|\^/| Maple 2016 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number 0
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
> if (years_int > 0) then # if number 1
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 2
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 7
# Begin Function number 8
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 8
# Begin Function number 9
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 9
# Begin Function number 10
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 7
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 7;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 10
# Begin Function number 11
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 7
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 11
# Begin Function number 12
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 12
# Begin Function number 13
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 16
# Begin Function number 17
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 17
# Begin Function number 18
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 6
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 7
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 8
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 9
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 10
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 11
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 12
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 12
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 19
# Begin Function number 20
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 20
# Begin Function number 21
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 12
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 12;
> if (errflag) then # if number 12
> quit;
> fi;# end if 12
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 21
# Begin Function number 22
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 12
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 13
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 13
> fi;# end if 12;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 22
# Begin Function number 23
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 12
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 12;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 23
# Begin Function number 24
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 24
# Begin Function number 25
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 25
# Begin Function number 26
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalf(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalf(in_val); ret end proc
# End Function number 26
# Begin Function number 27
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 12
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 27
# Begin Function number 28
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 28
# Begin Function number 29
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 12
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 13
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 15
> if (rcs > glob__0) then # if number 16
> rad_c := sqrt(rcs) * float_abs(glob_h);
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 16
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> fi;# end if 13
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 12;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := sqrt(rcs)*float_abs(glob_h)
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 29
# Begin Function number 30
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 30
# Begin Function number 31
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 31
# Begin Function number 32
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 12
> if (array_fact_1[nnn] = 0) then # if number 13
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 13;
> else
> ret := factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 32
# Begin Function number 33
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 12
> if (array_fact_2[mmm,nnn] = 0) then # if number 13
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 13;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 33
# Begin Function number 34
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 34
# Begin Function number 35
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 35
# Begin Function number 36
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 36
# Begin Function number 37
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 37
# Begin Function number 38
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 38
# Begin Function number 39
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 39
# Begin Function number 40
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 40
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(1.0)/ ( c(x) - c(6.0) ) / ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )) ;
> end;
exact_soln_y := proc(x)
return c(1.0)/((c(x) - c(6.0))*(c(x) - c(6.0))*(c(x) - c(6.0))*
(c(x) - c(6.0))*(c(x) - c(6.0)))
end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]);
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if (rad_given < glob_least_given_sing) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])*
(array_x[1] - array_given_rad_poles[1, 1])
+ array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if rad_given < glob_least_given_sing then
glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if array_rad_test_poles[1, 1] < glob_least_ratio_sing then
glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_float(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if array_rad_test_poles[1, 2] < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if array_rad_test_poles[1, 3] < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_5D0,
> array_const_6D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y[1]) < min_size) then # if number 3
> min_size := float_abs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < glob__1) then # if number 3
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_5D0,
array_const_6D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y[1]) < min_size then
min_size := float_abs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_5D0,
> array_const_6D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_5D0,
array_const_6D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := float_abs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_5D0,
> array_const_6D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
> est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
> fi;# end if 3;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 3
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_5D0,
array_const_6D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y[no_terms - 3]))
+ c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_5D0,
> array_const_6D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_5D0,
array_const_6D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_5D0,
> array_const_6D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 3
> if (iter >= 0) then # if number 4
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> closed_form_val_y := evalf(exact_soln_y(ind_var));
> omniout_float(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := float_abs(numeric_val - closed_form_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 5
> relerr := abserr*glob__100/float_abs(closed_form_val_y);
> if (c(relerr) > c(glob_prec)) then # if number 6
> glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 6;
> else
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 5;
> if (glob_good_digits < glob_min_good_digits) then # if number 5
> glob_min_good_digits := glob_good_digits;
> fi;# end if 5;
> if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 5
> glob_min_apfp_est_good_digits := glob_apfp_est_good_digits;
> fi;# end if 5;
> if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 5
> est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*53*ATS_MAX_TERMS/float_abs(numeric_val));
> if (evalf(est_rel_err) > glob_prec) then # if number 6
> glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
> else
> glob_est_digits := Digits;
> fi;# end if 6;
> else
> relerr := glob__m1 ;
> glob_est_digits := -16;
> fi;# end if 5;
> array_est_digits[1] := glob_est_digits;
> if (glob_iter = 1) then # if number 5
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 5;
> array_est_rel_error[1] := est_rel_err;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," ");
> omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," ");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 4;
> #BOTTOM DISPLAY ALOT
> fi;# end if 3;
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_5D0,
array_const_6D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
closed_form_val_y := evalf(exact_soln_y(ind_var));
omniout_float(ALWAYS, "y[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := float_abs(numeric_val - closed_form_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if c(glob_prec) < c(float_abs(closed_form_val_y)) then
relerr := abserr*glob__100/float_abs(closed_form_val_y);
if c(glob_prec) < c(relerr) then
glob_good_digits := -int_trunc(log10(c(relerr))) + 3
else glob_good_digits := Digits
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits
then glob_min_apfp_est_good_digits := glob_apfp_est_good_digits
end if;
if glob_prec < evalf(float_abs(numeric_val)) then
est_rel_err := evalf(array_max_est_error[1]*100.0*
sqrt(glob_iter)*53*ATS_MAX_TERMS/float_abs(numeric_val))
;
if glob_prec < evalf(est_rel_err) then
glob_est_digits := -int_trunc(log10(est_rel_err)) + 3
else glob_est_digits := Digits
end if
else relerr := glob__m1; glob_est_digits := -16
end if;
array_est_digits[1] := glob_est_digits;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
array_est_rel_error[1] := est_rel_err;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Desired digits ", 32,
glob_desired_digits_correct, 4, " ");
omniout_int(INFO, "Estimated correct digits ", 32,
glob_est_digits, 4, " ");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_5D0,
> array_const_6D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr((glob_clock_sec));
> if (c(percent_done) < glob__100) then # if number 3
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 3;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr((left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_5D0,
array_const_6D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(glob_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(left_sec);
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_5D0,
> array_const_6D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 3;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 4
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_rad_test_poles[1,1]) then # if number 6
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,2]) then # if number 8
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 9
> glob_min_pole_est := rad_c;
> fi;# end if 9;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[1,3]) then # if number 10
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 11
> glob_min_pole_est := rad_c;
> fi;# end if 11;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test1
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 10;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 9;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 9
> display_poles();
> fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_5D0,
array_const_6D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4],
array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
if
float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_poles() end if
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_5D0,
> array_const_6D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre neg ID_CONST $eq_no = 1
> array_tmp1[1] := neg(array_const_5D0[1]);
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_x[1] - array_const_6D0[1];
> #emit pre div CONST - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_tmp1[1] / array_tmp2[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 1
> array_tmp4[1] := array_x[1] - array_const_6D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp5[1] := array_tmp3[1] / array_tmp4[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 1
> array_tmp6[1] := array_x[1] - array_const_6D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp7[1] := array_tmp5[1] / array_tmp6[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 1
> array_tmp8[1] := array_x[1] - array_const_6D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp9[1] := array_tmp7[1] / array_tmp8[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 1
> array_tmp10[1] := array_x[1] - array_const_6D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp11[1] := array_tmp9[1] / array_tmp10[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 1
> array_tmp12[1] := array_x[1] - array_const_6D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp13[1] := array_tmp11[1] / array_tmp12[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp14[1] := array_const_0D0[1] + array_tmp13[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp14[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_x[2];
> #emit pre div CONST - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := neg(array_tmp3[1])* array_tmp2[2] / array_tmp2[1];
> #emit pre div CONST - LINEAR $eq_no = 1 i = 3
> #emit pre div CONST - LINEAR $eq_no = 1 i = 4
> #emit pre div CONST - LINEAR $eq_no = 1 i = 5
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 2
> array_tmp4[2] := array_x[2];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp5[2] := (array_tmp3[2] - array_tmp5[1] * array_tmp4[2]) / array_tmp4[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 2
> array_tmp6[2] := array_x[2];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp7[2] := (array_tmp5[2] - array_tmp7[1] * array_tmp6[2]) / array_tmp6[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 2
> array_tmp8[2] := array_x[2];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp9[2] := (array_tmp7[2] - array_tmp9[1] * array_tmp8[2]) / array_tmp8[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 2
> array_tmp10[2] := array_x[2];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp11[2] := (array_tmp9[2] - array_tmp11[1] * array_tmp10[2]) / array_tmp10[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 2
> array_tmp12[2] := array_x[2];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp13[2] := (array_tmp11[2] - array_tmp13[1] * array_tmp12[2]) / array_tmp12[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp14[2] := array_tmp13[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp14[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> array_tmp3[3] := neg(array_tmp3[2])* array_tmp2[2] / array_tmp2[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp5[3] := (array_tmp3[3] - array_tmp5[2] * array_tmp4[2]) / array_tmp4[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp7[3] := (array_tmp5[3] - array_tmp7[2] * array_tmp6[2]) / array_tmp6[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp9[3] := (array_tmp7[3] - array_tmp9[2] * array_tmp8[2]) / array_tmp8[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp11[3] := (array_tmp9[3] - array_tmp11[2] * array_tmp10[2]) / array_tmp10[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp13[3] := (array_tmp11[3] - array_tmp13[2] * array_tmp12[2]) / array_tmp12[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp14[3] := array_tmp13[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp14[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> array_tmp3[4] := neg(array_tmp3[3])* array_tmp2[2] / array_tmp2[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp5[4] := (array_tmp3[4] - array_tmp5[3] * array_tmp4[2]) / array_tmp4[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp7[4] := (array_tmp5[4] - array_tmp7[3] * array_tmp6[2]) / array_tmp6[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp9[4] := (array_tmp7[4] - array_tmp9[3] * array_tmp8[2]) / array_tmp8[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp11[4] := (array_tmp9[4] - array_tmp11[3] * array_tmp10[2]) / array_tmp10[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp13[4] := (array_tmp11[4] - array_tmp13[3] * array_tmp12[2]) / array_tmp12[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp14[4] := array_tmp13[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp14[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> array_tmp3[5] := neg(array_tmp3[4])* array_tmp2[2] / array_tmp2[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp5[5] := (array_tmp3[5] - array_tmp5[4] * array_tmp4[2]) / array_tmp4[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp7[5] := (array_tmp5[5] - array_tmp7[4] * array_tmp6[2]) / array_tmp6[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp9[5] := (array_tmp7[5] - array_tmp9[4] * array_tmp8[2]) / array_tmp8[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp11[5] := (array_tmp9[5] - array_tmp11[4] * array_tmp10[2]) / array_tmp10[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp13[5] := (array_tmp11[5] - array_tmp13[4] * array_tmp12[2]) / array_tmp12[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp14[5] := array_tmp13[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp14[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit div CONST LINEAR (NOP) $eq_no = 1 i = 1
