756941013162446999441651
y1[1] (numeric) = 0.56398505756941013215318556261634
absolute error = 5.2871556819983e-19
relative error = 9.3746378756632309378488691020833e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.82578499310560805298105642394338
y2[1] (numeric) = -0.82578499310560805360790704673718
absolute error = 6.2685062279380e-19
relative error = 7.5909665109842130620198303800212e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7018.3MB, alloc=40.3MB, time=90.62
TOP MAIN SOLVE Loop
x[1] = 2.18
y1[1] (closed_form) = 0.57221457085243670057822486766249
y1[1] (numeric) = 0.57221457085243670111320637319855
absolute error = 5.3498150553606e-19
relative error = 9.3493163716381769158705127939925e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.82010394762137421327400974608394
y2[1] (numeric) = -0.82010394762137421390032305716313
absolute error = 6.2631331107919e-19
relative error = 7.6369991010986631573674142562118e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7060.4MB, alloc=40.3MB, time=91.17
TOP MAIN SOLVE Loop
x[1] = 2.19
y1[1] (closed_form) = 0.58038686315522191209020516379695
y1[1] (numeric) = 0.5803868631552219126314465243359
absolute error = 5.4124136053895e-19
relative error = 9.3255274179801237212557157582636e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.814340892425795914434327645905
y2[1] (numeric) = -0.81434089242579591505996162291702
absolute error = 6.2563397701202e-19
relative error = 7.6827036789022454759816301449575e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7102.5MB, alloc=40.3MB, time=91.71
TOP MAIN SOLVE Loop
x[1] = 2.2
y1[1] (closed_form) = 0.58850111725534570852414261265493
y1[1] (numeric) = 0.58850111725534570907163632028312
absolute error = 5.4749370762819e-19
relative error = 9.3031889247992211244404254462350e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.80849640381959018430403691041612
y2[1] (numeric) = -0.80849640381959018492884846334816
absolute error = 6.2481155293204e-19
relative error = 7.7280684240552533120105258708350e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7144.8MB, alloc=40.3MB, time=92.26
TOP MAIN SOLVE Loop
x[1] = 2.21
y1[1] (closed_form) = 0.59655652173415993337760917751863
y1[1] (numeric) = 0.59655652173415993393134628817706
absolute error = 5.5373711065843e-19
relative error = 9.2822237371363228121479787854722e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.80257106624674725251897404255597
y2[1] (numeric) = -0.80257106624674725314281903609646
absolute error = 6.2384499354049e-19
relative error = 7.7730810363987300915994822133709e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7187.1MB, alloc=40.3MB, time=92.80
TOP MAIN SOLVE Loop
x[1] = 2.22
y1[1] (closed_form) = 0.60455227105792951991771443750015
y1[1] (numeric) = 0.60455227105792952047768456064423
absolute error = 5.5997012314408e-19
relative error = 9.2625592517280021752461708338296e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.79656547223608663852085674960916
y2[1] (numeric) = -0.79656547223608663914359002572657
absolute error = 6.2273327611741e-19
relative error = 7.8177287093463658291008884565525e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7229.2MB, alloc=40.3MB, time=93.34
TOP MAIN SOLVE Loop
x[1] = 2.23
y1[1] (closed_form) = 0.61248756565838519341190391068563
y1[1] (numeric) = 0.61248756565838519397809519917177
absolute error = 5.6619128848614e-19
relative error = 9.2441270685637570650751652100710e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.79048022234200476337771012718854
y2[1] (numeric) = -0.79048022234200476399918552792444
absolute error = 6.2147540073590e-19
relative error = 7.8619981015415705108005459242427e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7271.4MB, alloc=40.3MB, time=93.89
TOP MAIN SOLVE Loop
x[1] = 2.24
y1[1] (closed_form) = 0.62036161201267963175076226631044
y1[1] (numeric) = 0.62036161201267963232316140651158
absolute error = 5.7239914020114e-19
relative error = 9.2268626735956169690976201181363e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.7843159250844200106020886706045
y2[1] (numeric) = -0.78431592508442001122215906107767
absolute error = 6.2007039047317e-19
relative error = 7.9058753066429014848760277778067e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7313.6MB, alloc=40.3MB, time=94.43
TOP MAIN SOLVE Loop
x[1] = 2.25
y1[1] (closed_form) = 0.6281736227227390889133890573964
y1[1] (numeric) = 0.62817362272273908949198125954876
absolute error = 5.7859220215236e-19
relative error = 9.2107051493904711460164906982990e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.77807319688792124141096667558776
y2[1] (numeric) = -0.77807319688792124202948396720624
absolute error = 6.1851729161848e-19
relative error = 7.9493458210921418119777836965470e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7355.8MB, alloc=40.3MB, time=94.97
TOP MAIN SOLVE Loop
x[1] = 2.26
y1[1] (closed_form) = 0.63592281659400254617912656874484
y1[1] (numeric) = 0.63592281659400254676389555752766
absolute error = 5.8476898878282e-19
relative error = 9.1955969108772974443835248431011e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.77175266202012584952506163774032
y2[1] (numeric) = -0.77175266202012585014187681161829
absolute error = 6.1681517387797e-19
relative error = 7.9923945097047767238576144727889e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7398.0MB, alloc=40.3MB, time=95.52
TOP MAIN SOLVE Loop
x[1] = 2.27
y1[1] (closed_form) = 0.6436084187135405172361343481243
y1[1] (numeric) = 0.64360841871354051782706235347486
absolute error = 5.9092800535056e-19
relative error = 9.1814834636830985954079728826042e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.76535495252925351965074260193472
y2[1] (numeric) = -0.76535495252925352026570573251102
absolute error = 6.1496313057630e-19
relative error = 8.0350055689068632592354680502902e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7440.1MB, alloc=40.3MB, time=96.06
TOP MAIN SOLVE Loop
x[1] = 2.28
y1[1] (closed_form) = 0.6512296605275456953713983504607
y1[1] (numeric) = 0.65122966052754569596846609862643
absolute error = 5.9706774816573e-19
relative error = 9.1683131828187859972273146917640e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.75888070818092193221665357630092
y2[1] (numeric) = -0.75888070818092193282961385515575
absolute error = 6.1296027885483e-19
relative error = 8.0771624874234701930879417365004e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7482.2MB, alloc=40.3MB, time=96.60
TOP MAIN SOLVE Loop
x[1] = 2.29
y1[1] (closed_form) = 0.65878577991818769374203101818895
y1[1] (numeric) = 0.65878577991818769434521772301882
absolute error = 6.0318670482987e-19
relative error = 9.1560371097381253616786091870097e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.75233057639417073474190827797365
y2[1] (numeric) = -0.75233057639417073535271403784059
absolute error = 6.1080575986694e-19
relative error = 8.1188480042172149027741028092938e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7524.3MB, alloc=40.3MB, time=97.15
TOP MAIN SOLVE Loop
x[1] = 2.3
y1[1] (closed_form) = 0.66627602127982419331788057116602
y1[1] (numeric) = 0.6662760212798241939271639256429
absolute error = 6.0928335447688e-19
relative error = 9.1446087659965737065710630822311e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.7457052121767201773854062116435
y2[1] (numeric) = -0.74570521217672017799390495061312
absolute error = 6.0849873896962e-19
relative error = 8.1600440634363644029844795896841e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7566.5MB, alloc=40.3MB, time=97.69
TOP MAIN SOLVE Loop
x[1] = 2.31
y1[1] (closed_form) = 0.67369963559456087744416432347103
y1[1] (numeric) = 0.67369963559456087805952049148706
absolute error = 6.1535616801603e-19
relative error = 9.1339839819411368229940271708913e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.73900527805947088675876419209826
y2[1] (numeric) = -0.73900527805947088736480259801033
absolute error = 6.0603840591207e-19
relative error = 8.2007317661308979308770634990408e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7608.6MB, alloc=40.3MB, time=98.23
TOP MAIN SOLVE Loop
x[1] = 2.32
y1[1] (closed_form) = 0.68105588050715259709363616600823
y1[1] (numeric) = 0.68105588050715259771503977438503
absolute error = 6.2140360837680e-19
relative error = 9.1241207390217062232973229234663e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.73223144403025132797089867772467
y2[1] (numeric) = -0.73223144403025132857432265274547
absolute error = 6.0342397502080e-19
relative error = 8.2408913184540898983203372343004e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7650.8MB, alloc=40.3MB, time=98.78
TOP MAIN SOLVE Loop
x[1] = 2.33
y1[1] (closed_form) = 0.688344020399238276754180427816
y1[1] (numeric) = 0.68834402039923827738160455857163
absolute error = 6.2742413075563e-19
relative error = 9.1149790244669394841569459427315e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.72538438746681958010284419247542
y2[1] (numeric) = -0.72538438746681958070349887785671
absolute error = 6.0065468538129e-19
relative error = 8.2805019760473553513370587279546e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7693.1MB, alloc=40.3MB, time=99.33
TOP MAIN SOLVE Loop
x[1] = 2.34
y1[1] (closed_form) = 0.69556332646290213752310557206135
y1[1] (numeric) = 0.69556332646290213815652175492565
absolute error = 6.3341618286430e-19
relative error = 9.1065206971932446361768726103828e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.71846479306912612487942868679401
y2[1] (numeric) = -0.71846479306912612547715848781047
absolute error = 5.9772980101646e-19
relative error = 8.3195419842785564328342955776835e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7735.2MB, alloc=40.3MB, time=99.87
TOP MAIN SOLVE Loop
x[1] = 2.35
y1[1] (closed_form) = 0.70271307677355388134712911225892
y1[1] (numeric) = 0.7027130767735538819865073174392
absolute error = 6.3937820518028e-19
relative error = 9.0987093639402521325425707697329e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.71147335279084442220249118201321
y2[1] (numeric) = -0.71147335279084442279713979307457
absolute error = 5.9464861106136e-19
relative error = 8.3579885139587510550967671612046e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7777.4MB, alloc=40.3MB, time=100.42
TOP MAIN SOLVE Loop
x[1] = 2.36
y1[1] (closed_form) = 0.7097925563621205484503630346451
y1[1] (numeric) = 0.70979255636212054909567166584374
absolute error = 6.4530863119864e-19
relative error = 9.0915102647176498659959733544009e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.7044107657701761194310307129327
y2[1] (numeric) = -0.7044107657701761200224411428675
absolute error = 5.9141042993480e-19
relative error = 8.3958175921427631609700151762356e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7819.6MB, alloc=40.3MB, time=100.96
TOP MAIN SOLVE Loop
x[1] = 2.37
y1[1] (closed_form) = 0.71680105728654282882471660882235
y1[1] (numeric) = 0.71680105728654282947592249650812
absolute error = 6.5120588768577e-19
relative error = 9.0848901667488610749327201005579e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.69727773825993781382969642028923
y2[1] (numeric) = -0.69727773825993781441771101779635
absolute error = 5.8801459750712e-19
relative error = 8.4330040275560086346253981889760e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7861.8MB, alloc=40.3MB, time=101.51
TOP MAIN SOLVE Loop
x[1] = 2.38