> array_tmp3[kkk] := array_tmp1[1] * array_tmp2[kkk];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp5[kkk] := neg(ats(kkk,array_tmp4,array_tmp5,2)) / array_tmp4[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp7[kkk] := neg(ats(kkk,array_tmp6,array_tmp7,2)) / array_tmp6[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp9[kkk] := neg(ats(kkk,array_tmp8,array_tmp9,2)) / array_tmp8[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp11[kkk] := neg(ats(kkk,array_tmp10,array_tmp11,2)) / array_tmp10[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp13[kkk] := neg(ats(kkk,array_tmp12,array_tmp13,2)) / array_tmp12[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp14[kkk] := array_tmp13[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp14[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_5D0,
array_const_6D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
array_tmp1[1] := neg(array_const_5D0[1]);
array_tmp2[1] := array_x[1] - array_const_6D0[1];
array_tmp3[1] := array_tmp1[1]/array_tmp2[1];
array_tmp4[1] := array_x[1] - array_const_6D0[1];
array_tmp5[1] := array_tmp3[1]/array_tmp4[1];
array_tmp6[1] := array_x[1] - array_const_6D0[1];
array_tmp7[1] := array_tmp5[1]/array_tmp6[1];
array_tmp8[1] := array_x[1] - array_const_6D0[1];
array_tmp9[1] := array_tmp7[1]/array_tmp8[1];
array_tmp10[1] := array_x[1] - array_const_6D0[1];
array_tmp11[1] := array_tmp9[1]/array_tmp10[1];
array_tmp12[1] := array_x[1] - array_const_6D0[1];
array_tmp13[1] := array_tmp11[1]/array_tmp12[1];
array_tmp14[1] := array_const_0D0[1] + array_tmp13[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp14[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp2[2] := array_x[2];
array_tmp3[2] := neg(array_tmp3[1])*array_tmp2[2]/array_tmp2[1];
array_tmp4[2] := array_x[2];
array_tmp5[2] :=
(-array_tmp4[2]*array_tmp5[1] + array_tmp3[2])/array_tmp4[1];
array_tmp6[2] := array_x[2];
array_tmp7[2] :=
(-array_tmp6[2]*array_tmp7[1] + array_tmp5[2])/array_tmp6[1];
array_tmp8[2] := array_x[2];
array_tmp9[2] :=
(-array_tmp8[2]*array_tmp9[1] + array_tmp7[2])/array_tmp8[1];
array_tmp10[2] := array_x[2];
array_tmp11[2] :=
(-array_tmp10[2]*array_tmp11[1] + array_tmp9[2])/array_tmp10[1];
array_tmp12[2] := array_x[2];
array_tmp13[2] :=
(-array_tmp12[2]*array_tmp13[1] + array_tmp11[2])/array_tmp12[1];
array_tmp14[2] := array_tmp13[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp14[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp3[3] := neg(array_tmp3[2])*array_tmp2[2]/array_tmp2[1];
array_tmp5[3] :=
(-array_tmp4[2]*array_tmp5[2] + array_tmp3[3])/array_tmp4[1];
array_tmp7[3] :=
(-array_tmp6[2]*array_tmp7[2] + array_tmp5[3])/array_tmp6[1];
array_tmp9[3] :=
(-array_tmp8[2]*array_tmp9[2] + array_tmp7[3])/array_tmp8[1];
array_tmp11[3] :=
(-array_tmp10[2]*array_tmp11[2] + array_tmp9[3])/array_tmp10[1];
array_tmp13[3] :=
(-array_tmp12[2]*array_tmp13[2] + array_tmp11[3])/array_tmp12[1];
array_tmp14[3] := array_tmp13[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp14[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp3[4] := neg(array_tmp3[3])*array_tmp2[2]/array_tmp2[1];
array_tmp5[4] :=
(-array_tmp4[2]*array_tmp5[3] + array_tmp3[4])/array_tmp4[1];
array_tmp7[4] :=
(-array_tmp6[2]*array_tmp7[3] + array_tmp5[4])/array_tmp6[1];
array_tmp9[4] :=
(-array_tmp8[2]*array_tmp9[3] + array_tmp7[4])/array_tmp8[1];
array_tmp11[4] :=
(-array_tmp10[2]*array_tmp11[3] + array_tmp9[4])/array_tmp10[1];
array_tmp13[4] :=
(-array_tmp12[2]*array_tmp13[3] + array_tmp11[4])/array_tmp12[1];
array_tmp14[4] := array_tmp13[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp14[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp3[5] := neg(array_tmp3[4])*array_tmp2[2]/array_tmp2[1];
array_tmp5[5] :=
(-array_tmp4[2]*array_tmp5[4] + array_tmp3[5])/array_tmp4[1];
array_tmp7[5] :=
(-array_tmp6[2]*array_tmp7[4] + array_tmp5[5])/array_tmp6[1];
array_tmp9[5] :=
(-array_tmp8[2]*array_tmp9[4] + array_tmp7[5])/array_tmp8[1];
array_tmp11[5] :=
(-array_tmp10[2]*array_tmp11[4] + array_tmp9[5])/array_tmp10[1];
array_tmp13[5] :=
(-array_tmp12[2]*array_tmp13[4] + array_tmp11[5])/array_tmp12[1];
array_tmp14[5] := array_tmp13[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp14[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp3[kkk] := array_tmp1[1]*array_tmp2[kkk];
array_tmp5[kkk] :=
neg(ats(kkk, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp7[kkk] :=
neg(ats(kkk, array_tmp6, array_tmp7, 2))/array_tmp6[1];
array_tmp9[kkk] :=
neg(ats(kkk, array_tmp8, array_tmp9, 2))/array_tmp8[1];
array_tmp11[kkk] :=
neg(ats(kkk, array_tmp10, array_tmp11, 2))/array_tmp10[1];
array_tmp13[kkk] :=
neg(ats(kkk, array_tmp12, array_tmp13, 2))/array_tmp12[1];
array_tmp14[kkk] := array_tmp13[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y_set_initial[1, kkk + order_d] then
temporary := c(array_tmp14[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_5D0,
> array_const_6D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 30;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=64;
> max_terms:=30;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(30),[]);
> array_norms:= Array(0..(30),[]);
> array_fact_1:= Array(0..(30),[]);
> array_1st_rel_error:= Array(0..(2),[]);
> array_last_rel_error:= Array(0..(2),[]);
> array_est_rel_error:= Array(0..(2),[]);
> array_max_est_error:= Array(0..(2),[]);
> array_type_pole:= Array(0..(2),[]);
> array_type_real_pole:= Array(0..(2),[]);
> array_type_complex_pole:= Array(0..(2),[]);
> array_est_digits:= Array(0..(2),[]);
> array_y:= Array(0..(30),[]);
> array_x:= Array(0..(30),[]);
> array_tmp0:= Array(0..(30),[]);
> array_tmp1:= Array(0..(30),[]);
> array_tmp2:= Array(0..(30),[]);
> array_tmp3:= Array(0..(30),[]);
> array_tmp4:= Array(0..(30),[]);
> array_tmp5:= Array(0..(30),[]);
> array_tmp6:= Array(0..(30),[]);
> array_tmp7:= Array(0..(30),[]);
> array_tmp8:= Array(0..(30),[]);
> array_tmp9:= Array(0..(30),[]);
> array_tmp10:= Array(0..(30),[]);
> array_tmp11:= Array(0..(30),[]);
> array_tmp12:= Array(0..(30),[]);
> array_tmp13:= Array(0..(30),[]);
> array_tmp14:= Array(0..(30),[]);
> array_m1:= Array(0..(30),[]);
> array_y_higher := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..30+ 1),[]);
> array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(30) ,(0..30+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 30) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp6[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp7[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp8[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp9[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp10[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp11[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp12[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp13[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp14[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=30) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> zero_ats_ar(array_tmp6);
> zero_ats_ar(array_tmp7);
> zero_ats_ar(array_tmp8);
> zero_ats_ar(array_tmp9);
> zero_ats_ar(array_tmp10);
> zero_ats_ar(array_tmp11);
> zero_ats_ar(array_tmp12);
> zero_ats_ar(array_tmp13);
> zero_ats_ar(array_tmp14);
> 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_5D0);
> array_const_5D0[1] := c(5.0);
> zero_ats_ar(array_const_6D0);
> array_const_6D0[1] := c(6.0);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_h := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 1000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 30;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/sing7_backpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = neg ( 5.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=64;");
> 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(3.0);");
> omniout_str(ALWAYS,"x_end := c(2.0);");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"");
> 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 := 1;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(6.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=100000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=false;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"return(c(1.0)/ ( c(x) - c(6.0) ) / ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )) ;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := c(3.0);
> x_end := c(2.0);
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_type_given_pole := 1;
> array_given_rad_poles[1,1] := c(6.0);
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=100000;
> glob_upper_ratio_limit:=c(1.000001);
> glob_lower_ratio_limit:=c(0.999999);
> glob_look_poles:=false;
> glob_h:=c(0.001);
> glob_display_interval:=c(0.01);
> #END OVERRIDE BLOCK
> #END BLOCK 2
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
> # after second input block
> glob_check_sign := c(my_check_sign(x_start,x_end));
> glob__pi := arccos(glob__m1);
> glob_prec = expt(10.0,c(-Digits));
> if (glob_optimize) then # if number 9
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> found_h := false;
> glob_min_pole_est := glob_larger_float;
> last_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> glob_min_h := float_abs(glob_min_h) * glob_check_sign;
> glob_max_h := float_abs(glob_max_h) * glob_check_sign;
> glob_h := float_abs(glob_min_h) * glob_check_sign;
> glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign));
> display_max := c(x_end) - c(x_start)/glob__10;
> if ((glob_display_interval) > (display_max)) then # if number 10
> glob_display_interval := c(display_max);
> fi;# end if 10;
> chk_data();
> min_value := glob_larger_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := glob_small_float;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> atomall();
> if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> glob_h := glob_check_sign * float_abs(glob_min_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
> glob_h_reason := 2;
> glob_h := glob_display_interval;
> found_h := true;
> fi;# end if 10;
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if ( not found_h) then # if number 10
> est_answer := est_size_answer();
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := test_suggested_h();
> omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
> if (estimated_step_error < est_needed_step_err) then # if number 11
> omniout_str(ALWAYS,"Double H and LOOP");
> glob_h := glob_h*glob__2;
> else
> omniout_str(ALWAYS,"Found H for OPTIMAL");
> found_h := true;
> glob_h_reason := 3;
> glob_h := glob_h/glob__2;
> fi;# end if 11;
> fi;# end if 10;
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 10
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 10;
> if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MAX H");
> glob_h := glob_check_sign * float_abs(glob_max_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> else
> found_h := true;
> glob_h := glob_h * glob_check_sign;
> fi;# end if 9;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 9
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 9;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 9
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> glob_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and (glob_check_sign * array_x[1] < glob_check_sign * x_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1
> #left paren 0001C
> if (reached_interval()) then # if number 10
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 10;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> track_estimated_error();
> atomall();
> track_estimated_error();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if (reached_interval()) then # if number 10
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 10;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 10
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 10;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 10;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = neg ( 5.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2016-08-26T17:09:04-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sing7_back")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = neg ( 5.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 308.maple.seems.ok | ")
> ;
> logitem_str(html_log_file,"sing7_back diffeq.mxt")
> ;
> logitem_str(html_log_file,"sing7_back maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> fi;# end if 14
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_5D0,
array_const_6D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
ATS_MAX_TERMS := 30;
Digits := 64;
max_terms := 30;
glob_html_log := true;
array_y_init := Array(0 .. 30, []);
array_norms := Array(0 .. 30, []);
array_fact_1 := Array(0 .. 30, []);
array_1st_rel_error := Array(0 .. 2, []);
array_last_rel_error := Array(0 .. 2, []);
array_est_rel_error := Array(0 .. 2, []);
array_max_est_error := Array(0 .. 2, []);
array_type_pole := Array(0 .. 2, []);
array_type_real_pole := Array(0 .. 2, []);
array_type_complex_pole := Array(0 .. 2, []);
array_est_digits := Array(0 .. 2, []);
array_y := Array(0 .. 30, []);
array_x := Array(0 .. 30, []);
array_tmp0 := Array(0 .. 30, []);
array_tmp1 := Array(0 .. 30, []);
array_tmp2 := Array(0 .. 30, []);
array_tmp3 := Array(0 .. 30, []);
array_tmp4 := Array(0 .. 30, []);
array_tmp5 := Array(0 .. 30, []);
array_tmp6 := Array(0 .. 30, []);
array_tmp7 := Array(0 .. 30, []);
array_tmp8 := Array(0 .. 30, []);
array_tmp9 := Array(0 .. 30, []);
array_tmp10 := Array(0 .. 30, []);
array_tmp11 := Array(0 .. 30, []);
array_tmp12 := Array(0 .. 30, []);
array_tmp13 := Array(0 .. 30, []);
array_tmp14 := Array(0 .. 30, []);
array_m1 := Array(0 .. 30, []);
array_y_higher := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []);
array_y_set_initial := Array(0 .. 2, 0 .. 31, []);
array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
array_fact_2 := Array(0 .. 30, 0 .. 31, []);
term := 1;
while term <= 30 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 30 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 30 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp6[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp7[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp8[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp9[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp10[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 30 do array_tmp11[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 30 do array_tmp12[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 30 do array_tmp13[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 30 do array_tmp14[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 30 do
term := 1;
while term <= 30 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
zero_ats_ar(array_tmp6);
zero_ats_ar(array_tmp7);
zero_ats_ar(array_tmp8);
zero_ats_ar(array_tmp9);
zero_ats_ar(array_tmp10);
zero_ats_ar(array_tmp11);
zero_ats_ar(array_tmp12);
zero_ats_ar(array_tmp13);
zero_ats_ar(array_tmp14);
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_5D0);
array_const_5D0[1] := c(5.0);
zero_ats_ar(array_const_6D0);
array_const_6D0[1] := c(6.0);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_h := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 1000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 30;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/sing7_backpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = neg ( 5.0 ) / \
( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) /\
( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=64;");
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(3.0);");
omniout_str(ALWAYS, "x_end := c(2.0);");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "");
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 := 1;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(6.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=100000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=false;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "return(c(1.0)/ ( c(x) - c(6.0) ) / ( c(x) - c(6.\
0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )) ;\
");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := c(3.0);
x_end := c(2.0);
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 1;
array_given_rad_poles[1, 1] := c(6.0);
glob_desired_digits_correct := 8;
glob_max_minutes := 3.0;
glob_subiter_method := 3;
glob_max_iter := 100000;
glob_upper_ratio_limit := c(1.000001);
glob_lower_ratio_limit := c(0.999999);
glob_look_poles := false;
glob_h := c(0.001);
glob_display_interval := c(0.01);
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
glob_check_sign := c(my_check_sign(x_start, x_end));
glob__pi := arccos(glob__m1);
glob_prec = expt(10.0, c(-Digits));
if glob_optimize then
omniout_str(ALWAYS, "START of Optimize");
found_h := false;
glob_min_pole_est := glob_larger_float;
last_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
glob_min_h := float_abs(glob_min_h)*glob_check_sign;
glob_max_h := float_abs(glob_max_h)*glob_check_sign;
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_display_interval :=
c(float_abs(c(glob_display_interval))*glob_check_sign);
display_max := c(x_end) - c(x_start)/glob__10;
if display_max < glob_display_interval then
glob_display_interval := c(display_max)
end if;
chk_data();
min_value := glob_larger_float;
est_answer := est_size_answer();
opt_iter := 1;
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
;
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := glob_small_float;
while opt_iter <= 100 and not found_h do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] :=
array_y_init[it]*expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
atomall();
if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if;
if
glob_check_sign*glob_display_interval <= glob_check_sign*glob_h
then
omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL");
glob_h_reason := 2;
glob_h := glob_display_interval;
found_h := true
end if;
if glob_look_poles then check_for_pole() end if;
if not found_h then
est_answer := est_size_answer();
est_needed_step_err := estimated_needed_step_error(x_start,
x_end, glob_h, est_answer);
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := test_suggested_h();
omniout_float(ALWAYS, "estimated_step_error", 32,
estimated_step_error, 32, "");
if estimated_step_error < est_needed_step_err then
omniout_str(ALWAYS, "Double H and LOOP");
glob_h := glob_h*glob__2
else
omniout_str(ALWAYS, "Found H for OPTIMAL");
found_h := true;
glob_h_reason := 3;
glob_h := glob_h/glob__2
end if
end if;
opt_iter := opt_iter + 1
end do;
if not found_h and opt_iter = 1 then
omniout_str(ALWAYS, "Beginning glob_h too large.");
found_h := false
end if;
if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then
omniout_str(ALWAYS, "SETTING H FOR MAX H");
glob_h := float_abs(glob_max_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if
else found_h := true; glob_h := glob_check_sign*glob_h
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
glob_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
glob_clock_sec - glob_orig_start_sec < glob_max_sec do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
track_estimated_error();
atomall();
track_estimated_error();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = neg ( 5.0 ) \
/ ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0\
) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6\
.0 ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2016-08-26T17:09:04-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sing7_back");
logitem_str(html_log_file, "diff ( y , x , 1 ) = ne\
g ( 5.0 ) / ( x - 6.0 ) / ( x - 6.0 ) \
/ ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6\
.0 ) / ( x - 6.0 ) ; ");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 308.maple.seems.ok | ");
logitem_str(html_log_file, "sing7_back diffeq.mxt");
logitem_str(html_log_file, "sing7_back maple results");
logitem_str(html_log_file, "OK");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
##############ECHO OF PROBLEM#################
##############temp/sing7_backpostode.ode#################
diff ( y , x , 1 ) = neg ( 5.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=64;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(3.0);
x_end := c(2.0);
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 1;
array_given_rad_poles[1,1] := c(6.0);
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=100000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=false;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(1.0)/ ( c(x) - c(6.0) ) / ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )) ;
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=0.09
x[1] = 2.999
y[1] (closed_form) = -0.0041083744802657093950780428399777
y[1] (numeric) = -0.0041083744802657093944857661080764
absolute error = 5.9227673190131747068171893954906e-22
relative error = 1.4416327789647158292137470656978e-17 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 64
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.998
y[1] (closed_form) = -0.0041015363085463932069181756758744
y[1] (numeric) = -0.0041015363085463932057357894065657
absolute error = 1.1823862693086793667282175364401e-21
relative error = 2.8827887414892189421896662900447e-17 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 64
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.997
y[1] (closed_form) = -0.0040947117904110049780678777201631
y[1] (numeric) = -0.0040947117904110049762975404599509
absolute error = 1.7703372602122282351285122475233e-21
relative error = 4.3234722022634256643534768105309e-17 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 64
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.996
y[1] (closed_form) = -0.0040879008940647811499001256073957
y[1] (numeric) = -0.0040879008940647811475439872921659
absolute error = 2.3561383152297782109631676002449e-21
relative error = 5.7636874676943681814732105802677e-17 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 64
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.995
y[1] (closed_form) = -0.0040811035877975467982956684209535
y[1] (numeric) = -0.0040811035877975467953558704131728
absolute error = 2.9397980077806853263474892971272e-21
relative error = 7.2034388359331232243867457156676e-17 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 64
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.994
y[1] (closed_form) = -0.0040743198399834625427422014083783
y[1] (numeric) = -0.0040743198399834625392208765341194
absolute error = 3.5213248742588514171045382113724e-21
relative error = 8.6427305969016519230562692621790e-17 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 64
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.993
y[1] (closed_form) = -0.0040675496190807722965461955972546
y[1] (numeric) = -0.0040675496190807722924454681830498
absolute error = 4.1007274142048662307742267261038e-21
relative error = 1.0081567032319551154750745127198e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.992
y[1] (closed_form) = -0.0040607928936315518550835510449983
y[1] (numeric) = -0.004060792893631551850405536954521
absolute error = 4.6780140904772923135834240066508e-21
relative error = 1.1519952415730716709862324585498e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.991
y[1] (closed_form) = -0.0040540496322614583190274918609333
y[1] (numeric) = -0.0040540496322614583137742985315102
absolute error = 5.2531933294230972281758663715522e-21
relative error = 1.2957891012529918597573091262068e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (closed_form) = -0.0040473198036794803495043186704984
y[1] (numeric) = -0.0040473198036794803436780451494511
absolute error = 5.8262735210472376282287646172088e-21
relative error = 1.4395387079989288812304553839120e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.989
y[1] (closed_form) = -0.0040406033766776892521397790949967
y[1] (numeric) = -0.0040406033766776892457425160758153
absolute error = 6.3972630191813996905643501162352e-21
relative error = 1.5832444867284721880603862046796e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.988
y[1] (closed_form) = -0.004033900320130990886970909340439
y[1] (numeric) = -0.0040339003201309908800047391987871
absolute error = 6.9661701416519003799982403575067e-21
relative error = 1.7269068615522188506847799037931e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.987
y[1] (closed_form) = -0.0040272106029968784012102403689784
y[1] (numeric) = -0.0040272106029968783936772371985317
absolute error = 7.5330031704467539969514733328694e-21
relative error = 1.8705262557763962634878170401636e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.986
y[1] (closed_form) = -0.0040205341943151857818612506082185
y[1] (numeric) = -0.0040205341943151857737634802563366
absolute error = 8.0977703518819084327884061623927e-21
relative error = 2.0141030919054762241420241351120e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.985
y[1] (closed_form) = -0.0040138710632078422251958839781218
y[1] (numeric) = -0.0040138710632078422165354040813551
absolute error = 8.6604798967666555329274502583130e-21
relative error = 2.1576377916447804175879343667676e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.984
y[1] (closed_form) = -0.0040072211788786273201168374219896
y[1] (numeric) = -0.0040072211788786273108956974414214
absolute error = 9.2211399805682199430048830955042e-21
relative error = 2.3011307759030773359859657560725e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.983
y[1] (closed_form) = -0.0040005845106129270424391563554543
y[1] (numeric) = -0.0040005845106129270326593976118788
absolute error = 9.7797587435755307887528014445483e-21
relative error = 2.4445824647951706658503445604244e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.982
y[1] (closed_form) = -0.0039939610277774905571374597328887
y[1] (numeric) = -0.0039939610277774905468011154418265
absolute error = 1.0336344291062180515779735073227e-20
relative error = 2.5879932776444791734508651348498e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.981
y[1] (closed_form) = -0.0039873506998201878256168490101593
y[1] (numeric) = -0.0039873506998201878147259443167108
absolute error = 1.0890904693448575191115601911392e-20
relative error = 2.7313636329856081194447749222696e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (closed_form) = -0.0039807534962697680150772373911478
y[1] (numeric) = -0.0039807534962697680036337894046845
absolute error = 1.1443447986463280544200640074859e-20
relative error = 2.8746939485669122335781020202090e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.979
y[1] (closed_form) = -0.0039741693867356187070524676166617
y[1] (numeric) = -0.0039741693867356186950584854453581
absolute error = 1.1993982171303568000959789580373e-20
relative error = 3.0179846413530502801733004798283e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.978
y[1] (closed_form) = -0.0039675983409075259022171684208513
y[1] (numeric) = -0.0039675983409075258896746532060561
absolute error = 1.2542515214795164940708813689921e-20
relative error = 3.1612361275275312449981726752154e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.977
y[1] (closed_form) = -0.0039610403285554348185658318734518
y[1] (numeric) = -0.0039610403285554348054767768239006
absolute error = 1.3089055049551213381885349201235e-20
relative error = 3.3044488224952521739896362994447e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.976
y[1] (closed_form) = -0.0039544953195292114800800763763693
y[1] (numeric) = -0.0039544953195292114664464668022389
absolute error = 1.3633609574130441278986165181500e-20
relative error = 3.4476231408850276941850333740173e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.975
y[1] (closed_form) = -0.0039479632837584050930114933194635
y[1] (numeric) = -0.003947963283758405078835306666269
absolute error = 1.4176186653194550589620305038330e-20
relative error = 3.5907594965521112470933276870147e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.974
y[1] (closed_form) = -0.0039414441912520112069188595508464
y[1] (numeric) = -0.0039414441912520111922020654331815
absolute error = 1.4716794117664826247255607696122e-20
relative error = 3.7338583025807080646187029016315e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.973
y[1] (closed_form) = -0.0039349380120982356576098331084949
y[1] (numeric) = -0.003934938012098235642354393343617
absolute error = 1.5255439764877970152042476061769e-20
relative error = 3.8769199712864799175297538116280e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.972
y[1] (closed_form) = -0.0039284447164642592891485363182159
y[1] (numeric) = -0.0039284447164642592733564049594747
absolute error = 1.5792131358741164269042816750446e-20
relative error = 4.0199449142190416663486554863809e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.971
y[1] (closed_form) = -0.0039219642745960034521016686126328
y[1] (numeric) = -0.0039219642745960034357747919827464
absolute error = 1.6326876629886366900272951753327e-20
relative error = 4.1629335421644496444163969801272e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (closed_form) = -0.0039154966568178962752069814904192
y[1] (numeric) = -0.0039154966568178962583472982145953
absolute error = 1.6859683275823846174186143602921e-20
relative error = 4.3058862651476819027723755239041e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.969
y[1] (closed_form) = -0.0039090418335326397076590901368851
y[1] (numeric) = -0.0039090418335326396902685311757901
absolute error = 1.7390558961094954773572329512164e-20
relative error = 4.4488034924351103463693613324290e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.968
y[1] (closed_form) = -0.0039025997752209773292186905875625
y[1] (numeric) = -0.0039025997752209773112991792701383
absolute error = 1.7919511317424149900338881420516e-20
relative error = 4.5916856325369647910280600111873e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.967
y[1] (closed_form) = -0.003896170452441462925362298155847
y[1] (numeric) = -0.0038961704524414629069157502119768
absolute error = 1.8446547943870262453255857932195e-20
relative error = 4.7345330932097889704192167222498e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.966
y[1] (closed_form) = -0.0038897538358302298247006223831775
y[1] (numeric) = -0.0038897538358302298057289459762005
absolute error = 1.8971676406977019372501456365298e-20
relative error = 4.8773462814588885222454214532425e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.965
y[1] (closed_form) = -0.0038833498961007609959046462237191
y[1] (numeric) = -0.0038833498961007609764097419827963
absolute error = 1.9494904240922823082727379624023e-20
relative error = 5.0201256035407709826794856362595e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.964
y[1] (closed_form) = -0.0038769586040436599013893827620472
y[1] (numeric) = -0.0038769586040436598813731438143774
absolute error = 2.0016238947669791944378779890617e-20
relative error = 5.1628714649655778180014646974942e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.963
y[1] (closed_form) = -0.0038705799305264221050161416977984
y[1] (numeric) = -0.0038705799305264220844804537006863
absolute error = 2.0535687997112065601148511155643e-20
relative error = 5.3055842704995085222620966104038e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.962
y[1] (closed_form) = -0.0038642138464932076310849503305178
y[1] (numeric) = -0.0038642138464932076100316915032944
absolute error = 2.1053258827223379089719802689021e-20
relative error = 5.4482644241672368096866109129712e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.961
y[1] (closed_form) = -0.0038578603229646140718995400547569
y[1] (numeric) = -0.003857860322964614050330581210553
absolute error = 2.1568958844203909556354348365754e-20
relative error = 5.5909123292543189304195336819017e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (closed_form) = -0.0038515193310374504411980296425951
y[1] (numeric) = -0.0038515193310374504191152342199687
absolute error = 2.2082795422626399403413390268532e-20
relative error = 5.7335283883095941380982693933111e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.959
y[1] (closed_form) = -0.0038451908418845117707531110598515
y[1] (numeric) = -0.0038451908418845117481583351542699
absolute error = 2.2594775905581559667556862431722e-20
relative error = 5.8761130031475773376308782115907e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.958
y[1] (closed_form) = -0.0038388748267543544474561724439467
y[1] (numeric) = -0.0038388748267543544243512648391239
absolute error = 2.3104907604822757410149260435581e-20
relative error = 6.0186665748508439414415848176190e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.957
y[1] (closed_form) = -0.0038325712569710722882103763752763
y[1] (numeric) = -0.0038325712569710722645971785743663
absolute error = 2.3613197800909990879309828469230e-20
relative error = 6.1611895037724069623361502072105e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.956
y[1] (closed_form) = -0.0038262801039340733499682499086228