y1[1] (closed_form) = 0.72373787870256867821114760736753
y1[1] (numeric) = 0.72373787870256867886821600230225
absolute error = 6.5706839493472e-19
relative error = 9.0788172661714789419731868378926e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.6900749835569363594511131070202
y2[1] (numeric) = -0.69007498355693636003557358628487
absolute error = 5.8446047926467e-19
relative error = 8.4695213301620522940852612144922e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7904.0MB, alloc=40.3MB, time=102.05
TOP MAIN SOLVE Loop
x[1] = 2.39
y1[1] (closed_form) = 0.73060232693383715926915829261806
y1[1] (numeric) = 0.73060232693383715993205285964018
absolute error = 6.6289456702212e-19
relative error = 9.0732610968285524347348672675379e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.68280322193063978086250031101305
y2[1] (numeric) = -0.68280322193063978144324777748368
absolute error = 5.8074746647063e-19
relative error = 8.5053416243197404813976035307646e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7946.1MB, alloc=40.3MB, time=102.60
TOP MAIN SOLVE Loop
x[1] = 2.4
y1[1] (closed_form) = 0.73739371554124549960882222733478
y1[1] (numeric) = 0.73739371554124550027750503940159
absolute error = 6.6868281206681e-19
relative error = 9.0681924455512638174013440872208e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.67546318055115092656577152534128
y2[1] (numeric) = -0.67546318055115092714264650166363
absolute error = 5.7687497632235e-19
relative error = 8.5404355549275550898665104118833e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=7988.3MB, alloc=40.3MB, time=103.14
TOP MAIN SOLVE Loop
x[1] = 2.41
y1[1] (closed_form) = 0.74411136539159243003734439556795
y1[1] (numeric) = 0.74411136539159243071177592805785
absolute error = 6.7443153248990e-19
relative error = 9.0635832733851194452987459901931e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.66805559341649106468574980065472
y2[1] (numeric) = -0.66805559341649106525859225275968
absolute error = 5.7284245210496e-19
relative error = 8.5747721858804705836283429074993e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8030.5MB, alloc=40.3MB, time=103.68
TOP MAIN SOLVE Loop
x[1] = 2.42
y1[1] (closed_form) = 0.75075460472549093874353256891074
y1[1] (numeric) = 0.75075460472549093942367169418716
absolute error = 6.8013912527642e-19
relative error = 9.0594066422690663521269870364695e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.66058120127920069250633410656023
y2[1] (numeric) = -0.66058120127920069307498346990177
absolute error = 5.6864936334154e-19
relative error = 8.6083188900980417160997431272900e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8072.6MB, alloc=40.3MB, time=104.23
TOP MAIN SOLVE Loop
x[1] = 2.43
y1[1] (closed_form) = 0.7573227692245436502013552441779
y1[1] (numeric) = 0.75732276922454365088715922641631
absolute error = 6.8580398223841e-19
relative error = 9.0556366467184803372109784995030e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.6530407515722648997124970471899
y2[1] (numeric) = -0.65304075157226490027679225312934
absolute error = 5.6429520593944e-19
relative error = 8.6410412302883000435259420334143e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8114.8MB, alloc=40.3MB, time=104.77
TOP MAIN SOLVE Loop
x[1] = 2.44
y1[1] (closed_form) = 0.7638152020777741113106750925374
y1[1] (numeric) = 0.76381520207777411200209958281694
absolute error = 6.9142449027954e-19
relative error = 9.0522483501072939226560200967414e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.64543499833437069274006107298253
y2[1] (numeric) = -0.64543499833437069329984057531565
absolute error = 5.5977950233312e-19
relative error = 8.6729028295289860820704320031082e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8156.9MB, alloc=40.3MB, time=105.33
TOP MAIN SOLVE Loop
x[1] = 2.45
y1[1] (closed_form) = 0.77023125404730734170190306733649
y1[1] (numeric) = 0.7702312540473073423989020989975
absolute error = 6.9699903166101e-19
relative error = 9.0492177251768669009893748013319e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.63776470213450375443853285563378
y2[1] (numeric) = -0.63776470213450375499363465725687
absolute error = 5.5510180162309e-19
relative error = 8.7038652306288933631723744835731e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8199.2MB, alloc=40.3MB, time=106.22
TOP MAIN SOLVE Loop
x[1] = 2.46
y1[1] (closed_form) = 0.7765702835332930802042763146862
y1[1] (numeric) = 0.77657028353329308090680229895515
absolute error = 7.0252598426895e-19
relative error = 9.0465215984385699595900989976416e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.63003062999589217930819371861593
y2[1] (numeric) = -0.63003062999589217985845539832727
absolute error = 5.5026167971134e-19
relative error = 8.7338877431233418679836491882755e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8241.4MB, alloc=40.3MB, time=106.99
TOP MAIN SOLVE Loop
x[1] = 2.47
y1[1] (closed_form) = 0.78283165663806523520721558406155
y1[1] (numeric) = 0.7828316566380652359152193059446
absolute error = 7.0800372188305e-19
relative error = 9.0441375981603766623655513523375e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.62223355531930478987454240485577
y2[1] (numeric) = -0.62223355531930479041980114428868
absolute error = 5.4525873943291e-19
relative error = 8.7629272766092714933324038371985e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8283.6MB, alloc=40.3MB, time=107.53
TOP MAIN SOLVE Loop
x[1] = 2.48
y1[1] (closed_form) = 0.78901474722953112302319203359033
y1[1] (numeric) = 0.78901474722953112373662264803686
absolute error = 7.1343061444653e-19
relative error = 9.0420441056596239537747352997303e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.6143742578057117043045348806656
y2[1] (numeric) = -0.61437425780571170484462749134929
absolute error = 5.4009261068369e-19
relative error = 8.7909381589761796179808557984618e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8325.8MB, alloc=40.3MB, time=108.08
TOP MAIN SOLVE Loop
x[1] = 2.49
y1[1] (closed_form) = 0.79511893700378415538109133257157
y1[1] (numeric) = 0.79511893700378415609989636090901
absolute error = 7.1880502833744e-19
relative error = 9.0402202096466863573737458062235e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.6064535233783148891434102397918
y2[1] (numeric) = -0.60645352337831488967817319033635
absolute error = 5.3476295054455e-19
relative error = 8.8178719379119968527712467255403e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8368.0MB, alloc=40.3MB, time=108.62
TOP MAIN SOLVE Loop
x[1] = 2.5
y1[1] (closed_form) = 0.80114361554693371483350279046735
y1[1] (numeric) = 0.80114361554693371555762811710838
absolute error = 7.2412532664103e-19
relative error = 9.0386456633830376970079016423267e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.59847214410395649405185470218616
y2[1] (numeric) = -0.59847214410395649458112414558764
absolute error = 5.2926944340148e-19
relative error = 8.8436771638538323139051661836751e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8410.3MB, alloc=40.3MB, time=109.16
TOP MAIN SOLVE Loop
x[1] = 2.51
y1[1] (closed_form) = 0.80708818039614603514191750787841
y1[1] (numeric) = 0.80708818039614603587130737730184
absolute error = 7.2938986942343e-19
relative error = 9.0373008444433037070237879587964e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.59043091811391282764453715502405
y2[1] (numeric) = -0.59043091811391282816814895608611
absolute error = 5.2361180106206e-19
relative error = 8.8682991523326476056257883183917e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8452.4MB, alloc=40.3MB, time=109.70
TOP MAIN SOLVE Loop
x[1] = 2.52
y1[1] (closed_form) = 0.81295203709988998260266426045185
y1[1] (numeric) = 0.8129520370998899833372612744583
absolute error = 7.3459701400645e-19
relative error = 9.0361667168832956179132543004820e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.58233064952408189496642758229713
y2[1] (numeric) = -0.58233064952408189548421734516519
absolute error = 5.1778976286806e-19
relative error = 8.8916797233879263688425489592430e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8494.5MB, alloc=40.3MB, time=110.25
TOP MAIN SOLVE Loop
x[1] = 2.53
y1[1] (closed_form) = 0.81873459927738171378565517255499
y1[1] (numeric) = 0.81873459927738171452540028779839
absolute error = 7.3974511524340e-19
relative error = 9.0352247956334307324766581257821e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.5741721483545724777866405874022
y2[1] (numeric) = -0.5741721483545724782984436832063
absolute error = 5.1180309580410e-19
relative error = 8.9137569154267425805358594218442e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8536.6MB, alloc=40.3MB, time=110.79
TOP MAIN SOLVE Loop
x[1] = 2.54
y1[1] (closed_form) = 0.82443528867722226526970435580657
y1[1] (numeric) = 0.82443528867722226601453688160267
absolute error = 7.4483252579610e-19
relative error = 9.0344571129549521277680365876755e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.56595623044870279873476574798203
y2[1] (numeric) = -0.56595623044870279924041734258451
absolute error = 5.0565159460248e-19
relative error = 8.9344646705556730016467575467951e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8578.8MB, alloc=40.3MB, time=111.34
TOP MAIN SOLVE Loop
x[1] = 2.55
y1[1] (closed_form) = 0.83005353523522221166431047583229
y1[1] (numeric) = 0.83005353523522221241416807224518
absolute error = 7.4985759641289e-19
relative error = 9.0338461868052145818576385446918e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.55768371739141686934577028176624
y2[1] (numeric) = -0.55768371739141686984510536361035
absolute error = 4.9933508184411e-19
relative error = 8.9537324880088942252263104410692e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8621.0MB, alloc=40.3MB, time=111.87
TOP MAIN SOLVE Loop
x[1] = 2.56
y1[1] (closed_form) = 0.83558877713140760950028812338244
y1[1] (numeric) = 0.83558877713140761025510679958997
absolute error = 7.5481867620753e-19
relative error = 9.0333749909714809234647617611736e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.54935543642712668031068338313728
y2[1] (numeric) = -0.5493554364271266808035367911928
absolute error = 4.9285340805552e-19
relative error = 8.9714850418322599007197853361125e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8663.1MB, alloc=40.3MB, time=112.42
TOP MAIN SOLVE Loop
x[1] = 2.57
y1[1] (closed_form) = 0.84104046084620152644236372156713
y1[1] (numeric) = 0.84104046084620152720207783450627
absolute error = 7.5971411293914e-19
relative error = 9.0330269268468235477128462253726e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.54097222037698844964557254874584
y2[1] (numeric) = -0.5409722203769884501317790005477
absolute error = 4.8620645180186e-19
relative error = 8.9876417584443853096823414188089e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8705.3MB, alloc=40.3MB, time=112.97
TOP MAIN SOLVE Loop
x[1] = 2.58
y1[1] (closed_form) = 0.84640804121577553771763249456923
y1[1] (numeric) = 0.84640804121577553848217474786239
absolute error = 7.6454225329316e-19
relative error = 9.0327857967296246274939060957923e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.53253490755562120108505876447165
y2[1] (numeric) = -0.53253490755562120156445288424777
absolute error = 4.7939411977612e-19
relative error = 9.0021163490780019455472736213554e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8747.5MB, alloc=40.3MB, time=113.51
TOP MAIN SOLVE Loop
x[1] = 2.59
y1[1] (closed_form) = 0.85169098148656565465635974540831
y1[1] (numeric) = 0.85169098148656565542566118857114
absolute error = 7.6930144316283e-19
relative error = 9.0326357785316616604471057144079e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.52404434168727600077313024887591
y2[1] (numeric) = -0.52404434168727600124554659576002
absolute error = 4.7241634688411e-19
relative error = 9.0148162913669038390873352340471e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8789.7MB, alloc=40.3MB, time=114.06
TOP MAIN SOLVE Loop
x[1] = 2.6
y1[1] (closed_form) = 0.8568887533689472337977021516452
y1[1] (numeric) = 0.85688875336894723457169217957714
absolute error = 7.7399002793194e-19
relative error = 9.0325614018029496259439256045224e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.51550137182146423525772693520937
y2[1] (numeric) = -0.51550137182146423572300003153507
absolute error = 4.6527309632570e-19
relative error = 9.0256422535154764670957236833459e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8831.9MB, alloc=40.3MB, time=114.60
TOP MAIN SOLVE Loop
x[1] = 2.61
y1[1] (closed_form) = 0.86200083709006349911416744872265
y1[1] (numeric) = 0.86200083709006349989277380148068
absolute error = 7.7860635275803e-19
relative error = 9.0325475249704394010769962275333e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.5069068522480533678909866995555
y2[1] (numeric) = -0.50690685224805336834895105922749
absolute error = 4.5796435967199e-19
relative error = 9.0344874534835937865652100588045e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8874.0MB, alloc=40.3MB, time=115.14
TOP MAIN SOLVE Loop
x[1] = 2.62
y1[1] (closed_form) = 0.86702672144580239454661367674835
y1[1] (numeric) = 0.86702672144580239532976243960489
absolute error = 7.8314876285654e-19
relative error = 9.0325793137102801160562486431872e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.49826164241183866398876000999763
y2[1] (numeric) = -0.49826164241183866443925016693593
absolute error = 4.5049015693830e-19
relative error = 9.0412369444635456324898367008496e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
memory used=8916.2MB, alloc=40.3MB, time=115.68
TOP MAIN SOLVE Loop
x[1] = 2.63
y1[1] (closed_form) = 0.87196590385191656920784839019493
y1[1] (numeric) = 0.87196590385191656999546399398048
absolute error = 7.8761560378555e-19
relative error = 9.0326422203695302392355446744322e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.48956660682659942750568705361163
y2[1] (numeric) = -0.48956660682659942794853759026495
absolute error = 4.4285053665332e-19
relative error = 9.0457668165707657112394299806648e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=8958.4MB, alloc=40.3MB, time=116.22
TOP MAIN SOLVE Loop
x[1] = 2.64
y1[1] (closed_form) = 0.87681789039428138329890731626599
y1[1] (numeric) = 0.87681789039428138409091253799727
absolute error = 7.9200522173128e-19
relative error = 9.0327219643652182882989058711466e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.48082261498864834353055026953286
y2[1] (numeric) = -0.48082261498864834396559584545704
absolute error = 4.3504557592418e-19
relative error = 9.0479433030505629277260352778144e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9000.6MB, alloc=40.3MB, time=116.76
TOP MAIN SOLVE Loop
x[1] = 2.65
y1[1] (closed_form) = 0.88158219587828590897930236605381
y1[1] (numeric) = 0.88158219587828590977561832984799
absolute error = 7.9631596379418e-19
relative error = 9.0328045134899929294024551833467e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.47203054128988257159561077839739
y2[1] (numeric) = -0.47203054128988257202268615889478
absolute error = 4.2707538049739e-19
relative error = 9.0476217774034924836395805265891e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9042.7MB, alloc=40.3MB, time=117.31
TOP MAIN SOLVE Loop
x[1] = 2.66
y1[1] (closed_form) = 0.88625834387735198713231100388259
y1[1] (numeric) = 0.88625834387735198793285718215816
absolute error = 8.0054617827557e-19
relative error = 9.0328760660599933375435346213175e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.46319126493034528461814059379635
y2[1] (numeric) = -0.46319126493034528503708067861208
absolute error = 4.1894008481573e-19
relative error = 9.0446456255760829530740001688453e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9084.8MB, alloc=40.3MB, time=117.86
TOP MAIN SOLVE Loop
x[1] = 2.67
y1[1] (closed_form) = 0.89084586678057648816006285842974
y1[1] (numeric) = 0.89084586678057648896475707339467
absolute error = 8.0469421496493e-19
relative error = 9.0329230338465898661080931263632e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.4543056698303063972473913211913
y2[1] (numeric) = -0.45430566983030639765803117326241
absolute error = 4.1063985207111e-19
relative error = 9.0388449746729645009153579186536e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9127.0MB, alloc=40.3MB, time=118.40
TOP MAIN SOLVE Loop
x[1] = 2.68
y1[1] (closed_form) = 0.89534430583949201262204581862066
y1[1] (numeric) = 0.89534430583949201343080424404825
absolute error = 8.0875842542759e-19
relative error = 9.0329320257337491121235663469908e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.44537464454187127547089883192945
y2[1] (numeric) = -0.44537464454187127587307370618264
absolute error = 4.0217487425319e-19
relative error = 9.0300352564273579931338042783723e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9169.2MB, alloc=40.3MB, time=118.94
TOP MAIN SOLVE Loop
x[1] = 2.69
y1[1] (closed_form) = 0.89975321121394135568593488432887
y1[1] (numeric) = 0.89975321121394135649867204762184
absolute error = 8.1273716329297e-19
relative error = 9.0328898320510592804867463887761e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.43639908216012626653550411876099
y2[1] (numeric) = -0.43639908216012626692904949095505
absolute error = 3.9354537219406e-19
relative error = 9.0180155798232839400058319022379e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9211.3MB, alloc=40.3MB, time=119.48
TOP MAIN SOLVE Loop
x[1] = 2.7
y1[1] (closed_form) = 0.90407214201706114798252728194333
y1[1] (numeric) = 0.9040721420170611487991560664865
absolute error = 8.1662878454317e-19
relative error = 9.0327834095319246608926685636304e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.42737988023382993455605308585788
y2[1] (numeric) = -0.42737988023382993494080468146657
absolute error = 3.8475159560869e-19
relative error = 9.0025668826099871032834205301877e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9253.5MB, alloc=40.3MB, time=120.02
TOP MAIN SOLVE Loop
x[1] = 2.71
y1[1] (closed_form) = 0.90830066635937017453818459371608
y1[1] (numeric) = 0.90830066635937017535861624151811
absolute error = 8.2043164780203e-19
relative error = 9.0325998668531781185717973012403e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.41831794067565893261379068110859
y2[1] (numeric) = -0.41831794067565893298958450423994
absolute error = 3.7579382313135e-19
relative error = 8.9834498258519629339237015430106e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9295.6MB, alloc=40.3MB, time=120.56
TOP MAIN SOLVE Loop
x[1] = 2.72
y1[1] (closed_form) = 0.91243836139195796298962879998706
y1[1] (numeric) = 0.91243836139195796381377291461153
absolute error = 8.2414411462447e-19
relative error = 9.0323264507117842706765210207692e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.40921416967201748668244467400742
y2[1] (numeric) = -0.40921416967201748704911703635514
absolute error = 3.6667236234772e-19
relative error = 8.9604023888421441902392410151302e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9337.8MB, alloc=40.3MB, time=121.11
TOP MAIN SOLVE Loop
x[1] = 2.73
y1[1] (closed_form) = 0.91648481334876932225826112489279
y1[1] (numeric) = 0.91648481334876932308602567467889
absolute error = 8.2776454978610e-19
relative error = 9.0319505323989833906228251104580e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.40006947759241951035844795789445
y2[1] (numeric) = -0.40006947759241951071583550771742
absolute error = 3.5738754982297e-19
relative error = 8.9331371134257645086466554220870e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9380.0MB, alloc=40.3MB, time=121.65
TOP MAIN SOLVE Loop
x[1] = 2.74
y1[1] (closed_form) = 0.92043961758798060326537325177928
y1[1] (numeric) = 0.92043961758798060409666457335251
absolute error = 8.3129132157323e-19
relative error = 9.0314595948361672257979166354936e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.39088477889845241210831170164027
y2[1] (numeric) = -0.390884778898452412456251452766
absolute error = 3.4793975112573e-19
relative error = 8.9013379366230307895228803041600e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9422.1MB, alloc=40.3MB, time=122.19
TOP MAIN SOLVE Loop
x[1] = 2.75
y1[1] (closed_form) = 0.92430237863246354409665948952671
y1[1] (numeric) = 0.92430237863246354493138229159968
absolute error = 8.3472280207297e-19
relative error = 9.0308412200341890235870154892655e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.38166099205233169857656137237778
y2[1] (numeric) = -0.38166099205233169891489073322551
absolute error = 3.3832936084773e-19
relative error = 8.8646565379503008420395259522539e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9464.2MB, alloc=40.3MB, time=122.73
TOP MAIN SOLVE Loop
x[1] = 2.76
y1[1] (closed_form) = 0.9280727102093326532652331971401
y1[1] (numeric) = 0.92807271020933265410329056460354
absolute error = 8.3805736746344e-19
relative error = 9.0300830769435174430438026321854e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.37239903942505551841770059244975
y2[1] (numeric) = -0.37239903942505551874625739506922
absolute error = 3.2855680261947e-19
relative error = 8.8227081124249604452528025891131e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9506.4MB, alloc=40.3MB, time=123.27
TOP MAIN SOLVE Loop
x[1] = 2.77
y1[1] (closed_form) = 0.93175023528857217636777720782907
y1[1] (numeric) = 0.93175023528857217720907060613347
absolute error = 8.4129339830440e-19
relative error = 9.0291729096676127188272096966837e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.36309984720416833112128200917246
y2[1] (numeric) = -0.36309984720416833143990453829392
absolute error = 3.1862252912146e-19
relative error = 8.7750664610525416309761440931625e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9548.6MB, alloc=40.3MB, time=123.82
TOP MAIN SOLVE Loop
x[1] = 2.78
y1[1] (closed_form) = 0.93533458612073878346935166911759
y1[1] (numeric) = 0.93533458612073878431378094894526
absolute error = 8.4442927982767e-19
relative error = 9.0280985260034620027713751535120e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.35376434530114292438633931722734
y2[1] (numeric) = -0.35376434530114292469486633931886
absolute error = 3.0852702209152e-19
relative error = 8.7212582666827398370025757712815e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9590.7MB, alloc=40.3MB, time=124.37
TOP MAIN SOLVE Loop
x[1] = 2.79
y1[1] (closed_form) = 0.93882540427373620697953961962409
y1[1] (numeric) = 0.93882540427373620782700302185181
absolute error = 8.4746340222772e-19
relative error = 9.0268477862857500242936384255560e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.34439346725839004176626159556229
y2[1] (numeric) = -0.34439346725839004206453238789006
absolute error = 2.9827079232777e-19