y[1] (numeric) = -0.0038262801039340733258485961652696
absolute error = 2.4119653743353156182078126278614e-20
relative error = 6.3036821895380863710283087644013e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.955
y[1] (closed_form) = -0.0038200013391178574722598362041077
y[1] (numeric) = -0.0038200013391178574476355535533531
absolute error = 2.4624282650754609184323278047626e-20
relative error = 6.4461450310488707462580171564232e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.954
y[1] (closed_form) = -0.0038137349340717945495679062149797
y[1] (numeric) = -0.0038137349340717945244408145040287
absolute error = 2.5127091710951026335305442761870e-20
relative error = 6.5885784264832712453222770333432e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.953
y[1] (closed_form) = -0.0038074808604199035309171329576557
y[1] (numeric) = -0.0038074808604199035052890448765011
absolute error = 2.5628088081154568093200515063449e-20
relative error = 6.7309827732996679227297779813558e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.952
y[1] (closed_form) = -0.0038012390898606321440544906123635
y[1] (numeric) = -0.0038012390898606321179272117242701
absolute error = 2.6127278888093348607423006128885e-20
relative error = 6.8733584682386484245815585212844e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.951
y[1] (closed_form) = -0.00379500959416663734160845628397
y[1] (numeric) = -0.0037950095941666373149837850558188
absolute error = 2.6624671228151215293226709782224e-20
relative error = 7.0157059073253390861712990202216e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (closed_form) = -0.003788792345184566466624863894591
y[1] (numeric) = -0.0037887923451845664395045917270841
absolute error = 2.7120272167506841913827378932692e-20
relative error = 7.1580254858717284601907390622116e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.949
y[1] (closed_form) = -0.0037825873148348391348874875838706
y[1] (numeric) = -0.0037825873148348391072733988415985
absolute error = 2.7614088742272138765175475458312e-20
relative error = 7.3003175984789833028180509817107e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.948
y[1] (closed_form) = -0.0037763944751114298314416163598805
y[1] (numeric) = -0.0037763944751114298033354884012505
absolute error = 2.8106127958629983538509371682909e-20
relative error = 7.4425826390397570448597987899442e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.947
y[1] (closed_form) = -0.0037702137980816512187490227729405
y[1] (numeric) = -0.0037702137980816511901526259799692
absolute error = 2.8596396792971276415939437301929e-20
relative error = 7.5848210007404907750103655182686e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
memory used=48.3MB, alloc=40.3MB, time=0.74
x[1] = 2.946
y[1] (closed_form) = -0.0037640452558859381539128262748435
y[1] (numeric) = -0.0037640452558859381248279240828121
absolute error = 2.9084902192031322934550510505665e-20
relative error = 7.7270330760637067621864399736140e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.945
y[1] (closed_form) = -0.0037578888207376324124208068745308
y[1] (numeric) = -0.0037578888207376323828491558015052
absolute error = 2.9571651073025548134863599412450e-20
relative error = 7.8692192567902945437883139686600e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.944
y[1] (closed_form) = -0.0037517444649227681158657369048157
y[1] (numeric) = -0.0037517444649227680858090865810312
absolute error = 3.0056650323784545489966567793930e-20
relative error = 8.0113799340017896066343511834188e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.943
y[1] (closed_form) = -0.0037456121607998578611112683689116
y[1] (numeric) = -0.0037456121607998578305713615660232
absolute error = 3.0539906802888464092207310201628e-20
relative error = 8.1535154980826446872100468753619e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.942
y[1] (closed_form) = -0.0037394918807996795483818406349611
y[1] (numeric) = -0.0037394918807996795173604132951604
absolute error = 3.1021427339800737555040803424857e-20
relative error = 8.2956263387224937177686016322145e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.941
y[1] (closed_form) = -0.0037333835974250639057649583852025
y[1] (numeric) = -0.0037333835974250638742637396502013
absolute error = 3.1501218735001158068432725813385e-20
relative error = 8.4377128449184084447158802151982e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (closed_form) = -0.0037272872832506827076240328966126
y[1] (numeric) = -0.0037272872832506826756447451364943
absolute error = 3.1979287760118299027146360093311e-20
relative error = 8.5797754049771477456090162409545e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.939
y[1] (closed_form) = -0.0037212029109228376844297811236562
y[1] (numeric) = -0.0037212029109228376519741399655949
absolute error = 3.2455641158061289632275540189437e-20
relative error = 8.7218144065173996709947529777138e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.938
y[1] (closed_form) = -0.0037151304531592501215279368620387
y[1] (numeric) = -0.0037151304531592500885976512188877
absolute error = 3.2930285643150944847533774097495e-20
relative error = 8.8638302364720162372108778754419e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.937
y[1] (closed_form) = -0.0037090698827488511443707466850426
y[1] (numeric) = -0.0037090698827488511109675187837923
absolute error = 3.3403227901250254073067683406677e-20
relative error = 9.0058232810902409961718116105084e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.936
y[1] (closed_form) = -0.0037030211725515726877494005501637
y[1] (numeric) = -0.0037030211725515726538749259602695
absolute error = 3.3874474589894231880930860533902e-20
relative error = 9.1477939259399294080575494124736e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.935
y[1] (closed_form) = -0.0036969842954981391465741831614289
y[1] (numeric) = -0.0036969842954981391122301508230098
absolute error = 3.4344032338419134137831476437645e-20
relative error = 9.2897425559097620427237212732078e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.934
y[1] (closed_form) = -0.0036909592245898597057587275291672
y[1] (numeric) = -0.0036909592245898596709468197810762
absolute error = 3.4811907748091042822352798306319e-20
relative error = 9.4316695552114506355495363457488e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.933
y[1] (closed_form) = -0.0036849459328984213467743068803722
y[1] (numeric) = -0.0036849459328984213114961994881384
absolute error = 3.5278107392233822825539526643175e-20
relative error = 9.5735753073819370233398034607340e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.932
y[1] (closed_form) = -0.003678944393565682528449615324487
y[1] (numeric) = -0.0036789443935656824927069775081306
absolute error = 3.5742637816356454005543866848977e-20
relative error = 9.7154601952855849857970722701292e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.931
y[1] (closed_form) = -0.0036729545798034675396009616559187
y[1] (numeric) = -0.0036729545798034675033954561176389
absolute error = 3.6205505538279741748932848731630e-20
relative error = 9.8573246011163650179802161291016e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (closed_form) = -0.0036669764648933615210872345593818
y[1] (numeric) = -0.0036669764648933614844205175111194
absolute error = 3.6666717048262409273271939558533e-20
relative error = 9.9991689064000320590664765144953e-16 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 18
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.929
y[1] (closed_form) = -0.0036610100221865061548933914599409
y[1] (numeric) = -0.0036610100221865061177671126508143
absolute error = 3.7126278809126574887718807807460e-20
relative error = 1.0140993491996296202635107629158e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.928
y[1] (closed_form) = -0.0036550552251033960178555775081179
y[1] (numeric) = -0.0036550552251033959802713802517353
absolute error = 3.7584197256382617410584535415231e-20
relative error = 1.0282798738100986413592296941415e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.927
y[1] (closed_form) = -0.0036491120471336755976502958925343
y[1] (numeric) = -0.0036491120471336755596098170941809
absolute error = 3.8040478798353432925147000046379e-20
relative error = 1.0424585024248207276758990853710e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.926
y[1] (closed_form) = -0.0036431804618359369686793260082526
y[1] (numeric) = -0.0036431804618359369301841961919546
absolute error = 3.8495129816298086037431913880171e-20
relative error = 1.0566352729312488802045622588516e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.925
y[1] (closed_form) = -0.003637260442837518125491322157382
y[1] (numeric) = -0.0036372604428375180865431654928471
absolute error = 3.8948156664534858782210473985939e-20
relative error = 1.0708102231510929311040519837071e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.924
y[1] (closed_form) = -0.0036313519638343019713902225978593
y[1] (numeric) = -0.0036313519638343019319906569272956
absolute error = 3.9399565670563700306098118006463e-20
relative error = 1.0849833908405331429741960860333e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.923
y[1] (closed_form) = -0.0036254549985905159598897570639812
y[1] (numeric) = -0.0036254549985905159200403939287931
absolute error = 3.9849363135188080439375858191954e-20
relative error = 1.0991548136904331212067447694218e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.922
y[1] (closed_form) = -0.0036195695209385323866824605347474
y[1] (numeric) = -0.0036195695209385323463849052021112
absolute error = 4.0297555332636250250993461501887e-20
relative error = 1.1133245293265520418677772033923e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.921
y[1] (closed_form) = -0.0036136955047786693298006821990392
y[1] (numeric) = -0.0036136955047786692890565336883573
absolute error = 4.0744148510681912664151732253831e-20
relative error = 1.1274925753097561975557861405468e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (closed_form) = -0.0036078329240789922356561214348795
y[1] (numeric) = -0.0036078329240789921944669725441152
absolute error = 4.1189148890764306192898719411371e-20
relative error = 1.1416589891362298636701208535889e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.919
y[1] (closed_form) = -0.003601981752875116148653427357459
y[1] (numeric) = -0.0036019817528751161070208646893513
absolute error = 4.1632562668107704843311199832395e-20
relative error = 1.1558238082376854875149903575261e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.918
y[1] (closed_form) = -0.0035961419652700085820823652703501
y[1] (numeric) = -0.0035961419652700085400079692585098
absolute error = 4.2074396011840337206067672383591e-20
relative error = 1.1699870699815732026547905181090e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.917
y[1] (closed_form) = -0.0035903135354337930280019823486359
y[1] (numeric) = -0.0035903135354337929854873272835231
absolute error = 4.2514655065112727750551730453173e-20
relative error = 1.1841488116712896709271200634903e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.916
y[1] (closed_form) = -0.0035844964376035531038390962629572
y[1] (numeric) = -0.0035844964376035530608857503177417
absolute error = 4.2953345945215463314054460667956e-20
relative error = 1.1983090705463862545104915316969e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.915
y[1] (closed_form) = -0.0035786906460831373334322843903306
y[1] (numeric) = -0.0035786906460831372900418096466342
absolute error = 4.3390474743696387763170846042744e-20
relative error = 1.2124678837827765204344236221791e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.914
y[1] (closed_form) = -0.0035728961352429645602613679207506
y[1] (numeric) = -0.0035728961352429645164353203942733
absolute error = 4.3826047526477227788107438726529e-20
relative error = 1.2266252884929430799103210966820e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.913
y[1] (closed_form) = -0.0035671128795198299906111647270093
y[1] (numeric) = -0.0035671128795198299463510943930396
absolute error = 4.4260070333969652774336221168826e-20
relative error = 1.2407813217261437648523071150869e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.912
y[1] (closed_form) = -0.0035613408534167118644270274869486
y[1] (numeric) = -0.0035613408534167118197344783057578
absolute error = 4.4692549181190771679842008933000e-20
relative error = 1.2549360204686171439479705186874e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.911
y[1] (closed_form) = -0.0035555800315025787516283893998019
y[1] (numeric) = -0.0035555800315025787065048993419239
absolute error = 4.5123490057878069830117381342816e-20
relative error = 1.2690894216437873806298269104137e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (closed_form) = -0.0035498303884121974716552090878715
y[1] (numeric) = -0.0035498303884121974261023101592678
absolute error = 4.5552898928603788527059379237886e-20
relative error = 1.2832415621124684352891672535213e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.909
y[1] (closed_form) = -0.0035440918988459416340308390871979
y[1] (numeric) = -0.0035440918988459415880500573543091
absolute error = 4.5980781732888750352015507645007e-20
relative error = 1.2973924786730676140648809427363e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.908
y[1] (closed_form) = -0.0035383645375696007977334388709855
y[1] (numeric) = -0.0035383645375696007513262944856698
absolute error = 4.6407144385315633027412354169563e-20
relative error = 1.3115422080617884665307917212048e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.907
y[1] (closed_form) = -0.0035326482794141902471766137814284
y[1] (numeric) = -0.0035326482794141902003446210057867
absolute error = 4.6831992775641694685677814085228e-20
relative error = 1.3256907869528330345960342500559e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.906
y[1] (closed_form) = -0.0035269430992757613826084857325097
y[1] (numeric) = -0.0035269430992757613353531529635987
absolute error = 4.7255332768910953378536936824175e-20
relative error = 1.3398382519586034549240264130244e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.905
y[1] (closed_form) = -0.0035212489721152127227468902508203
y[1] (numeric) = -0.0035212489721152126750697200452545
absolute error = 4.7677170205565823644221215854239e-20
relative error = 1.3539846396299029171666573852936e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.904
y[1] (closed_form) = -0.0035155658729581015174768475051586
y[1] (numeric) = -0.0035155658729581014693793366036004
absolute error = 4.8097510901558212934681178396767e-20
relative error = 1.3681299864561359803014139432451e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.903
y[1] (closed_form) = -0.0035098937768944559684448725995485
y[1] (numeric) = -0.0035098937768944559199285119510885
absolute error = 4.8516360648460080689531840300296e-20
relative error = 1.3822743288655082493503072706874e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.902
y[1] (closed_form) = -0.0035042326590785880553930727284975
y[1] (numeric) = -0.0035042326590785880064593475149241
absolute error = 4.8933725213573462828189425415519e-20
relative error = 1.3964177032252254147506394587658e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.901
y[1] (closed_form) = -0.0034985824947289069660843259771673
y[1] (numeric) = -0.0034985824947289069167347156371274
absolute error = 4.9349610340039964416475162330824e-20
relative error = 1.4105601458416916566388628333092e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (closed_form) = -0.0034929432591277331276781487512501
y[1] (numeric) = -0.0034929432591277330779141270043004
absolute error = 4.9764021746949723248867422155281e-20
relative error = 1.4247016929607074163000360078643e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.899
y[1] (closed_form) = -0.0034873149276211128374251361995574
y[1] (numeric) = -0.0034873149276211127872481710701076
absolute error = 5.0176965129449847072576410499708e-20
relative error = 1.4388423807676665370266679868934e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.898
y[1] (closed_form) = -0.0034816974756186334905561027037067
y[1] (numeric) = -0.0034816974756186334399676565448544
absolute error = 5.0588446158852327164695539697043e-20
relative error = 1.4529822453877527766220655662070e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.897
y[1] (closed_form) = -0.0034760908785932394032502577101362
y[1] (numeric) = -0.0034760908785932393522517872273948
absolute error = 5.0998470482741430958849951856304e-20
relative error = 1.4671213228861356937746595320518e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.896
y[1] (closed_form) = -0.0034704951120810482285749260255497
y[1] (numeric) = -0.0034704951120810481771678823004691
absolute error = 5.1407043725080576403014911217353e-20