relative error = 8.6607563930353150220360824222738e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9632.8MB, alloc=40.3MB, time=124.91
TOP MAIN SOLVE Loop
x[1] = 2.8
y1[1] (closed_form) = 0.94222234066865815258678811736615
y1[1] (numeric) = 0.94222234066865815343718227831848
absolute error = 8.5039416095233e-19
relative error = 9.0254085925073554976345690445919e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.33498815015590491954385375271242
y2[1] (numeric) = -0.33498815015590491983170813239973
absolute error = 2.8785437968731e-19
relative error = 8.5929720067214717614623126718369e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9675.0MB, alloc=40.3MB, time=125.45
TOP MAIN SOLVE Loop
x[1] = 2.81
y1[1] (closed_form) = 0.94552505561469589898972047835884
y1[1] (numeric) = 0.94552505561469589984294043535195
absolute error = 8.5321995699311e-19
relative error = 9.0237688776890489458827392397536e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.32554933451756006810510128120633
y2[1] (numeric) = -0.32554933451756006838237963428729
absolute error = 2.7727835308096e-19
relative error = 8.5172452738036132981993748821888e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9717.2MB, alloc=40.3MB, time=126.00
TOP MAIN SOLVE Loop
x[1] = 2.82
y1[1] (closed_form) = 0.94873321884310709569453606376004
y1[1] (numeric) = 0.94873321884310709655047526093607
absolute error = 8.5593919717603e-19
relative error = 9.0219165954763250437697007160954e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.31607796421705366845541285602457
y2[1] (numeric) = -0.3160779642170536687219561664881
absolute error = 2.6654331046353e-19
relative error = 8.4328343206011108551585701864564e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9759.3MB, alloc=40.3MB, time=126.54
TOP MAIN SOLVE Loop
x[1] = 2.83
y1[1] (closed_form) = 0.95184650954024236202702511272453
y1[1] (numeric) = 0.95184650954024236288557540717628
absolute error = 8.5855029445175e-19
relative error = 9.0198397099385700326160778783282e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.3065749863835229889603130778681
y2[1] (numeric) = -0.30657498638352298921596295668813
absolute error = 2.5564987882003e-19
relative error = 8.3389020688143792459342098526274e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9801.4MB, alloc=40.3MB, time=127.08
TOP MAIN SOLVE Loop
x[1] = 2.84
y1[1] (closed_form) = 0.95486461637962638472681949358624
y1[1] (numeric) = 0.9548646163796263855878711617721
absolute error = 8.6105166818586e-19
relative error = 9.0175261855501713711005933601654e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.29704135130683226089025606809731
y2[1] (numeric) = -0.29704135130683226113485478224496
absolute error = 2.4459871414765e-19
relative error = 8.2345004515882693017287574412003e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9843.6MB, alloc=40.3MB, time=127.63
TOP MAIN SOLVE Loop
x[1] = 2.85
y1[1] (closed_form) = 0.95778723755309030604085410717493
y1[1] (numeric) = 0.95778723755309030690429585162385
absolute error = 8.6344174444892e-19
relative error = 9.0149639773317534975988671375336e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.28747801234254448390307892669172
y2[1] (numeric) = -0.28747801234254448413646942812518
absolute error = 2.3339050143346e-19
relative error = 8.1185513817788436873145543410903e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9885.8MB, alloc=40.3MB, time=128.17
TOP MAIN SOLVE Loop
x[1] = 2.86
y1[1] (closed_form) = 0.96061408080095228910317316639277
y1[1] (numeric) = 0.96061408080095228996889212269895
absolute error = 8.6571895630618e-19
relative error = 9.0121410211304679392216937017112e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.27788592581658666420435690975324
y2[1] (numeric) = -0.27788592581658666442638286438115
absolute error = 2.2202595462791e-19
relative error = 7.9898236650694580726242332371494e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9928.0MB, alloc=40.3MB, time=128.72
TOP MAIN SOLVE Loop
x[1] = 2.87
y1[1] (closed_form) = 0.96334486344124324256969375873794
y1[1] (numeric) = 0.96334486344124324343757550284501
absolute error = 8.6788174410707e-19
relative error = 9.0090452240212129235134218975369e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.26826605092961801878239892098714
y2[1] (numeric) = -0.2682660509296180189929047376013
absolute error = 2.1050581661416e-19
relative error = 7.8469048127669375024589529850557e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=9970.2MB, alloc=40.3MB, time=129.26
TOP MAIN SOLVE Loop
x[1] = 2.88
y1[1] (closed_form) = 0.96597931239797478195981790476552
y1[1] (numeric) = 0.96597931239797478282974646053993
absolute error = 8.6992855577441e-19
relative error = 9.0056644548098486111199119700293e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.25861934966111070881776692011768
y2[1] (numeric) = -0.25861934966111070901659777929081
absolute error = 1.9883085917313e-19
relative error = 7.6881663894706148562308457343316e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=10012.4MB, alloc=40.3MB, time=129.80
TOP MAIN SOLVE Loop
x[1] = 2.89
y1[1] (closed_form) = 0.96851716422844660093231550720928
y1[1] (numeric) = 0.96851716422844660180417335430237
absolute error = 8.7185784709309e-19
relative error = 9.0019865346180140329738552299950e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.24894678667315269411404584058049
y2[1] (numeric) = -0.2489467866731526943010477235248
absolute error = 1.8700188294431e-19
relative error = 7.5117210968394052945485261011626e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=10054.6MB, alloc=40.3MB, time=130.34
TOP MAIN SOLVE Loop
x[1] = 2.9
y1[1] (closed_form) = 0.97095816514959052178110666934553
y1[1] (numeric) = 0.9709581651495905226547747513441
absolute error = 8.7366808199857e-19
relative error = 8.9979992275359099540266067759715e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.23924932921398232818425691873958
y2[1] (numeric) = -0.23924932921398232835927663612206
absolute error = 1.7501971738248e-19
relative error = 7.3153691990477443188998908307662e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=10096.7MB, alloc=40.3MB, time=130.88
TOP MAIN SOLVE Loop
x[1] = 2.91
y1[1] (closed_form) = 0.97330207106334859076784710660275
y1[1] (numeric) = 0.97330207106334859164320483946749
absolute error = 8.7535773286474e-19
relative error = 8.9936902313214767607776225400484e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.22952794702126434045301822382699
y2[1] (numeric) = -0.22952794702126434061590344453698
absolute error = 1.6288522070999e-19
relative error = 7.0965310683887960158784476445179e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=10139.0MB, alloc=40.3MB, time=131.43
TOP MAIN SOLVE Loop
x[1] = 2.92
y1[1] (closed_form) = 0.97554864758108268050293173515827
y1[1] (numeric) = 0.97554864758108268137985701594956
absolute error = 8.7692528079129e-19
relative error = 8.9890471681311453619135267704820e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.21978361222511687789562909306458
y2[1] (numeric) = -0.21978361222511687804622837292958
absolute error = 1.5059927986500e-19
relative error = 6.8521614664675854168420973511225e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=10181.2MB, alloc=40.3MB, time=131.97
TOP MAIN SOLVE Loop
x[1] = 2.93
y1[1] (closed_form) = 0.97769767004701315843501960467633
y1[1] (numeric) = 0.97769767004701315931338882056702
absolute error = 8.7836921589069e-19
relative error = 8.9840575752671386419736767338669e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.21001729925089930332910403425911
y2[1] (numeric) = -0.21001729925089930346726684470455
absolute error = 1.3816281044544e-19
relative error = 6.5786395186609076803462078813140e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=10223.4MB, alloc=40.3MB, time=132.51
x[1] = 2.94
y1[1] (closed_form) = 0.97974892356068427760176338132832
y1[1] (numeric) = 0.97974892356068427848145141890272
absolute error = 8.7968803757440e-19
relative error = 8.9787088959216738928669685300339e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.20022998472177047149431709442312
y2[1] (numeric) = -0.20022998472177047161989385107187
absolute error = 1.2557675664875e-19
relative error = 6.2716259417012468373482995239586e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=10265.6MB, alloc=40.3MB, time=133.06
x[1] = 2.95
y1[1] (closed_form) = 0.98170220299845404312138940470197
y1[1] (numeric) = 0.98170220299845404400226965954057
absolute error = 8.8088025483860e-19
relative error = 8.9729884699055441085189701224434e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.19042264736102722702044731405738
y2[1] (numeric) = -0.19042264736102722713328940526472
absolute error = 1.1284209120734e-19
relative error = 5.9258755600325079972931127737186e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=10307.7MB, alloc=40.3MB, time=133.60
x[1] = 2.96
y1[1] (closed_form) = 0.98355731303400640545638732297616
y1[1] (numeric) = 0.98355731303400640633833170952533
absolute error = 8.8194438654917e-19
relative error = 8.9668835243429973085777795518223e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.18059626789423289034054450880135
y2[1] (numeric) = -0.18059626789423289044050432412136
absolute error = 9.995981532001e-20
relative error = 5.5349878757490142023206292953963e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=10349.9MB, alloc=40.3MB, time=134.15
x[1] = 2.97
y1[1] (closed_form) = 0.98531406815788372924707637480614
y1[1] (numeric) = 0.98531406815788373012995533653222
absolute error = 8.8287896172608e-19
relative error = 8.9603811643193768002731861419597e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.17075182895114551862806449866797
y2[1] (numeric) = -0.17075182895114551871499545724694
absolute error = 8.693095857897e-20
relative error = 5.0910704214970464829998352667485e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=10392.2MB, alloc=40.3MB, time=134.70
x[1] = 2.98
y1[1] (closed_form) = 0.9869722926960375844844419643954
y1[1] (numeric) = 0.98697229269603758536812448422217
absolute error = 8.8368251982677e-19
relative error = 8.9534683634621725607043887847143e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.16089031496745574884655395454133
y2[1] (numeric) = -0.16089031496745574892031053343413
absolute error = 7.375657889280e-20
relative error = 4.5842771149847762171828653139993e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=10434.4MB, alloc=40.3MB, time=135.24
x[1] = 2.99
y1[1] (closed_form) = 0.98853182082739600495858418721084
y1[1] (numeric) = 0.98853182082739600584293779823989
absolute error = 8.8435361102905e-19
relative error = 8.9461319544458428875452678217276e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.15101271208634404904629503561052
y2[1] (numeric) = -0.1510127120863440491067327980156
absolute error = 6.043776240508e-20
relative error = 4.0021638953496641019771726938524e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=10476.6MB, alloc=40.3MB, time=135.79
x[1] = 3
y1[1] (closed_form) = 0.98999249660044545727157279473126
y1[1] (numeric) = 0.98999249660044545815646359124427
absolute error = 8.8489079651301e-19
relative error = 8.9383586194001850005102986365498e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.14112000805986722210074480280811
y2[1] (numeric) = -0.14112000805986722214772042621711
absolute error = 4.697562340900e-20
relative error = 3.3287713099528431763160466857245e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=10518.9MB, alloc=40.3MB, time=136.33
x[1] = 3.01
y1[1] (closed_form) = 0.99135417394882586223162557418242
y1[1] (numeric) = 0.99135417394882586311691822292442
absolute error = 8.8529264874200e-19
relative error = 8.9301348802077994303677787082898e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.13121319215018402315021812468485
y2[1] (numeric) = -0.1312131921501840231835894289425
absolute error = 3.337130425765e-20
relative error = 2.5432888043340844519063242228870e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=10561.1MB, alloc=40.3MB, time=136.88
x[1] = 3.02
y1[1] (closed_form) = 0.99261671670593710913946653326304
y1[1] (numeric) = 0.9926167167059371100250242850059
absolute error = 8.8555775174286e-19
relative error = 8.9214470886772971017329099189995e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.12129325503062976810875799633911
y2[1] (numeric) = -0.12129325503062976812838397160925
absolute error = 1.962597527014e-20
relative error = 1.6180599049125955134640272118166e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=10603.3MB, alloc=40.3MB, time=137.42
x[1] = 3.03
y1[1] (closed_form) = 0.99377999861855560232760730870843
y1[1] (numeric) = 0.99377999861855560321329201009346
absolute error = 8.8568470138503e-19
relative error = 8.9122814165732065783219948632333e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.11136118868664982569090503291726
y2[1] (numeric) = -0.11136118868664982569664586755088
absolute error = 5.74083463362e-21
relative error = 5.1551484869415921643258953027738e-18 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=10645.6MB, alloc=40.3MB, time=137.96
x[1] = 3.04
y1[1] (closed_form) = 0.99484390335945947830924495484319
y1[1] (numeric) = 0.99484390335945947919491706050189
absolute error = 8.8567210565870e-19
relative error = 8.9026238454887203313515009054846e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.10141798631660189952660831260879
y2[1] (numeric) = -0.10141798631660189951832542090987
absolute error = 8.28289169892e-21
relative error = 8.1670835714119370078836364741009e-18 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
memory used=10687.7MB, alloc=40.3MB, time=138.50
x[1] = 3.05
y1[1] (closed_form) = 0.99580832453906123102558220156492
y1[1] (numeric) = 0.99580832453906123191110078651696
absolute error = 8.8551858495204e-19
relative error = 8.8924601565459694642664869754305e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.091464642232437020053401588696418
y2[1] (numeric) = -0.091464642232437020030957638581427
absolute error = 2.2443950114991e-20
relative error = 2.4538389444474837398001561629002e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.06
y1[1] (closed_form) = 0.99667316571604658193873927179315
y1[1] (numeric) = 0.99667316571604658282396204412028
absolute error = 8.8522277232713e-19
relative error = 8.8817759199040286300945190914356e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.081502151760269178003890088835723
y2[1] (numeric) = -0.081502151760269177967149029382618
absolute error = 3.6741059453105e-20
relative error = 4.5079864346619128968375363039518e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=10729.9MB, alloc=40.3MB, time=139.05
TOP MAIN SOLVE Loop
x[1] = 3.07
y1[1] (closed_form) = 0.99743834040701853109211366272677
y1[1] (numeric) = 0.99743834040701853197689697652175
absolute error = 8.8478331379498e-19
relative error = 8.8705564840622821154913150547967e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.071531511140843542442340790318903
y2[1] (numeric) = -0.071531511140843542391167879201546
absolute error = 5.1172911117357e-20
relative error = 7.1538976740752716563364139518646e-17 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.001
memory used=10772.1MB, alloc=40.3MB, time=139.59
TOP MAIN SOLVE Loop
x[1] = 3.08
y1[1] (closed_form) = 0.99810377209514562474111853735979
y1[1] (numeric) = 0.99810377209514562562531740594901
absolute error = 8.8419886858922e-19
relative error = 8.8587869649382761572936630033024e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.061553717429913216445629637135705
y2[1] (numeric) = -0.061553717429913216379891467939497
absolute error = 6.5738169196208e-20
relative error = 1.0679804882793523774145037507409e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=10814.3MB, alloc=40.3MB, time=140.13
TOP MAIN SOLVE Loop
x[1] = 3.09
y1[1] (closed_form) = 0.99866939423781357473474351808576
y1[1] (numeric) = 0.99866939423781357561821162752439
absolute error = 8.8346810943863e-19
relative error = 8.8464522347047050591246153857491e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.051569768398534492669958510574615
y2[1] (numeric) = -0.051569768398534492589523039989277
absolute error = 8.0435470585338e-20
relative error = 1.5597407761021438199893543315866e-16 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 18
h = 0.001
memory used=10856.6MB, alloc=40.3MB, time=140.68
TOP MAIN SOLVE Loop
x[1] = 3.1
y1[1] (closed_form) = 0.99913515027327946449237605454147
y1[1] (numeric) = 0.99913515027327946537496577737997
absolute error = 8.8258972283850e-19
relative error = 8.8335369103679074483176977190210e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.041580662433290579194698271596673
y2[1] (numeric) = -0.041580662433290579099434846482064
absolute error = 9.5263425114609e-20
relative error = 2.2910511651285906341929970395002e-16 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 18
h = 0.001
memory used=10898.8MB, alloc=40.3MB, time=141.22
TOP MAIN SOLVE Loop
x[1] = 3.11
y1[1] (closed_form) = 0.99950099362632787616083083671683
y1[1] (numeric) = 0.99950099362632787704239324603746
absolute error = 8.8156240932063e-19
relative error = 8.8200253420679415571304796704708e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.031587398436453773187626872703365
y2[1] (numeric) = -0.031587398436453773077406257024229
absolute error = 1.10220615679136e-19
relative error = 3.4893856770405860954034327959142e-16 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 18
h = 0.001
memory used=10941.0MB, alloc=40.3MB, time=141.77
TOP MAIN SOLVE Loop
x[1] = 3.12
y1[1] (closed_form) = 0.99976688771292837334358497397559
y1[1] (numeric) = 0.99976688771292837422396985769753
absolute error = 8.8038488372194e-19
relative error = 8.8059016010813557738058977293446e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.021590975726096066090998104201892
y2[1] (numeric) = -0.021590975726096065965692505827468
absolute error = 1.25305598374424e-19
relative error = 5.8036098027275633968527432505434e-16 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 18
h = 0.001
memory used=10983.2MB, alloc=40.3MB, time=142.31
TOP MAIN SOLVE Loop
x[1] = 3.13
y1[1] (closed_form) = 0.99993280594389387365782723913921
y1[1] (numeric) = 0.99993280594389387453688311459103
absolute error = 8.7905587545182e-19
relative error = 8.7911494675087571261433051911091e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.011592393936158169184681483118307
y2[1] (numeric) = -0.011592393936158169044164580482733
absolute error = 1.40516902635574e-19
relative error = 1.2121474081145887339645651708919e-15 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 17
h = 0.001
memory used=11025.4MB, alloc=40.3MB, time=142.86
TOP MAIN SOLVE Loop
x[1] = 3.14
y1[1] (closed_form) = 0.99999873172753954528511430634505
y1[1] (numeric) = 0.9999987317275395461626884351031
absolute error = 8.7757412875805e-19
relative error = 8.7757524176256110434463345312954e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = -0.0015926529164869525405414363244433
y2[1] (numeric) = -0.0015926529164869523846884049438909
absolute error = 1.558530313805524e-19
relative error = 9.7857499124373211639763879375552e-15 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 17
h = 0.001
memory used=11067.6MB, alloc=40.3MB, time=143.40
TOP MAIN SOLVE Loop
x[1] = 3.15
y1[1] (closed_form) = 0.99996465847134196162819465679473
y1[1] (numeric) = 0.99996465847134196250413305978588
absolute error = 8.7593840299115e-19
relative error = 8.7596936108742843491460186874842e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.008407247367148706459141516571067
y2[1] (numeric) = 0.0084072473671487066304539777285557
absolute error = 1.713124611574887e-19
relative error = 2.0376759916318344744151681559954e-15 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 17
h = 0.001
memory used=11109.8MB, alloc=40.3MB, time=143.94
TOP MAIN SOLVE Loop
x[1] = 3.16
y1[1] (closed_form) = 0.99983058958259834815991709427395
y1[1] (numeric) = 0.99983058958259834903406456714139
absolute error = 8.7414747286744e-19
relative error = 8.7429558764787584912832019252770e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.01840630693305366670737927118737
y2[1] (numeric) = 0.018406306933053666894272913483379
absolute error = 1.86893642296009e-19
relative error = 1.0153782775424072078359415689610e-15 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 17
h = 0.001
memory used=11152.0MB, alloc=40.3MB, time=144.49
TOP MAIN SOLVE Loop
x[1] = 3.17
y1[1] (closed_form) = 0.99959653846808585554008835013528
y1[1] (numeric) = 0.99959653846808585641228847886562
absolute error = 8.7220012873034e-19
relative error = 8.7255216996550929532964628885254e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.028403525883603859571285274896733
y2[1] (numeric) = 0.028403525883603859773880273959307
absolute error = 2.02594999062574e-19
relative error = 7.1327411918082827252994895257856e-16 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 18
h = 0.001
memory used=11194.2MB, alloc=40.3MB, time=145.03
TOP MAIN SOLVE Loop
x[1] = 3.18
y1[1] (closed_form) = 0.99926252853272089307268415386031
y1[1] (numeric) = 0.9992625285327208939427793306706
absolute error = 8.7009517681029e-19
relative error = 8.7073732073983068127594310572338e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.03839790450523521805369524672612
y2[1] (numeric) = 0.038397904505235218272110176545931
absolute error = 2.18414929819811e-19
relative error = 5.6881992034235106980179690669161e-16 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 18
h = 0.001
memory used=11236.4MB, alloc=40.3MB, time=145.58
TOP MAIN SOLVE Loop
x[1] = 3.19
y1[1] (closed_form) = 0.99882859317721865656895082969948
y1[1] (numeric) = 0.9988285931772186574367822691824
absolute error = 8.6783143948292e-19
relative error = 8.6884921538178644159924724738587e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.048388443368414200108007148451169
y2[1] (numeric) = 0.048388443368414200342358955641004
absolute error = 2.34351807189835e-19
relative error = 4.8431358993211449609409118223489e-16 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 18
h = 0.001
memory used=11278.6MB, alloc=40.3MB, time=146.12
TOP MAIN SOLVE Loop
x[1] = 3.2
y1[1] (closed_form) = 0.99829477579475308466166072228358
y1[1] (numeric) = 0.99829477579475308552706847780925
absolute error = 8.6540775552567e-19
relative error = 8.6688599049985980844210799867337e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.058374143427579909137217414619095
y2[1] (numeric) = 0.058374143427579909387621392840611
absolute error = 2.50403978221516e-19
relative error = 4.2896385885674196890366533042442e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=11320.7MB, alloc=40.3MB, time=146.66
TOP MAIN SOLVE Loop
x[1] = 3.21
y1[1] (closed_form) = 0.99766112976661757757210666520424
y1[1] (numeric) = 0.99766112976661757843492964557687
absolute error = 8.6282298037263e-19