relative error = 1.4812596492681659105211815826112e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.895
y[1] (closed_form) = -0.0034649101516811679632974613425867
y[1] (numeric) = -0.003464910151681167911483289856268
absolute error = 5.1814171486318690715514410522309e-20
relative error = 1.4953972604795697530079963229775e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.894
y[1] (closed_form) = -0.0034593359730555145434781073620878
y[1] (numeric) = -0.0034593359730555144912582480185917
absolute error = 5.2219859343496056191632819175316e-20
relative error = 1.5095341924066432727513609547193e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.893
y[1] (closed_form) = -0.0034537725519286300267606325850877
y[1] (numeric) = -0.0034537725519286299741365197347381
absolute error = 5.2624112850349645698779222609775e-20
relative error = 1.5236704808764456505888892325593e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.892
y[1] (closed_form) = -0.0034482198640875013592856028142004
y[1] (numeric) = -0.0034482198640875013062586652767824
absolute error = 5.3026937537417950483734747635728e-20
relative error = 1.5378061616569919855060357327392e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.891
y[1] (closed_form) = -0.0034426778853813797251591597821814
y[1] (numeric) = -0.0034426778853813796717308208700361
absolute error = 5.3428338912145302901187126021956e-20
relative error = 1.5519412704574454705129913105084e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
memory used=94.9MB, alloc=44.3MB, time=1.43
x[1] = 2.89
y[1] (closed_form) = -0.003437146591721600476418145266291
y[1] (numeric) = -0.0034371465917216004225898228073053
absolute error = 5.3828322458985696658513509885440e-20
relative error = 1.5660758429283089577389906587174e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.889
y[1] (closed_form) = -0.0034316259590814036414403477009852
y[1] (numeric) = -0.0034316259590814035872134540614791
absolute error = 5.4226893639506107157611612585978e-20
relative error = 1.5802099146616159149026779573869e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.888
y[1] (closed_form) = -0.0034261159634957550097565528181125
y[1] (numeric) = -0.0034261159634957549551324949256232
absolute error = 5.4624057892489314500500105968416e-20
relative error = 1.5943435211911207753088565677839e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.887
y[1] (closed_form) = -0.0034206165810611677912289513720974
y[1] (numeric) = -0.0034206165810611677362091307380612
absolute error = 5.5019820634036231711411360390746e-20
relative error = 1.6084766979924886835136634171392e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.886
y[1] (closed_form) = -0.0034151277879355248475682956957787
y[1] (numeric) = -0.0034151277879355247921541084381109
absolute error = 5.5414187257667740714182572653004e-20
relative error = 1.6226094804834846387919579856352e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.885
y[1] (closed_form) = -0.0034096495603379014941700028281388
y[1] (numeric) = -0.0034096495603379014383628396937128
absolute error = 5.5807163134426038589914596505096e-20
relative error = 1.6367419040241620385324994903505e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.884
y[1] (closed_form) = -0.0034041818745483888702571754048947
y[1] (numeric) = -0.0034041818745483888140584217919192
absolute error = 5.6198753612975496626110881822178e-20
relative error = 1.6508740039170506236783038069189e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.883
y[1] (closed_form) = -0.0033987247069079178753262525529166
y[1] (numeric) = -0.0033987247069079178187372885332136
absolute error = 5.6588964019703034654831355888353e-20
relative error = 1.6650058154073438283214237249063e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.882
y[1] (closed_form) = -0.0033932780338180836698987118250772
y[1] (numeric) = -0.0033932780338180836129209121662592
absolute error = 5.6977799658818013163797360730051e-20
relative error = 1.6791373736830855355532821442636e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.881
y[1] (closed_form) = -0.003387841831740970738589919898091
y[1] (numeric) = -0.0033878418317409706812246540856394
absolute error = 5.7365265812451645650863414388201e-20
relative error = 1.6932687138753562416636076353152e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (closed_form) = -0.0033824160771989785135138744761813
y[1] (numeric) = -0.0033824160771989784557625067354253
absolute error = 5.7751367740755933678829114782442e-20
relative error = 1.7073998710584586307729752519885e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.879
y[1] (closed_form) = -0.0033770007467746475560501927412978
y[1] (numeric) = -0.0033770007467746474979140820592957
absolute error = 5.8136110682002127074199478820986e-20
relative error = 1.7215308802501025619759424564859e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.878
y[1] (closed_form) = -0.0033715958171104862950072829087187
y[1] (numeric) = -0.00337159581711048623648778305604
absolute error = 5.8519499852678711700213936095505e-20
relative error = 1.7356617764115894710637903331897e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.877
y[1] (closed_form) = -0.0033662012649087983192231851271279
y[1] (numeric) = -0.003366201264908798260321644679539
absolute error = 5.8901540447588927221252608330538e-20
relative error = 1.7497925944479961888879337908284e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.876
y[1] (closed_form) = -0.0033608170669315102226530862459082
y[1] (numeric) = -0.0033608170669315101633708486059604
absolute error = 5.9282237639947817262592938179196e-20
relative error = 1.7639233692083581784171510261013e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.875
y[1] (closed_form) = -0.0033554432
y[1] (numeric) = -0.0033554431999999999403384034185212
absolute error = 5.9661596581478814356429722388595e-20
relative error = 1.7780541354858521925339020010410e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.874
y[1] (closed_form) = -0.0033500796409949259909525600741339
y[1] (numeric) = -0.003350079640994925930912937671624
absolute error = 6.0039622402509862052086696165724e-20
relative error = 1.7921849280179783546071579230940e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.873
y[1] (closed_form) = -0.0033447263668560563711012984427811
y[1] (numeric) = -0.003344726366856056310684978230712
absolute error = 6.0416320212069076555437552053033e-20
relative error = 1.8063157814867416638713485646256e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.872
y[1] (closed_form) = -0.0033393833545820991876121754783259
y[1] (numeric) = -0.003339383354582099126820480380346
absolute error = 6.0791695097979950249718204978560e-20
relative error = 1.8204467305188329276332515714126e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.871
y[1] (closed_form) = -0.0033340505812305329377434917156476
y[1] (numeric) = -0.0033340505812305328765777395886915
absolute error = 6.1165752126956099437149785473601e-20
relative error = 1.8345778096858091223208975424833e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (closed_form) = -0.0033287280239174376882996439937289
y[1] (numeric) = -0.0033287280239174376267611476490333
absolute error = 6.1538496344695558628102808318527e-20
relative error = 1.8487090535042731853808464719083e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.869
y[1] (closed_form) = -0.0033234156598173267341224911006682
y[1] (numeric) = -0.0033234156598173266722125583246936
absolute error = 6.1909932775974623691916779902822e-20
relative error = 1.8628404964360532400225049830238e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.868
y[1] (closed_form) = -0.0033181134661629787937283661634666
y[1] (numeric) = -0.0033181134661629787314482997387254
absolute error = 6.2280066424741246170945733019805e-20
relative error = 1.8769721728883812548004995139756e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.867
y[1] (closed_form) = -0.0033128214202452707402060149834797
y[1] (numeric) = -0.0033128214202452706775571127092717
absolute error = 6.2648902274207981046928374124307e-20
relative error = 1.8911041172140711400184980879650e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.866
y[1] (closed_form) = -0.0033075394994130108654979514570697
y[1] (numeric) = -0.0033075394994130108024815061701252
absolute error = 6.3016445286944490236381259522565e-20
relative error = 1.9052363637116962829302823804173e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.865
y[1] (closed_form) = -0.0033022676810727726761949032727598
y[1] (numeric) = -0.0033022676810727726128122028677902
absolute error = 6.3382700404969604079384250573012e-20
relative error = 1.9193689466257665237063123374004e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.864
y[1] (closed_form) = -0.0032970059426887292189801733744113
y[1] (numeric) = -0.0032970059426887291552325008245683
absolute error = 6.3747672549842943073869003547903e-20
relative error = 1.9335019001469045741264974645999e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.863
y[1] (closed_form) = -0.0032917542617824879338678653573148
y[1] (numeric) = -0.0032917542617824878697564987345587
absolute error = 6.4111366622756102095332999870915e-20
relative error = 1.9476352584120218809523919542831e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.862
y[1] (closed_form) = -0.0032865126159329260333860141526854
y[1] (numeric) = -0.003286512615932925968912226648062
absolute error = 6.4473787504623399329783192258044e-20
relative error = 1.9617690555044939359245649098976e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.861
y[1] (closed_form) = -0.003281280982776026405862727187303
y[1] (numeric) = -0.0032812809827760263410277871311308
absolute error = 6.4834940056172192135664309804072e-20
relative error = 1.9759033254543350343234619258534e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (closed_form) = -0.0032760593400047140409804758097651
y[1] (numeric) = -0.0032760593400047139757856466917323
absolute error = 6.5194829118032762038546810914754e-20
relative error = 1.9900381022383724840246700459019e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.859
y[1] (closed_form) = -0.0032708476653686929757706822831913
y[1] (numeric) = -0.0032708476653686929102172227723635
absolute error = 6.5553459510827771050437980492614e-20
relative error = 2.0041734197804202669721245202698e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.858
y[1] (closed_form) = -0.0032656459366742837592277241858148
y[1] (numeric) = -0.0032656459366742836933168881505535
absolute error = 6.5910836035261291493736322897668e-20
relative error = 2.0183093119514521549854526729097e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.857
y[1] (closed_form) = -0.0032604541317842614337284257646506
y[1] (numeric) = -0.0032604541317842613674614622924432
absolute error = 6.6266963472207411498073793510341e-20
relative error = 2.0324458125697742818103374401261e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.856
y[1] (closed_form) = -0.003255272228617694031450024781679
y[1] (numeric) = -0.0032552722286176939648281781988806
absolute error = 6.6621846582798418326582130423052e-20
relative error = 2.0465829554011971733135006152865e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.855
y[1] (closed_form) = -0.0032501002051497815839864938044474
y[1] (numeric) = -0.0032501002051497815170110036959348
absolute error = 6.6975490108512561676478187675961e-20
relative error = 2.0607207741592072377166533968764e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.854
y[1] (closed_form) = -0.0032449380394116956433699568507794
y[1] (numeric) = -0.003244938039411695576042058079518
absolute error = 6.7327898771261399087288328907153e-20
relative error = 2.0748593025051377177565393549368e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.853
y[1] (closed_form) = -0.0032397857094904193127107759268964
y[1] (numeric) = -0.0032397857094904192450316986534197
absolute error = 6.7679077273476725578523214245154e-20
relative error = 2.0889985740483391066510022707599e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.852
y[1] (closed_form) = -0.0032346431935285877846766874256066
y[1] (numeric) = -0.0032346431935285877166476571274095
absolute error = 6.8029030298197089627171305214427e-20
relative error = 2.1031386223463490297438483340226e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.851
y[1] (closed_form) = -0.0032295104697243293860381457015995
y[1] (numeric) = -0.0032295104697243293176603831924456
absolute error = 6.8377762509153897584001726361874e-20
relative error = 2.1172794809050615936941387683897e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (closed_form) = -0.0032243875163311071265137805390143
y[1] (numeric) = -0.0032243875163311070577885019881572
absolute error = 6.8725278550857108616354364765113e-20
relative error = 2.1314211831788962050684449697016e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.849
y[1] (closed_form) = -0.0032192743116575607501565967964315
y[1] (numeric) = -0.003219274311657560681085013747751
absolute error = 6.9071583048680522253846868566011e-20
relative error = 2.1455637625709658601875235494940e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.848
y[1] (closed_form) = -0.0032141708340673492875282383798077
y[1] (numeric) = -0.0032141708340673492181115577708611
absolute error = 6.9416680608946660602244134678067e-20
relative error = 2.1597072524332449080718231507253e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.847
y[1] (closed_form) = -0.0032090770619789941069153049775527
y[1] (numeric) = -0.0032090770619789940371547291585414
absolute error = 6.9760575819011247279615567796962e-20
relative error = 2.1738516860667362883232184127514e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.846
y[1] (closed_form) = -0.0032039929738657224628483488163023
y[1] (numeric) = -0.003203992973865722392745075568955
absolute error = 7.0103273247347285117848464198165e-20
relative error = 2.1879970967216382457733788799841e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.845
y[1] (closed_form) = -0.0031989185482553115401907901827341
y[1] (numeric) = -0.0031989185482553114697460127391053
absolute error = 7.0444777443628734661591943360371e-20
relative error = 2.2021435175975105237222218450591e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.844
y[1] (closed_form) = -0.0031938537637299329920715747271969
y[1] (numeric) = -0.0031938537637299329212864817883831
absolute error = 7.0785092938813795485774539447615e-20
relative error = 2.2162909818434400375829679651308e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.843
y[1] (closed_form) = -0.0031887985989259979699419527396006
y[1] (numeric) = -0.0031887985989259978988177284943728
absolute error = 7.1124224245227792341969496751447e-20
relative error = 2.2304395225582060307434168621037e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.842
y[1] (closed_form) = -0.0031837530325340026440432907869833
y[1] (numeric) = -0.0031837530325340025725811149303377
absolute error = 7.1462175856645668133074614352987e-20
relative error = 2.2445891727904447144461866877947e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.841
y[1] (closed_form) = -0.0031787170432983742125793294449096
y[1] (numeric) = -0.0031787170432983741407803771965355
absolute error = 7.1798952248374085705027783893265e-20
relative error = 2.2587399655388133934838166774192e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (closed_form) = -0.0031736906100173173978927774602678
y[1] (numeric) = -0.0031736906100173173257582195829347
absolute error = 7.2134557877333140433594791168048e-20
relative error = 2.2728919337521540794978149041839e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.839
y[1] (closed_form) = -0.0031686737115426614279525826694723
y[1] (numeric) = -0.0031686737115426613554835854873346
absolute error = 7.2468997182137685573642140352604e-20
relative error = 2.2870451103296565936639446595647e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.838
y[1] (closed_form) = -0.0031636663267797075014646434813133
y[1] (numeric) = -0.0031636663267797074286623688981351
absolute error = 7.2802274583178272327744244392909e-20
relative error = 2.3011995281210211605392819940190e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.837
y[1] (closed_form) = -0.0031586684346870767349251218349678
y[1] (numeric) = -0.0031586684346870766617907273522661
absolute error = 7.3134394482701706580470944155165e-20
relative error = 2.3153552199266204948398438380075e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.836
y[1] (closed_form) = -0.0031536800142765585899418893776481
y[1] (numeric) = -0.0031536800142765585164765281127569
absolute error = 7.3465361264891224234257612275126e-20
relative error = 2.3295122184976613829108806604342e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.835
y[1] (closed_form) = -0.0031487010446129597791559832891499
y[1] (numeric) = -0.0031487010446129597053608039932036
memory used=141.4MB, alloc=44.3MB, time=2.11
absolute error = 7.3795179295946287072375707534511e-20
relative error = 2.3436705565363457606452496886986e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.834
y[1] (closed_form) = -0.0031437315048139536491012668277221
y[1] (numeric) = -0.0031437315048139535749774139035601
absolute error = 7.4123852924162001064196216512562e-20
relative error = 2.3578302666960312895986341898025e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.833
y[1] (closed_form) = -0.0031387713740499300383467823982469
y[1] (numeric) = -0.0031387713740499299638953959182388
absolute error = 7.4451386480008159017671597957616e-20
relative error = 2.3719913815813914330437510742670e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.832
y[1] (closed_form) = -0.0031338206315438456092725518641623
y[1] (numeric) = -0.0031338206315438455344947675879543
absolute error = 7.4777784276207909473753280764514e-20
relative error = 2.3861539337485750336990930134526e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.831
y[1] (closed_form) = -0.0031288792565710746518358200528139
y[1] (numeric) = -0.0031288792565710745767327694449979
absolute error = 7.5103050607816053727311109809406e-20
relative error = 2.4003179557053653948611822362809e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (closed_form) = -0.0031239472284592603576909530533877
y[1] (numeric) = -0.0031239472284592602822637633010907
absolute error = 7.5427189752296972849028038562531e-20
relative error = 2.4144834799113388666627710739302e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.829
y[1] (closed_form) = -0.0031190245265881665630323930901006
y[1] (numeric) = -0.0031190245265881664872821871204984
absolute error = 7.5750205969602186572707488933505e-20
relative error = 2.4286505387780229391729090319941e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.828
y[1] (closed_form) = -0.0031141111303895299585362365832556
y[1] (numeric) = -0.0031141111303895298824641330810081
absolute error = 7.6072103502247545902451794933349e-20
relative error = 2.4428191646690538440483075705746e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.827
y[1] (closed_form) = -0.0031092070193469127647821415988725
y[1] (numeric) = -0.0031092070193469126883892550234824
absolute error = 7.6392886575390061284247677347855e-20
relative error = 2.4569893899003336664389717461299e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.826
y[1] (closed_form) = -0.0031043121729955558715433853451773
y[1] (numeric) = -0.003104312172995555794830825948273
absolute error = 7.6712559396904368176628423733541e-20
relative error = 2.4711612467401869688446322974487e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.825
y[1] (closed_form) = -0.0030994265709222324393389818119967
y[1] (numeric) = -0.0030994265709222323623078556545378
absolute error = 7.7031126157458831845272035821859e-20
relative error = 2.4853347674095169286121025252827e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.824
y[1] (closed_form) = -0.0030945501927651019616478341772835
y[1] (numeric) = -0.0030945501927651018842992431466922
absolute error = 7.7348591030591293196639721113275e-20
relative error = 2.4995099840819609907573013048818e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.823
y[1] (closed_form) = -0.0030896830182135647861909363333039
y[1] (numeric) = -0.0030896830182135647085259781605194
absolute error = 7.7664958172784457456059415422117e-20
relative error = 2.5136869288840460377893266674459e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.822
y[1] (closed_form) = -0.0030848250270081170936936529226052
y[1] (numeric) = -0.0030848250270081170157134211990643
absolute error = 7.7980231723540927486014198841975e-20
relative error = 2.5278656338953430782076334753686e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.821
y[1] (closed_form) = -0.0030799761989402063325460977294541
y[1] (numeric) = -0.0030799761989402062542516819239962
absolute error = 7.8294415805457883530805181556652e-20
relative error = 2.5420461311486214553370636826910e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (closed_form) = -0.0030751365138520871077855962541089
y[1] (numeric) = -0.0030751365138520870291780817298074
absolute error = 7.8607514524301411164222362696869e-20
relative error = 2.5562284526300025781591984025290e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.819
y[1] (closed_form) = -0.0030703059516366775228311599127426
y[1] (numeric) = -0.0030703059516366774439116279436622
absolute error = 7.8919531969080479207374781655240e-20
relative error = 2.5704126302791131757922473840483e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.818
y[1] (closed_form) = -0.0030654844922374159724058166621798
y[1] (numeric) = -0.0030654844922374158931753444500592
absolute error = 7.9230472212120569374402665568309e-20
relative error = 2.5845986959892380772654634200305e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.817
y[1] (closed_form) = -0.0030606721156481183850885360524965
y[1] (numeric) = -0.0030606721156481183055481967433595
absolute error = 7.9540339309136959394418909718166e-20
relative error = 2.5987866816074725182278665499264e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.816
y[1] (closed_form) = -0.0030558688019128359139433558680881
y[1] (numeric) = -0.0030558688019128358340942185687804
absolute error = 7.9849137299307661348704792063995e-20
relative error = 2.6129766189348739762248855807874e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.815
y[1] (closed_form) = -0.0030510745311257130736791627346611
y[1] (numeric) = -0.0030510745311257129935222925293151
absolute error = 8.0156870205346016952915003642595e-20
relative error = 2.6271685397266135361703723083806e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.814
y[1] (closed_form) = -0.003046289283430846322799400450891
y[1] (numeric) = -0.003046289283430846242335858417318
absolute error = 8.0463542033572951504829559810069e-20
relative error = 2.6413624756921267876353167724294e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.813
y[1] (closed_form) = -0.0030415130390221430892067774538526
y[1] (numeric) = -0.0030415130390221430084376206798637
absolute error = 8.0769156773988888209024631832168e-20
relative error = 2.6555584584952642555684898131133e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.812
y[1] (closed_form) = -0.0030367457781431812377338188509102
y[1] (numeric) = -0.0030367457781431811566601004505649
absolute error = 8.1073718400345324580720494716705e-20
relative error = 2.6697565197544413660581620010400e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.811
y[1] (closed_form) = -0.0030319874810870689780758589512211
y[1] (numeric) = -0.003031987481087068896698628081005
absolute error = 8.1377230870216072622002317904909e-20
relative error = 2.6839566910427879487379955807338e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (closed_form) = -0.0030272381281963052116087973105244
y[1] (numeric) = -0.0030272381281963051299290991854562
absolute error = 8.1679698125068164454598124911755e-20
relative error = 2.6981590038882972774341782896452e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.809
y[1] (closed_form) = -0.0030224976998626403155796450661427
y[1] (numeric) = -0.0030224976998626402335985209758103
absolute error = 8.1981124090332425084437612553154e-20
relative error = 2.7123634897739746506448646826408e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.808
y[1] (closed_form) = -0.0030177661765269373631635688873278
y[1] (numeric) = -0.0030177661765269372808820562118541
absolute error = 8.2281512675473713964305348245727e-20
relative error = 2.7265701801379855134370117982938e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.807
y[1] (closed_form) = -0.0030130435386790337778867973009496
y[1] (numeric) = -0.0030130435386790336953059295268888
absolute error = 8.2580867774060837012041855125643e-20
relative error = 2.7407791063738031223397415409389e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.806
y[1] (closed_form) = -0.0030083297668576034209203885753165
y[1] (numeric) = -0.0030083297668576033380411953114804
absolute error = 8.2879193263836130732935951394931e-20
relative error = 2.7549902998303557548074319147902e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.805
y[1] (closed_form) = -0.0030036248416500191097554708563885
y[1] (numeric) = -0.0030036248416500190265789778496038
absolute error = 8.3176493006784720086191136218257e-20
relative error = 2.7692037918121734648198331273407e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.804
y[1] (closed_form) = -0.0029989287436922155667761539511093
y[1] (numeric) = -0.0029989287436922154833033831019058
absolute error = 8.3472770849203451726637515362347e-20
relative error = 2.7834196135795343861806224731674e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.803
y[1] (closed_form) = -0.0029942414536685527962518781418635
y[1] (numeric) = -0.002994241453668552712483847520094
absolute error = 8.3768030621769504244198443135012e-20
relative error = 2.7976377963486105850699537110397e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.802
y[1] (closed_form) = -0.0029895629523116798882765087935255
y[1] (numeric) = -0.0029895629523116798042142326539169
absolute error = 8.4062276139608677015007432408402e-20
relative error = 2.8118583712916134634007222522664e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.801
y[1] (closed_form) = -0.0029848932204023992481870063791007
y[1] (numeric) = -0.0029848932204023991638314951767374
absolute error = 8.4355511202363359269505662783781e-20
relative error = 2.8260813695369387145224567823807e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (closed_form) = -0.00298023223876953125
y[1] (numeric) = -0.0029802322387695311653522604057398
absolute error = 8.4647739594260180974333311257515e-20
relative error = 2.8403068221693108328109608379251e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.799
y[1] (closed_form) = -0.0029755799882897793124100686105117
y[1] (numeric) = -0.0029755799882897792274711035263343
absolute error = 8.4938965084177347116358654855866e-20
relative error = 2.8545347602299271786760642521014e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.798
y[1] (closed_form) = -0.0029709364498875953958989880705429
y[1] (numeric) = -0.0029709364498875953106697966448313
absolute error = 8.5229191425711656968767167174463e-20
relative error = 2.8687652147166016005141041647241e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.797
y[1] (closed_form) = -0.0029663016045350459195106339432652
y[1] (numeric) = -0.00296630160453504583399221158602
absolute error = 8.5518422357245209910758368909429e-20
relative error = 2.8829982165839076151260383610796e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.796
y[1] (closed_form) = -0.0029616754332516780958516397215057
y[1] (numeric) = -0.0029616754332516780100449781194939
absolute error = 8.5806661602011799364070716379538e-20
relative error = 2.8972337967433211481163999592211e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.795
y[1] (closed_form) = -0.0029570579171043866828832980047398
y[1] (numeric) = -0.0029570579171043865967893851365768
absolute error = 8.6093912868162996401274043535366e-20
relative error = 2.9114719860633628357826318047059e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.794
y[1] (closed_form) = -0.0029524490372072811510755581530497
y[1] (numeric) = -0.0029524490372072810646953783042158
absolute error = 8.6380179848833924572534735588198e-20
relative error = 2.9257128153697398899986912550278e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.793
y[1] (closed_form) = -0.0029478487747215532644993182106839
y[1] (numeric) = -0.0029478487747215531778338519884752
absolute error = 8.6665466222208727489370631446171e-20
relative error = 2.9399563154454875275911912427348e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.792
y[1] (closed_form) = -0.0029432571108553450744385315146825
y[1] (numeric) = -0.0029432571108553449874887558630968
absolute error = 8.6949775651585730695770354606026e-20
relative error = 2.9542025170311099657007414966257e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.791
y[1] (closed_form) = -0.0029386740268636173241089494777961
y[1] (numeric) = -0.0029386740268636172368758376923538
absolute error = 8.7233111785442299348955086703420e-20
relative error = 2.9684514508247209846155744751294e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (closed_form) = -0.0029340995040480182630756016535392
y[1] (numeric) = -0.0029340995040480181755601233960398
absolute error = 8.7515478257499393224009454948783e-20
relative error = 2.9827031474821840595589838261074e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.789
y[1] (closed_form) = -0.002929533523756752869966372448179
y[1] (numeric) = -0.0029295335237567527821694937613931
absolute error = 8.7796878686785820548601936222053e-20
relative error = 2.9969576376172520629065689344398e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.788
y[1] (closed_form) = -0.0029249760673844524820842708328028
y[1] (numeric) = -0.0029249760673844523940069541551006
absolute error = 8.8077316677702192166053720387492e-20
relative error = 3.0112149518017065383037672549018e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.787
y[1] (closed_form) = -0.0029204271163720448305262052209679
y[1] (numeric) = -0.0029204271163720447421694094008833
absolute error = 8.8356795820084577517098058793603e-20
relative error = 3.0254751205654965481486665554878e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.786
y[1] (closed_form) = -0.0029158866522066244794212704059756
y[1] (numeric) = -0.0029158866522066243907859507167077
absolute error = 8.8635319689267863922799487962085e-20
relative error = 3.0397381743968770958996218184456e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.785
y[1] (closed_form) = -0.0029113546564213236679067271883089
y[1] (numeric) = -0.0029113546564213235789938353421601
absolute error = 8.8912891846148820643273701796447e-20
relative error = 3.0540041437425471246617562662289e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.784
y[1] (closed_form) = -0.002906831110595183553465008159529
y[1] (numeric) = -0.0029068311105951834642754923222801
absolute error = 8.9189515837248869179063988531669e-20
relative error = 3.0682730590077870935010027012157e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.783
y[1] (closed_form) = -0.0029023159963530258552502151348642
y[1] (numeric) = -0.0029023159963530257657850199400876
absolute error = 8.9465195194776561274288792989435e-20
relative error = 3.0825449505565961329289399756656e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.782
y[1] (closed_form) = -0.0028978092953653248960376850333076
y[1] (numeric) = -0.0028978092953653248062977515966179
absolute error = 8.9739933436689766072976853989978e-20
relative error = 3.0968198487118287809962998467310e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.781
y[1] (closed_form) = -0.0028933109893480800414352916813302
y[1] (numeric) = -0.0028933109893480799514215576145726
absolute error = 9.0013734066757567872351246083538e-20
relative error = 3.1110977837553313014276616255961e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (closed_form) = -0.0028888210600626885350002211539505
y[1] (numeric) = -0.0028888210600626884447136205793286
absolute error = 9.0286600574621875909211270765617e-20
relative error = 3.1253787859280775852245158055973e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.779
y[1] (closed_form) = -0.0028843394893158187279100079540976
y[1] (numeric) = -0.0028843394893158186373514715182389
memory used=188.2MB, alloc=44.3MB, time=2.79
absolute error = 9.0558536435858747607991243265091e-20
relative error = 3.1396628854303046371585631575607e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.778
y[1] (closed_form) = -0.0028798662589592837018416486567674
y[1] (numeric) = -0.002879866258959283611012103544728
absolute error = 9.0829545112039426711547556638208e-20
relative error = 3.1539501124216476485718225180684e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.777
y[1] (closed_form) = -0.0028754013508899152837176186967938
y[1] (numeric) = -0.0028754013508899151926179886460027
absolute error = 9.1099630050791097708239726610361e-20
relative error = 3.1682404970212746578948485748722e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.776
y[1] (closed_form) = -0.0028709447470494384509826068461201
y[1] (numeric) = -0.0028709447470494383596138121602627
absolute error = 9.1368794685857357961427181267888e-20
relative error = 3.1825340693080208002891102805826e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.775
y[1] (closed_form) = -0.002866496429424346126079750695825
y[1] (numeric) = -0.0028664964294243460344427082586666
absolute error = 9.1637042437158408940101113730675e-20
relative error = 3.1968308593205221478143510088704e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.774