relative error = 8.6484574233584683646318825800782e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.068354006121047817548388360676863
y2[1] (numeric) = 0.068354006121047817814958125238572
absolute error = 2.66569764561709e-19
relative error = 3.8998411313250863785168712955394e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=11362.9MB, alloc=40.3MB, time=147.21
TOP MAIN SOLVE Loop
x[1] = 3.22
y1[1] (closed_form) = 0.99692771845688691225434273747586
y1[1] (numeric) = 0.99692771845688691311441872384358
absolute error = 8.6007598636772e-19
relative error = 8.6272652514768532276414796487328e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.078327033470865103073444147916042
y2[1] (numeric) = 0.078327033470865103356291610546437
absolute error = 2.82847462630395e-19
relative error = 3.6111090909067083608383528847489e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=11405.0MB, alloc=40.3MB, time=147.75
TOP MAIN SOLVE Loop
x[1] = 3.23
y1[1] (closed_form) = 0.99609461520608088772070849458495
y1[1] (numeric) = 0.99609461520608088857787415760095
absolute error = 8.5716566301600e-19
relative error = 8.6052634953624557641094146768222e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.088292228182607612405875728529723
y2[1] (numeric) = 0.088292228182607612705111072329469
absolute error = 2.99235343799746e-19
relative error = 3.3891470399961132585063856881019e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=11447.2MB, alloc=40.3MB, time=148.30
TOP MAIN SOLVE Loop
x[1] = 3.24
y1[1] (closed_form) = 0.99516190332383033417882384374247
y1[1] (numeric) = 0.99516190332383033503291476097584
absolute error = 8.5409091723337e-19
relative error = 8.5824318071332441670338685729177e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.098248593745108472540154959437637
y2[1] (numeric) = 0.098248593745108472855886614014704
absolute error = 3.15731654577067e-19
relative error = 3.2135997324927249794497831260803e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=11489.4MB, alloc=40.3MB, time=148.84
TOP MAIN SOLVE Loop
x[1] = 3.25
y1[1] (closed_form) = 0.9941296760805462193730292251716
y1[1] (numeric) = 0.99412967608054622022387989876572
absolute error = 8.5085067359412e-19
relative error = 8.5587493670713287266570822325247e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.10819513453010837703583084256083
y2[1] (numeric) = 0.10819513453010837736816545935245
absolute error = 3.3233461679162e-19
relative error = 3.0716225663469037940949283925849e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=11531.6MB, alloc=40.3MB, time=149.38
TOP MAIN SOLVE Loop
x[1] = 3.26
y1[1] (closed_form) = 0.99299803669809268521269456717166
y1[1] (numeric) = 0.99299803669809268606013844174859
absolute error = 8.4744387457693e-19
relative error = 8.5341948650255346431983628257588e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.11813085589181758226072311033608
y2[1] (numeric) = 0.11813085589181758260976553812137
absolute error = 3.4904242778529e-19
relative error = 2.9547100556431901038458034606905e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=11573.8MB, alloc=40.3MB, time=149.93
TOP MAIN SOLVE Loop
x[1] = 3.27
y1[1] (closed_form) = 0.99176709833946494737596174049474
y1[1] (numeric) = 0.99176709833946494821983122130335
absolute error = 8.4386948080861e-19
relative error = 8.5087464811195811857345379848972e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.12805476426637965749655689075362
y2[1] (numeric) = 0.12805476426637965786241015136072
absolute error = 3.6585326060710e-19
relative error = 2.8570062402836622013353001420977e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=11616.1MB, alloc=40.3MB, time=150.47
TOP MAIN SOLVE Loop
x[1] = 3.28
y1[1] (closed_form) = 0.99043698409747309009035841613171
y1[1] (numeric) = 0.99043698409747309093048488743786
absolute error = 8.4012647130615e-19
relative error = 8.4823818657348280405292363354021e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.13796586727122704261491407058525
y2[1] (numeric) = 0.13796586727122704299767933479674
absolute error = 3.8276526421149e-19
relative error = 2.7743475381415312096281392176885e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=11658.3MB, alloc=40.3MB, time=151.02
TOP MAIN SOLVE Loop
x[1] = 3.29
y1[1] (closed_form) = 0.98900782698243288770137512553948
y1[1] (numeric) = 0.98900782698243288853758896925612
absolute error = 8.3621384371664e-19
relative error = 8.4550781187244651672562330676997e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.14786317380431847785052978374264
y2[1] (numeric) = 0.14786317380431847825030634740312
absolute error = 3.9977656366048e-19
relative error = 2.7036925650570890393207487382646e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=11700.5MB, alloc=40.3MB, time=151.56
TOP MAIN SOLVE Loop
x[1] = 3.3
y1[1] (closed_form) = 0.98747976990886488393659105110285
y1[1] (numeric) = 0.98747976990886488476872166565801
absolute error = 8.3213061455516e-19
relative error = 8.4268117678193837515321654457751e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.15774569414324838201165427760248
y2[1] (numeric) = 0.15774569414324838242853953793193
absolute error = 4.1688526032945e-19
relative error = 2.6427679220890667933442263784427e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=11742.7MB, alloc=40.3MB, time=152.11
TOP MAIN SOLVE Loop
x[1] = 3.31
y1[1] (closed_form) = 0.98585296568120305894633807058553
y1[1] (numeric) = 0.98585296568120305977421389002607
absolute error = 8.2787581944054e-19
relative error = 8.3975587461817465796427552101302e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.16761244004421826827224999431698
y2[1] (numeric) = 0.16761244004421826870633942643382
absolute error = 4.3408943211684e-19
relative error = 2.5898401813273630052746329106075e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=11784.9MB, alloc=40.3MB, time=152.65
TOP MAIN SOLVE Loop
x[1] = 3.32
y1[1] (closed_form) = 0.98412757697851451324228958473119
y1[1] (numeric) = 0.98412757697851451406573809806041
absolute error = 8.2344851332922e-19
relative error = 8.3672943690632656586599988331419e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.17746242484086030048692055230841
y2[1] (numeric) = 0.17746242484086030093830768596586
absolute error = 4.5138713365745e-19
relative error = 2.5435645549317389242480857283659e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=11827.0MB, alloc=40.3MB, time=153.20
TOP MAIN SOLVE Loop
x[1] = 3.33
y1[1] (closed_form) = 0.98230377633823169655284671485927
y1[1] (numeric) = 0.98230377633823169737169448560587
absolute error = 8.1884777074660e-19
relative error = 8.3359933095141668685490667275719e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.18729466354290310775529282413595
y2[1] (numeric) = 0.18729466354290310822406922067534
absolute error = 4.6877639653939e-19
relative error = 2.5028817568633427416715233392474e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=11869.2MB, alloc=40.3MB, time=153.74
TOP MAIN SOLVE Loop
x[1] = 3.34
y1[1] (closed_form) = 0.98038174613889880835887990106991
y1[1] (numeric) = 0.98038174613889880917295258708654
absolute error = 8.1407268601663e-19
relative error = 8.3036295730999215761029339569839e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.19710817293466999073661691059272
y2[1] (numeric) = 0.19710817293466999122287214011766
absolute error = 4.8625522952494e-19
relative error = 2.4669460544698245901288933560807e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=11911.3MB, alloc=40.3MB, time=154.28
TOP MAIN SOLVE Loop
x[1] = 3.35
y1[1] (closed_form) = 0.97836167858193409545539437527153
y1[1] (numeric) = 0.97836167858193409626451674876025
absolute error = 8.0912237348872e-19
relative error = 8.2701764715630065140025821014854e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.20690197167339966997603411602551
y2[1] (numeric) = 0.20690197167339967047985573480027
absolute error = 5.0382161877476e-19
relative error = 2.4350740338523983864638234867822e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=11953.5MB, alloc=40.3MB, time=154.83
TOP MAIN SOLVE Loop
x[1] = 3.36
y1[1] (closed_form) = 0.97624377567240987029416530777832
y1[1] (numeric) = 0.9762437756724098710981612755411
absolute error = 8.0399596776278e-19
relative error = 8.2356065953814628292055211616919e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.21667508038737974424961398190553
y2[1] (numeric) = 0.21667508038737974477108750998154
absolute error = 5.2147352807601e-19
relative error = 2.4067074402081692427597869796518e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=11995.8MB, alloc=40.3MB, time=155.37
TOP MAIN SOLVE Loop
x[1] = 3.37
y1[1] (closed_form) = 0.97402824919885217208949176597085
y1[1] (numeric) = 0.97402824919885217288818438988264
absolute error = 7.9869262391179e-19
relative error = 8.1998917851584135190954500858938e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.22642652177388304566410348430857
y2[1] (numeric) = 0.22642652177388304620331238338234
absolute error = 5.3920889907377e-19
relative error = 2.3813857795874358728131926263982e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12038.0MB, alloc=40.3MB, time=155.92
TOP MAIN SOLVE Loop
x[1] = 3.38
y1[1] (closed_form) = 0.97171532071206209070412534999057
y1[1] (numeric) = 0.97171532071206209149733686769255
absolute error = 7.9321151770198e-19
relative error = 8.1630031017800922855906062597783e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.23615532069689709795749177758963
y2[1] (numeric) = 0.23615532069689709851451742909594
absolute error = 5.5702565150631e-19
relative error = 2.3587258159694256473810983856034e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12080.2MB, alloc=40.3MB, time=156.46
TOP MAIN SOLVE Loop
x[1] = 3.39
y1[1] (closed_form) = 0.96930522150296087116533607467248
y1[1] (numeric) = 0.96930522150296087195288792048318
absolute error = 7.8755184581070e-19
relative error = 8.1249107952762051492831444416483e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.24586050428463690513600137155794
y2[1] (numeric) = 0.24586050428463690571092305500169
absolute error = 5.7492168344375e-19
relative error = 2.3384060205869965488589602542584e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12122.3MB, alloc=40.3MB, time=157.02
TOP MAIN SOLVE Loop
x[1] = 3.4
y1[1] (closed_form) = 0.96679819257946101428220153976569
y1[1] (numeric) = 0.96679819257946101506391436580769
absolute error = 7.8171282604200e-19
relative error = 8.0855842723118364463200886882312e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.25554110202683131924990242936374
y2[1] (numeric) = 0.25554110202683131984279730089397
absolute error = 5.9289487153023e-19
relative error = 2.3201546319854924565522824171489e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12164.5MB, alloc=40.3MB, time=157.56
TOP MAIN SOLVE Loop
x[1] = 3.41
y1[1] (closed_form) = 0.96419448464236568623478364095296
y1[1] (numeric) = 0.96419448464236568701047733849249
absolute error = 7.7569369753953e-19
relative error = 8.0449920622315789489532327274589e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.26519614587177325875244430757411
y2[1] (numeric) = 0.26519614587177325936338737880386
absolute error = 6.1094307122975e-19
relative error = 2.3037403851455334583467159899241e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12206.7MB, alloc=40.3MB, time=158.11
TOP MAIN SOLVE Loop
x[1] = 3.42
y1[1] (closed_form) = 0.96149435806029884717415014560141
y1[1] (numeric) = 0.96149435806029884794364386659862