y[1] (closed_form) = -0.0028620563800457743588001052170088
y[1] (numeric) = -0.0028620563800457742668957285061578
absolute error = 9.1904376710850967942009519270739e-20
relative error = 3.2111308970573491415165431149562e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.773
y[1] (closed_form) = -0.0028576245809893778951840053097259
y[1] (numeric) = -0.002857624580989377803013204410338
absolute error = 9.2170800899387901693313348430103e-20
relative error = 3.2254342124771396168268620827813e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.772
y[1] (closed_form) = -0.0028532010143752061316578922468273
y[1] (numeric) = -0.0028532010143752060392215738652497
absolute error = 9.2436318381577583201532283482292e-20
relative error = 3.2397408354987314236569388440384e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.771
y[1] (closed_form) = -0.0028487856623675794530950631657994
y[1] (numeric) = -0.0028487856623675793603941306431564
absolute error = 9.2700932522642973231299747515555e-20
relative error = 3.2540507960012946425705030486803e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (closed_form) = -0.0028443785071749659534936723420131
y[1] (numeric) = -0.0028443785071749658605290256677327
absolute error = 9.2964646674280427765248145414008e-20
relative error = 3.2683641238244633984064049625533e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.769
y[1] (closed_form) = -0.002839979531049858537970162976393
y[1] (numeric) = -0.0028399795310498584447426988016748
absolute error = 9.3227464174718232805186777468502e-20
relative error = 3.2826808487684672727228991757512e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.768
y[1] (closed_form) = -0.0028355887162886524047711387341376
y[1] (numeric) = -0.0028355887162886523112817503853627
absolute error = 9.3489388348774867861616124117608e-20
relative error = 3.2970010005942623164279893359079e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.767
y[1] (closed_form) = -0.0028312060452315229060114953631499
y[1] (numeric) = -0.0028312060452315228122610728552329
absolute error = 9.3750422507916999472543040708988e-20
relative error = 3.3113246090236616639555695851204e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.766
y[1] (closed_form) = -0.0028268315002623037858514244852452
y[1] (numeric) = -0.002826831500262303691840854534928
absolute error = 9.4010569950317206085521591934102e-20
relative error = 3.3256517037394657503420551890894e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.765
y[1] (closed_form) = -0.0028224650638083657948296741735869
y[1] (numeric) = -0.0028224650638083657005598402126755
absolute error = 9.4269833960911435629843565910324e-20
relative error = 3.3399823143855921325531719143757e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.764
y[1] (closed_form) = -0.0028181067183404956790752042893647
y[1] (numeric) = -0.0028181067183404955845469864779085
absolute error = 9.4528217811456197098840908374258e-20
relative error = 3.3543164705672049164055709468021e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.763
y[1] (closed_form) = -0.0028137564463727755431241088322913
y[1] (numeric) = -0.0028137564463727754483383840717058
absolute error = 9.4785724760585487455339180134203e-20
relative error = 3.3686542018508437904229534637741e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.762
y[1] (closed_form) = -0.0028094142304624625850733928454889
y[1] (numeric) = -0.0028094142304624624900310347916215
absolute error = 9.5042358053867455166416439240167e-20
relative error = 3.3829955377645526679614262888637e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.761
y[1] (closed_form) = -0.0028050800532098692028078877878226
y[1] (numeric) = -0.0028050800532098691075097668639618
absolute error = 9.5298120923860801666775458095823e-20
relative error = 3.3973405077980079389338672820128e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (closed_form) = -0.0028007538972582434700412668273836
y[1] (numeric) = -0.0028007538972582433744882502372127
absolute error = 9.5553016590170922043228681175718e-20
relative error = 3.4116891414026463324581561671608e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.759
y[1] (closed_form) = -0.0027964357452936499809167802999351
y[1] (numeric) = -0.0027964357452936498851097320404293
absolute error = 9.5807048259505786226024588719160e-20
relative error = 3.4260414679917923917492232854073e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.758
y[1] (closed_form) = -0.0027921255800448510619179716966192
y[1] (numeric) = -0.0027921255800448509658577525708876
absolute error = 9.6060219125731561966010934716494e-20
relative error = 3.4403975169407855625699852007817e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.757
y[1] (closed_form) = -0.0027878233842831883498442560766431
y[1] (numeric) = -0.0027878233842831882535317237067152
absolute error = 9.6312532369927980869934454011754e-20
relative error = 3.4547573175871068965513720924992e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.756
y[1] (closed_form) = -0.002783529140822464734610845823177
y[1] (numeric) = -0.0027835291408224646380468546627336
absolute error = 9.6563991160443448759517865098796e-20
relative error = 3.4691208992305053706868073578353e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.755
y[1] (closed_form) = -0.0027792428325188266656370932541249
y[1] (numeric) = -0.002779242832518826568822494601175
absolute error = 9.6814598652949901613333115210301e-20
relative error = 3.4834882911331238243016747394211e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.754
y[1] (closed_form) = -0.0027749644422706468205918858431953
y[1] (numeric) = -0.0027749644422706467235275278526979
absolute error = 9.7064357990497408343904606950264e-20
relative error = 3.4978595225196245147935024962162e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.753
y[1] (closed_form) = -0.0027706939530184071352692777798779
y[1] (numeric) = -0.0027706939530184070379560054763094
absolute error = 9.7313272303568521655927396686711e-20
relative error = 3.5122346225773142934338075754109e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.752
y[1] (closed_form) = -0.0027664313477445821933720713782256
y[1] (numeric) = -0.0027664313477445820958107266680932
absolute error = 9.7561344710132378224972851206741e-20
relative error = 3.5266136204562694025177753301811e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.751
y[1] (closed_form) = -0.0027621766094735229749855735120937
y[1] (numeric) = -0.0027621766094735228771769951963951
absolute error = 9.7808578315698549429577779053908e-20
relative error = 3.5409965452694598951432019830836e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (closed_form) = -0.0027579297212713409625282458866717
y[1] (numeric) = -0.0027579297212713408644732696733011
absolute error = 9.8054976213370643863172406133149e-20
relative error = 3.5553834260928736788953976748433e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.749
y[1] (closed_form) = -0.0027536906662457926029704436303868
y[1] (numeric) = -0.0027536906662457925046699021464872
absolute error = 9.8300541483899662845897532488042e-20
relative error = 3.5697742919656401847100374816217e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.748
y[1] (closed_form) = -0.0027494594275461641251168944848172
y[1] (numeric) = -0.0027494594275461640265716172890801
absolute error = 9.8545277195737110149991580820488e-20
relative error = 3.5841691718901536621812561492227e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.747
y[1] (closed_form) = -0.0027452359883631567107530108600376
y[1] (numeric) = -0.0027452359883631566119638244549497
absolute error = 9.8789186405087857146093820801542e-20
relative error = 3.5985680948321961025776093991210e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.746
y[1] (closed_form) = -0.0027410203319287720184595492853784
y[1] (numeric) = -0.0027410203319287719194272771294156
absolute error = 9.9032272155962764571510621249081e-20
relative error = 3.6129710897210597908238704280928e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.745
y[1] (closed_form) = -0.0027368124415161980589045363971166
y[1] (numeric) = -0.0027368124415161979596299989168855
absolute error = 9.9274537480231062115226940818203e-20
relative error = 3.6273781854496694877019945703618e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.744
y[1] (closed_form) = -0.0027326123004396954204257676409721
y[1] (numeric) = -0.0027326123004396953209097822432996
absolute error = 9.9515985397672487008215214209864e-20
relative error = 3.6417894108747042435199679386903e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.743
y[1] (closed_form) = -0.0027284198920544838437215544039678
y[1] (numeric) = -0.0027284198920544837439649354879387
absolute error = 9.9756618916029182801398123542094e-20
relative error = 3.6562047948167188444926571292578e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.742
y[1] (closed_form) = -0.0027242351997566291444717474023656
y[1] (numeric) = -0.0027242351997566290444753063713082
absolute error = 9.9996441031057359507460263171141e-20
relative error = 3.6706243660602648930741966853594e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.741
y[1] (closed_form) = -0.0027200582069829304827153989148294
y[1] (numeric) = -0.0027200582069829303824799441882507
absolute error = 1.0023545472657871627657621184984e-19
relative error = 3.6850481533540115234768888881549e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (closed_form) = -0.0027158888972108079778157439371467
y[1] (numeric) = -0.0027158888972108078773420809626151
absolute error = 1.0047366297453162777002882083936e-19
relative error = 3.6994761854108657536070465005226e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.739
y[1] (closed_form) = -0.0027117272539581906678474806208848
y[1] (numeric) = -0.0027117272539581905671364118858627
absolute error = 1.0071106873502209538963141383232e-19
relative error = 3.7139084909080924746436832544794e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.738
y[1] (closed_form) = -0.0027075732607834048122456135170432
y[1] (numeric) = -0.0027075732607834047112979385606688
absolute error = 1.0094767495637446451484087888772e-19
relative error = 3.7283450984874340794814490659370e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.737
y[1] (closed_form) = -0.0027034269012850625365593892505383
y[1] (numeric) = -0.0027034269012850624353759046753564
absolute error = 1.0118348457518190889345511980544e-19
relative error = 3.7427860367552297312547171054669e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.736
y[1] (closed_form) = -0.0026992881591019508181591033753063
y[1] (numeric) = -0.0026992881591019507167406028589496
absolute error = 1.0141850051635668332582783145252e-19
relative error = 3.7572313342825342731552578732667e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.735
y[1] (closed_form) = -0.0026951570179129208117477893757277
y[1] (numeric) = -0.0026951570179129207100950636825475
absolute error = 1.0165272569318014577660587864880e-19
relative error = 3.7716810196052367807514812440536e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.734
y[1] (closed_form) = -0.0026910334614367775135340161603682
y[1] (numeric) = -0.0026910334614367774116478531530156
absolute error = 1.0188616300735255004209950065192e-19
relative error = 3.7861351212241787580127909868931e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.733
y[1] (closed_form) = -0.0026869174734321697629262190108198
y[1] (numeric) = -0.0026869174734321696608074036617772
absolute error = 1.0211881534904261009553294354460e-19
relative error = 3.8005936676052719782381774500975e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.732
y[1] (closed_form) = -0.0026828090376974805806131708734697
y[1] (numeric) = -0.0026828090376974804782624852765329
absolute error = 1.0235068559693683722659275257002e-19
relative error = 3.8150566871796159710837728567331e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.731
y[1] (closed_form) = -0.0026787081380707178418993661867664
y[1] (numeric) = -0.0026787081380707177393175895684777
absolute error = 1.0258177661828865108589264848698e-19
relative error = 3.8295242083436151568797099067465e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (closed_form) = -0.0026746147584294052841682381921137
y[1] (numeric) = -0.0026746147584294051813561469231464
absolute error = 1.0281209126896726573920748026910e-19
relative error = 3.8439962594590956294222580523842e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.729
y[1] (closed_form) = -0.0026705288826904738473502629536795
y[1] (numeric) = -0.0026705288826904737443086305601731
absolute error = 1.0304163239350635183059400603430e-19
relative error = 3.8584728688534215884228628299185e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.728
y[1] (closed_form) = -0.0026664504948101533462771191816306
y[1] (numeric) = -0.0026664504948101532430067163564781
absolute error = 1.0327040282515247594781302117070e-19
relative error = 3.8729540648196114227913819185048e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.727
y[1] (closed_form) = -0.0026623795787838644738071724847354
y[1] (numeric) = -0.002662379578783864370308767098822
absolute error = 1.0349840538591331827779544455591e-19
relative error = 3.8874398756164534459264970824570e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.726
y[1] (closed_form) = -0.0026583161186461111336116359417302
y[1] (numeric) = -0.0026583161186461110298859930551245
absolute error = 1.0372564288660566963425420899396e-19
relative error = 3.9019303294686212841819837628111e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.725
y[1] (closed_form) = -0.0026542600984703731015148259458244
y[1] (numeric) = -0.0026542600984703729975627078189212
absolute error = 1.0395211812690320893393400007120e-19
relative error = 3.9164254545667889196732397445936e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.724
y[1] (closed_form) = -0.0026502115023689990142859832124083
y[1] (numeric) = -0.0026502115023689989101081493170243
absolute error = 1.0417783389538406219241186921369e-19
relative error = 3.9309252790677453885842109648852e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
memory used=234.8MB, alloc=44.3MB, time=3.48
x[1] = 2.723
y[1] (closed_form) = -0.0026461703144930996847841637152855
y[1] (numeric) = -0.0026461703144930995803813707457074
absolute error = 1.0440279296957814410481333355974e-19
relative error = 3.9454298310945091361306060710586e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.722
y[1] (closed_form) = -0.0026421365190324417423617232001369
y[1] (numeric) = -0.0026421365190324416377347250841226
absolute error = 1.0462699811601428327129059017648e-19
relative error = 3.9599391387364420293310617163168e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.721
y[1] (closed_form) = -0.0026381101002153415974359218836655
y[1] (numeric) = -0.0026381101002153414925854697933984
absolute error = 1.0485045209026713212162173905987e-19
relative error = 3.9744532300493630287337077190079e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (closed_form) = -0.0026340910423085597291421630509013
y[1] (numeric) = -0.0026340910423085596240690054138975
absolute error = 1.0507315763700386258783225324866e-19
relative error = 3.9889721330556615202413850416445e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.719
y[1] (closed_form) = -0.0026300793296171952949863505790756
y[1] (numeric) = -0.002630079329617195189691233089045
absolute error = 1.0529511749003064856831218130430e-19
relative error = 4.0034958757444103081745899939174e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.718
y[1] (closed_form) = -0.0026260749464845810614178060116112
y[1] (numeric) = -0.0026260749464845809559014716392723
absolute error = 1.0551633437233893622150454446915e-19
relative error = 4.0180244860714782707070550604064e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.717
y[1] (closed_form) = -0.0026220778772921786542481257471176
y[1] (numeric) = -0.0026220778772921785485113147509661
absolute error = 1.0573681099615150312187192617549e-19
relative error = 4.0325579919596426788047302276161e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.716
y[1] (closed_form) = -0.0026180881064594741278452832625216
y[1] (numeric) = -0.0026180881064594740218887331995533
absolute error = 1.0595655006296830730550917444372e-19
relative error = 4.0470964212987011797947985661936e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.715
y[1] (closed_form) = -0.0026141056184438738520361901229917
y[1] (numeric) = -0.0026141056184438737458606358593796
absolute error = 1.0617555426361212722746027832316e-19
relative error = 4.0616398019455834466872460428135e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.714
y[1] (closed_form) = -0.0026101303977406007156548229102164
y[1] (numeric) = -0.0026101303977406006092609966319424
absolute error = 1.0639382627827399364751666917061e-19