absolute error = 7.6949372099721e-19
relative error = 8.0031017815806280464448663470351e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.2748246703231240725009433576662
y2[1] (numeric) = 0.27482467032312407313000747474142
absolute error = 6.2906411707522e-19
relative error = 2.2889652385850230632326926741924e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12248.9MB, alloc=40.3MB, time=158.66
TOP MAIN SOLVE Loop
x[1] = 3.43
y1[1] (closed_form) = 0.95869808284366860579948964122556
y1[1] (numeric) = 0.9586980828436686065626018200928
absolute error = 7.6311217886724e-19
relative error = 7.9598800970135862399914985413513e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.28442571253646236904429691459137
y2[1] (numeric) = 0.28442571253646236969155273751247
absolute error = 6.4725582292110e-19
relative error = 2.2756586145077305406380434764270e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12291.2MB, alloc=40.3MB, time=159.20
TOP MAIN SOLVE Loop
x[1] = 3.44
y1[1] (closed_form) = 0.95580593861766640355516501297249
y1[1] (numeric) = 0.95580593861766640431171338853805
absolute error = 7.5654837556556e-19
relative error = 7.9152926865020058425728318000365e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.29399831241556765639445181056032
y2[1] (numeric) = 0.29399831241556765705996779275979
absolute error = 6.6551598219947e-19
relative error = 2.2636727970695314770308657478001e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12333.3MB, alloc=40.3MB, time=159.74
TOP MAIN SOLVE Loop
x[1] = 3.45
y1[1] (closed_form) = 0.95281821459430472850678513994775
y1[1] (numeric) = 0.95281821459430472925658677762262
absolute error = 7.4980163767487e-19
relative error = 7.8693041987460740382392712089605e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.30354151270842916399808636621989
y2[1] (numeric) = 0.30354151270842916468192873439924
absolute error = 6.8384236817935e-19
relative error = 2.2528792259008865100677860779813e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12375.4MB, alloc=40.3MB, time=160.29
TOP MAIN SOLVE Loop
x[1] = 3.46
y1[1] (closed_form) = 0.94973520954349615510160537578203
y1[1] (numeric) = 0.94973520954349615584447668992689
absolute error = 7.4287131414486e-19
relative error = 7.8218782106849734227550282949840e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.31305435910297024610631577597493
y2[1] (numeric) = 0.31305435910297024680854851020439
absolute error = 7.0223273422946e-19
relative error = 2.2431654880693761483011402292553e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12417.6MB, alloc=40.3MB, time=160.83
TOP MAIN SOLVE Loop
x[1] = 3.47
y1[1] (closed_form) = 0.94655723176317660188518005352668
y1[1] (numeric) = 0.94655723176317660262093683001663
absolute error = 7.3575677648995e-19
relative error = 7.7729771830007241125248643653902e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.32253590032247879418185398715726
y2[1] (numeric) = 0.32253590032247879490253880124164
absolute error = 7.2068481408438e-19
relative error = 2.2344328596098071121779546628359e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12459.9MB, alloc=40.3MB, time=161.38
TOP MAIN SOLVE Loop
x[1] = 3.48
y1[1] (closed_form) = 0.94328459904847579482359814738228
y1[1] (numeric) = 0.94328459904847579555205556636653
absolute error = 7.2845741898425e-19
relative error = 7.7225624134971620043707303847237e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.33198518822073411538191643544275
y2[1] (numeric) = 0.3319851882207341161211127575565
absolute error = 7.3919632211375e-19
relative error = 2.2265942829421193352769062112036e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12502.1MB, alloc=40.3MB, time=161.92
TOP MAIN SOLVE Loop
x[1] = 3.49
y1[1] (closed_form) = 0.93991763865993801915927867276677
y1[1] (numeric) = 0.93991763865993801988025133162066
absolute error = 7.2097265885389e-19
relative error = 7.6705939882328108812769906190758e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.3414012778768207645082874807375
y2[1] (numeric) = 0.34140127787682076526605243433249
absolute error = 7.5776495359499e-19
relative error = 2.2195726926025018201398121704066e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12544.2MB, alloc=40.3MB, time=162.47
TOP MAIN SOLVE Loop
x[1] = 3.5
y1[1] (closed_form) = 0.93645668729079633769865762667176
y1[1] (numeric) = 0.93645668729079633841195956313826
absolute error = 7.1330193646650e-19
relative error = 7.6170307302744428579194505766841e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.35078322768961984812036880004364
y2[1] (numeric) = 0.35078322768961984889675718503271
absolute error = 7.7638838498907e-19
relative error = 2.2132996212579304749461016775618e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12586.4MB, alloc=40.3MB, time=163.01
TOP MAIN SOLVE Loop
x[1] = 3.51
y1[1] (closed_form) = 0.93290209103330354808266630575758
y1[1] (numeric) = 0.93290209103330354878811102127563
absolute error = 7.0544471551805e-19
relative error = 7.5618301459340005125381710031648e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.36013009947196835175953992341737
y2[1] (numeric) = 0.36013009947196835255460419763692
absolute error = 7.9506427421955e-19
relative error = 2.2077140327489784373925871233764e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12628.5MB, alloc=40.3MB, time=163.56
TOP MAIN SOLVE Loop
x[1] = 3.52
y1[1] (closed_form) = 0.92925420534412324591621651227224
y1[1] (numeric) = 0.92925420534412324661361699548903
absolute error = 6.9740048321679e-19
relative error = 7.5049483683372439590458186149777e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.36944095854447707443057432143296
y2[1] (numeric) = 0.3694409585444770752443645823877
absolute error = 8.1379026095474e-19
relative error = 2.2027613401635531430139303448011e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12670.7MB, alloc=40.3MB, time=164.10
TOP MAIN SOLVE Loop
x[1] = 3.53
y1[1] (closed_form) = 0.92551339500878445462153901468401
y1[1] (numeric) = 0.92551339500878445531070776514838
absolute error = 6.8916875046437e-19
relative error = 7.4463400981660432513903421366257e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.37871487382899778862484425400664
y2[1] (numeric) = 0.37871487382899778945740822089966
absolute error = 8.3256396689302e-19
relative error = 2.1983925755948787791668528926014e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12712.9MB, alloc=40.3MB, time=164.65
TOP MAIN SOLVE Loop
x[1] = 3.54
y1[1] (closed_form) = 0.92168003410520337652276888612977
y1[1] (numeric) = 0.92168003410520337720351793816383
absolute error = 6.8074905203406e-19
relative error = 7.3859585414037212642789476161578e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.38795091794173027924720110048451
y2[1] (numeric) = 0.38795091794173028009858409653579
absolute error = 8.5138299605128e-19
relative error = 2.1945636849328363055845887114677e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12755.1MB, alloc=40.3MB, time=165.19
TOP MAIN SOLVE Loop
x[1] = 3.55
y1[1] (closed_form) = 0.91775450596627591295627082271047
y1[1] (numeric) = 0.9177545059662759136284117694567
absolute error = 6.7214094674623e-19
relative error = 7.3237553439037944235435748202455e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.39714816728595995082022742343695
y2[1] (numeric) = 0.39714816728595995169047235849326
absolute error = 8.7024493505631e-19
relative error = 2.1912349262578985244359107746748e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12797.2MB, alloc=40.3MB, time=165.74
TOP MAIN SOLVE Loop
x[1] = 3.56
y1[1] (closed_form) = 0.91373720314154469412352061310366
y1[1] (numeric) = 0.91373720314154469478686463074432
absolute error = 6.6334401764066e-19
relative error = 7.2596805225835056001287028928123e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.40630570214441672928242142268591
y2[1] (numeric) = 0.40630570214441673017156877612524
absolute error = 8.8914735343933e-19
relative error = 2.1883703545053687455848738345807e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12839.3MB, alloc=40.3MB, time=166.27
TOP MAIN SOLVE Loop
x[1] = 3.57
y1[1] (closed_form) = 0.90962852735794445195161343603674
y1[1] (numeric) = 0.9096285273579444526059713081828
absolute error = 6.5435787214606e-19
relative error = 7.1936823930387368978257409901765e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.41542260677124602256709945606629
y2[1] (numeric) = 0.41542260677124602347518725999968
absolute error = 9.0808780393339e-19
relative error = 2.1859373783031308878818147280727e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12881.5MB, alloc=40.3MB, time=166.82
TOP MAIN SOLVE Loop
x[1] = 3.58
y1[1] (closed_form) = 0.90542888947962966139140085454902
y1[1] (numeric) = 0.90542888947962966203658299679561
absolute error = 6.4518214224659e-19
relative error = 7.1257074933558910641159652841597e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.42449796948358254294260094834376
y2[1] (numeric) = 0.42449796948358254386966477111772
absolute error = 9.2706382277396e-19
relative error = 2.1839063774598671882912912113746e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12923.8MB, alloc=40.3MB, time=167.37
TOP MAIN SOLVE Loop
x[1] = 3.59
y1[1] (closed_form) = 0.90113870946688846735564983934783
y1[1] (numeric) = 0.90113870946688846799146632399305
absolute error = 6.3581648464522e-19
relative error = 7.0557005038810010830669056335143e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.43353088275271783380787293204403
y2[1] (numeric) = 0.43353088275271783475394586204612
absolute error = 9.4607293000209e-19
relative error = 2.1822503716343585125198992996409e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=12966.0MB, alloc=40.3MB, time=167.91
TOP MAIN SOLVE Loop
x[1] = 3.6
y1[1] (closed_form) = 0.89675841633414700587029172526594
y1[1] (numeric) = 0.89675841633414700649655230619019
absolute error = 6.2626058092425e-19
relative error = 6.9836041626945261686312609253861e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.44252044329485238426672734749269
y2[1] (numeric) = 0.44252044329485238523183997726343
absolute error = 9.6511262977074e-19
relative error = 2.1809447323717951844005918886466e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=13008.2MB, alloc=40.3MB, time=168.45
TOP MAIN SOLVE Loop
x[1] = 3.61
y1[1] (closed_form) = 0.89228844810706831897164969353841
y1[1] (numeric) = 0.89228844810706831958816383124098
absolute error = 6.1651413770257e-19
relative error = 6.9093591765136541673565869339386e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.45146575216142325634494018639253
y2[1] (numeric) = 0.45146575216142325732912059704639
absolute error = 9.8418041065386e-19
relative error = 2.1799669320253613370614595335521e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=13050.4MB, alloc=40.3MB, time=169.00
TOP MAIN SOLVE Loop
x[1] = 3.62
y1[1] (closed_form) = 0.887729251778750153422404272068
y1[1] (numeric) = 0.88772925177875015402898115885796
absolute error = 6.0657688678996e-19
relative error = 6.8329041267318506585821536885388e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.46036591482899819216274354079485
y2[1] (numeric) = 0.46036591482899819316601728675311
absolute error = 1.00327374595826e-18
relative error = 2.1792963241662311408209124634917e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=13092.6MB, alloc=40.3MB, time=169.54
TOP MAIN SOLVE Loop
x[1] = 3.63
y1[1] (closed_form) = 0.88308128326502602342992354439801
y1[1] (numeric) = 0.88308128326502602402637212973615
absolute error = 5.9644858533814e-19
relative error = 6.7541753702771749948493800074854e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.46922004128872721172690481453191
y2[1] (numeric) = 0.46922004128872721274929490857016
absolute error = 1.02239009403825e-18
relative error = 2.1789139509689831222359739621621e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=13134.8MB, alloc=40.3MB, time=170.08
TOP MAIN SOLVE Loop
x[1] = 3.64
y1[1] (closed_form) = 0.87834500735887400722343724413409
y1[1] (numeric) = 0.87834500735887400780956626012282
absolute error = 5.8612901598873e-19
relative error = 6.6731069349523784264229681863170e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.47802724613534275625715663887291
y2[1] (numeric) = 0.47802724613534275729868353748597
absolute error = 1.04152689861306e-18
relative error = 2.1788023737838886308845518589717e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=13176.9MB, alloc=40.3MB, time=170.63
TOP MAIN SOLVE Loop
x[1] = 3.65
y1[1] (closed_form) = 0.87352089768393783657240447452827
y1[1] (numeric) = 0.87352089768393783714802246154627
absolute error = 5.7561798701800e-19
relative error = 6.5896304088911824101802061540873e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.48678664865569947710681138829532
y2[1] (numeric) = 0.48678664865569947816749297738228
absolute error = 1.06068158908696e-18
relative error = 2.1789455237034902392462378110358e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=13219.1MB, alloc=40.3MB, time=171.17
TOP MAIN SOLVE Loop
x[1] = 3.66
y1[1] (closed_form) = 0.86860943664716492709839092015993
y1[1] (numeric) = 0.86860943664716492766330625263834
absolute error = 5.6491533247841e-19
relative error = 6.5036748237387899580950967004835e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.49549737291684481637245114641035
y2[1] (numeric) = 0.49549737291684481745230272728223
absolute error = 1.07985158087188e-18
relative error = 2.1793285694233185518324824781295e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=13261.3MB, alloc=40.3MB, time=171.72
TOP MAIN SOLVE Loop
x[1] = 3.67
y1[1] (closed_form) = 0.86361111539056608553795618647981
y1[1] (numeric) = 0.86361111539056608609197709881673
absolute error = 5.5402091233692e-19
relative error = 6.4151665311343908766861248928124e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.50415854785361157220802405891391
y2[1] (numeric) = 0.50415854785361157330705833462688
absolute error = 1.09903427571297e-18
relative error = 2.1799378001066594377011586403934e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=13303.4MB, alloc=40.3MB, time=172.26
TOP MAIN SOLVE Loop
x[1] = 3.68
y1[1] (closed_form) = 0.85852643374210171794562486853616
y1[1] (numeric) = 0.85852643374210171848855948114615
absolute error = 5.4293461260999e-19
relative error = 6.3240290720400302005622903582331e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.51276930735572368965980922504404
y2[1] (numeric) = 0.51276930735572369077803628706047
absolute error = 1.11822706201643e-18
relative error = 2.1807605213014082005072391832029e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=13345.7MB, alloc=40.3MB, time=172.81
TOP MAIN SOLVE Loop
x[1] = 3.69
y1[1] (closed_form) = 0.85335590016569945017519302837216
y1[1] (numeric) = 0.85335590016569945070684937386751
absolute error = 5.3165634549535e-19
relative error = 6.2301830384264784435684091744711e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.52132879035440656651575454812466
y2[1] (numeric) = 0.52132879035440656765318186330463
absolute error = 1.13742731517997e-18
relative error = 2.1817849622437523211704586036621e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=13387.9MB, alloc=40.3MB, time=173.35
TOP MAIN SOLVE Loop
x[1] = 3.7
y1[1] (closed_form) = 0.8481000317104081588356701063544
y1[1] (numeric) = 0.84810003171040815935585615585475
absolute error = 5.2018604950035e-19
relative error = 6.1335459267848781991363125410985e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.52983614090849321321077762570121
y2[1] (numeric) = 0.52983614090849321436741002362715
absolute error = 1.15663239792594e-18
relative error = 2.1830001931214037987506623579720e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=13430.1MB, alloc=40.3MB, time=173.90
TOP MAIN SOLVE Loop
x[1] = 3.71
y1[1] (closed_form) = 0.84275935395869349727638917260975
y1[1] (numeric) = 0.84275935395869349778491286217693
absolute error = 5.0852368956718e-19
relative error = 6.0340319828963236384746930187240e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.53829050829001765624379404325037
y2[1] (numeric) = 0.53829050829001765741963370388699
absolute error = 1.17583966063662e-18
relative error = 2.1843960510689640043973801963197e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=13472.3MB, alloc=40.3MB, time=174.44
TOP MAIN SOLVE Loop
x[1] = 3.72
y1[1] (closed_form) = 0.83733440097388008700560008948967
y1[1] (numeric) = 0.83733440097388008750226934668417
absolute error = 4.9666925719450e-19
relative error = 5.9315520372367116242897303891034e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.54669104706928702583745896705622
y2[1] (numeric) = 0.54669104706928702703250540874846
absolute error = 1.19504644169224e-18
relative error = 2.1859630738397314928465168375457e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=13514.5MB, alloc=40.3MB, time=174.98
TOP MAIN SOLVE Loop
x[1] = 3.73
y1[1] (closed_form) = 0.83182571524674563027960569792163
y1[1] (numeric) = 0.83182571524674563076422846847732
absolute error = 4.8462277055569e-19
relative error = 5.8260133303517271869684606111625e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.55503691719942382070274923216573
y2[1] (numeric) = 0.55503691719942382191699929997686
absolute error = 1.21425006781113e-18
relative error = 2.1876924402397039385487890750740e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=13556.6MB, alloc=40.3MB, time=175.52
TOP MAIN SOLVE Loop
x[1] = 3.74
y1[1] (closed_form) = 0.82623384764127228440667735620253
y1[1] (numeric) = 0.82623384764127228487906163081644
absolute error = 4.7238427461391e-19
relative error = 5.7173193274818013769693665840472e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.56332728410036989575236111967948
y2[1] (numeric) = 0.56332728410036989698580897407178
absolute error = 1.23344785439230e-18
relative error = 2.1895759165333317913919272120886e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=13598.8MB, alloc=40.3MB, time=176.07
TOP MAIN SOLVE Loop
x[1] = 3.75
y1[1] (closed_form) = 0.82055935733956072258311240229071
y1[1] (numeric) = 0.8205593573395607230430662435241
absolute error = 4.5995384123339e-19
relative error = 5.6053695216475810352425147796157e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.57156131874234377243415557335029
y2[1] (numeric) = 0.57156131874234377368679267921071
absolute error = 1.25263710586042e-18
relative error = 2.1916058081339491149770881740174e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=13641.0MB, alloc=40.3MB, time=176.61
TOP MAIN SOLVE Loop
x[1] = 3.76
y1[1] (closed_form) = 0.81480281178591238980944513756309
y1[1] (numeric) = 0.81480281178591239025677670685072
absolute error = 4.4733156928763e-19
relative error = 5.4900592243558109604891089138884e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.57973819772874292602316503775395
y2[1] (numeric) = 0.57973819772874292729498015376679
absolute error = 1.27181511601284e-18
relative error = 2.1937749159801213662180401733902e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=13683.2MB, alloc=40.3MB, time=177.16
TOP MAIN SOLVE Loop
x[1] = 3.77
y1[1] (closed_form) = 0.80896478663008554561462174619622
y1[1] (numeric) = 0.80896478663008554604913933096
absolute error = 4.3451758476378e-19
relative error = 5.3712793429965621822745991506667e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.58785710337848275971251772647441
y2[1] (numeric) = 0.58785710337848276100349689484347
absolute error = 1.29097916836906e-18
relative error = 2.1960764970766763140507986364284e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=13725.4MB, alloc=40.3MB, time=177.70
TOP MAIN SOLVE Loop
x[1] = 3.78
y1[1] (closed_form) = 0.80304586566973076793658025923771
y1[1] (numeric) = 0.80304586566973076835809230010148
absolute error = 4.2151204086377e-19
relative error = 5.2489161439394739428546867268504e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.59591722380776403167448581090021
y2[1] (numeric) = 0.59591722380776403298461234742234
absolute error = 1.31012653652213e-18
relative error = 2.1985042287429530469153536723484e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=13767.6MB, alloc=40.3MB, time=178.25
TOP MAIN SOLVE Loop
x[1] = 3.79
y1[1] (closed_form) = 0.79704664079201167456087725184016
y1[1] (numeric) = 0.79704664079201167496919236994186
absolute error = 4.0831511810170e-19
relative error = 5.1228510002371281569875599009264e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.60391775301126055841709072023268
y2[1] (numeric) = 0.60391775301126055974634520472501
absolute error = 1.32925448449233e-18
relative error = 2.2010521761686726294850087088676e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=13809.7MB, alloc=40.3MB, time=178.79
TOP MAIN SOLVE Loop
x[1] = 3.8
y1[1] (closed_form) = 0.79096771191441669999656817435073
y1[1] (numeric) = 0.79096771191441670039149519874866
absolute error = 3.9492702439793e-19
relative error = 4.9929601227598706381725602035738e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.61185789094271907573358608611888
y2[1] (numeric) = 0.61185789094271907708194635320179
absolute error = 1.34836026708291e-18
relative error = 2.2037147629254663293047436231268e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=13851.9MB, alloc=40.3MB, time=179.33
TOP MAIN SOLVE Loop
x[1] = 3.81
y1[1] (closed_form) = 0.78480968692476784656233037436496
y1[1] (numeric) = 0.78480968692476784694367836953426
absolute error = 3.8134799516930e-19
relative error = 4.8591142734691571545201915898587e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.61973684359496319732588971051781
y2[1] (numeric) = 0.61973684359496319869333084075564
absolute error = 1.36744113023783e-18
relative error = 2.2064867441244760590399648575670e-16 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 18
h = 0.001
memory used=13894.1MB, alloc=40.3MB, time=179.88
TOP MAIN SOLVE Loop
x[1] = 3.82
y1[1] (closed_form) = 0.7785731816204324087577276566562
y1[1] (numeric) = 0.77857318162043240912530595007228
absolute error = 3.6757829341608e-19
relative error = 4.7211784594358226118209108525189e-17 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
y2[1] (closed_form) = 0.62755382307929347077277195688991
y2[1] (numeric) = 0.62755382307929347215926626829145
absolute error = 1.38649431140154e-18
relative error = 2.2093631819471075473088761288877e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = 0.001
Finished!
Maximum Time Reached before Solution Completed!
diff ( y1 , x , 1 ) = neg ( y2 ) ;
diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ;
Iterations = 3321
Total Elapsed Time = 3 Minutes 0 Seconds
Elapsed Time(since restart) = 3 Minutes 0 Seconds
Expected Time Remaining = 1 Minutes 3 Seconds
Optimized Time Remaining = 1 Minutes 3 Seconds
Expected Total Time = 4 Minutes 3 Seconds
Time to Timeout 0.0 Seconds
Percent Done = 73.82 %
> quit
memory used=13915.1MB, alloc=40.3MB, time=180.14