relative error = 4.0761881617244624943674080226772e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.713
y[1] (closed_form) = -0.0026061624288825906456769011906556
y[1] (numeric) = -0.0026061624288825905390655324140972
absolute error = 1.0661136877655841445602226853044e-19
relative error = 4.0907415284268656637738336086046e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.712
y[1] (closed_form) = -0.0026022016964403894408859643120828
y[1] (numeric) = -0.0026022016964403893340577798945544
absolute error = 1.0682818441752839344598738999658e-19
relative error = 4.1052999298117852751717437773570e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.711
y[1] (closed_form) = -0.0025982481850220499190195422252661
y[1] (numeric) = -0.0025982481850220498119752663755159
absolute error = 1.0704427584975024403261893703350e-19
relative error = 4.1198633936057889516283101494912e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (closed_form) = -0.0025943018792730293763479477428771
y[1] (numeric) = -0.0025943018792730292690883020315389
absolute error = 1.0725964571133819891620805764852e-19
relative error = 4.1344319475031296137919480973934e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.709
y[1] (closed_form) = -0.0025903627638760873586420347342749
y[1] (numeric) = -0.0025903627638760872511677381042761
absolute error = 1.0747429662999881667917835637923e-19
relative error = 4.1490056191658551470738006891687e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.708
y[1] (closed_form) = -0.0025864308235511837424900687769709
y[1] (numeric) = -0.0025864308235511836348018375538957
absolute error = 1.0768823122307518630298776161836e-19
relative error = 4.1635844362239177423255886160792e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.707
y[1] (closed_form) = -0.0025825060430553771259276438073638
y[1] (numeric) = -0.0025825060430553770180261917097729
absolute error = 1.0790145209759093058549504016106e-19
relative error = 4.1781684262752829111040156908433e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.706
y[1] (closed_form) = -0.0025785884071827235273483503984391
y[1] (numeric) = -0.0025785884071827234192343885481451
absolute error = 1.0811396185029400943434758032511e-19
relative error = 4.1927576168860381766079496662468e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.705
y[1] (closed_form) = -0.0025746779007641753916666585039955
y[1] (numeric) = -0.0025746779007641752833408954362952
absolute error = 1.0832576306770032400692027033379e-19
relative error = 4.2073520355905014413706439414051e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.704
y[1] (closed_form) = -0.0025707745086674809027082199107193
y[1] (numeric) = -0.0025707745086674807941713615845822
absolute error = 1.0853685832613712266233592110538e-19
relative error = 4.2219517098913290327853271301828e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.703
y[1] (closed_form) = -0.0025668782157970836008065232939264
y[1] (numeric) = -0.0025668782157970834920592731021402
absolute error = 1.0874725019178620968612556436335e-19
relative error = 4.2365566672596234275385643965520e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.702
y[1] (closed_form) = -0.0025629890070940223045885477426014
y[1] (numeric) = -0.0025629890070940221956316065218745
absolute error = 1.0895694122072695774314194122574e-19
relative error = 4.2511669351350406560218868491876e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.701
y[1] (closed_form) = -0.0025591068675358313359357589667575
y[1] (numeric) = -0.0025591068675358312267698250077784
absolute error = 1.0916593395897912500942142725717e-19
relative error = 4.2657825409258973877882930667921e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (closed_form) = -0.0025552317821364410471104761871179
y[1] (numeric) = -0.0025552317821364409377362452445724
absolute error = 1.0937423094254547792879836242450e-19
relative error = 4.2804035120092776991163499312394e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.699
y[1] (closed_form) = -0.0025513637359460786490413069953954
y[1] (numeric) = -0.0025513637359460785394594722979412
absolute error = 1.0958183469745422053521111447456e-19
relative error = 4.2950298757311395237407583126538e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.698
y[1] (closed_form) = -0.0025475027140511693397650023244597
y[1] (numeric) = -0.0025475027140511692299762545846585
absolute error = 1.0978874773980123127680104887040e-19
relative error = 4.3096616594064207878044027143246e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.697
y[1] (closed_form) = -0.0025436487015742377320257241425797
y[1] (numeric) = -0.0025436487015742376220307515667876
absolute error = 1.0999497257579210827309375542704e-19
relative error = 4.3242988903191452300830726815019e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.696
y[1] (closed_form) = -0.0025398016836738095790363446455992
y[1] (numeric) = -0.0025398016836738094688358329438152
absolute error = 1.1020051170178402393176623994367e-19
relative error = 4.3389415957225279085302275425462e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.695
y[1] (closed_form) = -0.0025359616455443137974100076259472
y[1] (numeric) = -0.0025359616455443136870046400216199
absolute error = 1.1040536760432738984674417811718e-19
relative error = 4.3535898028390803941853748197997e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.694
y[1] (closed_form) = -0.0025321285724159847862737804081215
y[1] (numeric) = -0.0025321285724159846756642376479142
absolute error = 1.1060954276020733289463959942954e-19
relative error = 4.3682435388607156534858463574053e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.693
y[1] (closed_form) = -0.002528302449554765041579808316784
y[1] (numeric) = -0.002528302449554764930766768680299
absolute error = 1.1081303963648498344183137201834e-19
relative error = 4.3829028309488526200179848008944e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.692
y[1] (closed_form) = -0.0025244832622622080646329531456343
y[1] (numeric) = -0.0025244832622622079536170924550957
absolute error = 1.1101586069053857656980844815464e-19
relative error = 4.3975677062345204567399964657532e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.691
y[1] (closed_form) = -0.0025206709958753815638574525823098
y[1] (numeric) = -0.0025206709958753814526394442122054
absolute error = 1.1121800837010436722173885714139e-19
relative error = 4.4122381918184625097049847867180e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (closed_form) = -0.0025168656357667709488286790759282
y[1] (numeric) = -0.0025168656357667708374091939626108
absolute error = 1.1141948511331736016859575237400e-19
relative error = 4.4269143147712399543089513838595e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.689
y[1] (closed_form) = -0.0025130671673441831155996042685226
y[1] (numeric) = -0.0025130671673441830039793109197708
absolute error = 1.1162029334875185568856528701520e-19
relative error = 4.4415961021333351350848392535203e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.688
y[1] (closed_form) = -0.0025092755760506505223550889082211
y[1] (numeric) = -0.0025092755760506504105346534127592
absolute error = 1.1182043549546181184887956414616e-19
relative error = 4.4562835809152546000599946300554e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.687
y[1] (closed_form) = -0.002505490847364335554430618179037
y[1] (numeric) = -0.002505490847364335442410704216016
absolute error = 1.1201991396302102427466123915235e-19
relative error = 4.4709767780976318306907406065694e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.686
y[1] (closed_form) = -0.0025017129667984351777355886777402
y[1] (numeric) = -0.0025017129667984350655168575261771
absolute error = 1.1221873115156312428483440213398e-19
relative error = 4.4856757206313296683840865881998e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.685
y[1] (closed_form) = -0.0024979419199010858796247259003803
y[1] (numeric) = -0.0024979419199010857672078364485589
absolute error = 1.1241688945182139627064899480573e-19
relative error = 4.5003804354375424386129430189899e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.684
y[1] (closed_form) = -0.0024941776922552688962646701272951
y[1] (numeric) = -0.0024941776922552687836502788821267
absolute error = 1.1261439124516841518788307902706e-19
relative error = 4.5150909494078977736275705123346e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.683
y[1] (closed_form) = -0.0024904202694787157255462140732362
y[1] (numeric) = -0.0024904202694787156127349751695807
absolute error = 1.1281123890365550502932863299024e-19
relative error = 4.5298072894045581347623664649495e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.682
y[1] (closed_form) = -0.0024866696372238139245961076557257
y[1] (numeric) = -0.0024866696372238138115886728656737
absolute error = 1.1300743479005201913973206723573e-19
relative error = 4.5445294822603220353334803851529e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.681
y[1] (closed_form) = -0.002482925781177513190945763786789
y[1] (numeric) = -0.0024829257811775130777427825289046
absolute error = 1.1320298125788444323095018794804e-19
relative error = 4.5592575547787249651191514580996e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (closed_form) = -0.0024791886870612317264176042674054
y[1] (numeric) = -0.00247918868706123161301972361593
absolute error = 1.1339788065147532195069575212556e-19
relative error = 4.5739915337341400174110782438402e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.679
y[1] (closed_form) = -0.0024754583406307628827931767167481
y[1] (numeric) = -0.0024754583406307627692010414107661
absolute error = 1.1359213530598200985388392175499e-19
relative error = 4.5887314458718782196215607993881e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.678
y[1] (closed_form) = -0.0024717347276761820883305520556518
y[1] (numeric) = -0.0024717347276761819745448045082166
absolute error = 1.1378574754743524762125169641763e-19
relative error = 4.6034773179082885684275998742629e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.677
y[1] (closed_form) = -0.0024680178340217540542018774415997
y[1] (numeric) = -0.0024680178340217539402231577488221
absolute error = 1.1397871969277756436560665098645e-19
relative error = 4.6182291765308577704295960914686e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.676
y[1] (closed_form) = -0.0024643076455258402599253117764733
y[1] (numeric) = -0.0024643076455258401457542577265718
absolute error = 1.1417105404990150686176889322779e-19
relative error = 4.6329870483983096892987641339985e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.675
y[1] (closed_form) = -0.0024606041480808067168689100337039
y[1] (numeric) = -0.0024606041480808066025061571160162
absolute error = 1.1436275291768769653200095199096e-19
relative error = 4.6477509601407045003838628524778e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.674
y[1] (closed_form) = -0.0024569073276129320089073487334041
y[1] (numeric) = -0.0024569073276129318943535301473614
absolute error = 1.1455381858604271501447417784503e-19
relative error = 4.6625209383595375537443418344465e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.673
y[1] (closed_form) = -0.0024532171700823156093156979874019
y[1] (numeric) = -0.002453217170082315494571444651465
absolute error = 1.1474425333593681913809705289246e-19
relative error = 4.6772970096278379465735182722937e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.672
y[1] (closed_form) = -0.0024495336614827864729877456954481
y[1] (numeric) = -0.0024495336614827863580536862560066
absolute error = 1.1493405943944148612283043422988e-19
relative error = 4.6920792004902668059719248775037e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.671
y[1] (closed_form) = -0.0024458567878418119030696667535876
y[1] (numeric) = -0.0024458567878418117879464275938209
absolute error = 1.1512323915976678982043706610018e-19
relative error = 4.7068675374632152830275100564226e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (closed_form) = -0.0024421865352204066911031045898858
y[1] (numeric) = -0.0024421865352204065757913098385871
absolute error = 1.1531179475129860880645755992804e-19
relative error = 4.7216620470349022591559255302407e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.669
y[1] (closed_form) = -0.00243852288971304252977499402526
y[1] (numeric) = -0.0024385228897130424142752655656243
absolute error = 1.1549972845963566713007233067150e-19
relative error = 4.7364627556654717656507039925861e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.668
y[1] (closed_form) = -0.0024348658374475576973747034217155
y[1] (numeric) = -0.0024348658374475575816876609000891
absolute error = 1.1568704252162640852439856454087e-19
relative error = 4.7512696897870901173897101955850e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
memory used=281.4MB, alloc=44.3MB, time=4.16
x[1] = 2.667
y[1] (closed_form) = -0.002431215364585067013062310380202
y[1] (numeric) = -0.0024312153645850668971885712147963
absolute error = 1.1587373916540570487568305018743e-19
relative error = 4.7660828758040427616408429832546e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.666
y[1] (closed_form) = -0.0024275714573198720620550489387584
y[1] (numeric) = -0.002427571457319871945995228328327
absolute error = 1.1605982061043139974578550675991e-19
relative error = 4.7809023400928308429065731937065e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.665
y[1] (closed_form) = -0.0024239341018793716898421773514917
y[1] (numeric) = -0.002423934101879371573596888283971
absolute error = 1.1624528906752068773830276233676e-19
relative error = 4.7957281090022674847435229731410e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.664
y[1] (closed_form) = -0.002420303284523972764541714152927
y[1] (numeric) = -0.0024203032845239726481115674140406
absolute error = 1.1643014673888633049466165048616e-19
relative error = 4.8105602088535737894899258295662e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.663
y[1] (closed_form) = -0.0024166789915470012065156763827935
y[1] (numeric) = -0.0024166789915470010899012805646208
absolute error = 1.1661439581817271010250767714986e-19
relative error = 4.8253986659404745568304536473698e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.662
y[1] (closed_form) = -0.0024130612092746132843636276155895
y[1] (numeric) = -0.0024130612092746131675655891250977
absolute error = 1.1679803849049172069473724150024e-19
relative error = 4.8402435065292937221245568303525e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.661
y[1] (closed_form) = -0.0024094499240657071764175048592452
y[1] (numeric) = -0.0024094499240657070594364279267867
absolute error = 1.1698107693245849901356335042616e-19
relative error = 4.8550947568590495154211366858971e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (closed_form) = -0.0024058451223118347968638425096333
y[1] (numeric) = -0.0024058451223118346797003291974063
absolute error = 1.1716351331222699471006822514026e-19
relative error = 4.8699524431415493420790550521300e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.659
y[1] (closed_form) = -0.0024022467904371138856226484240321
y[1] (numeric) = -0.0024022467904371137682772986345067
absolute error = 1.1734534978952538114578083907395e-19
relative error = 4.8848165915614843859096849490147e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.658
y[1] (closed_form) = -0.0023986549148981403611153118582303
y[1] (numeric) = -0.002398654914898140243588723342539
absolute error = 1.1752658851569130745892312846299e-19
relative error = 4.8996872282765239357544176493307e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.657
y[1] (closed_form) = -0.0023950694821839009350570355497792
y[1] (numeric) = -0.0023950694821839008173498039160722
absolute error = 1.1770723163370699265409526127507e-19
relative error = 4.9145643794174094364067659626956e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.656
y[1] (closed_form) = -0.0023914904788156859884123846747894
y[1] (numeric) = -0.0023914904788156858705251033965552
absolute error = 1.1788728127823416247031781755116e-19
relative error = 4.9294480710880482647854406517004e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.655
y[1] (closed_form) = -0.0023879178913470027076556338081958
y[1] (numeric) = -0.002387917891347002589588894232547
absolute error = 1.1806673957564882977851690669497e-19
relative error = 4.9443383293656072322615267005897e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.654
y[1] (closed_form) = -0.0023843517063634884804806694279448
y[1] (numeric) = -0.0023843517063634883622350607838689
absolute error = 1.1824560864407591925572700732666e-19
relative error = 4.9592351803006058140396485807209e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.653
y[1] (closed_form) = -0.002380791910482824550108269972216
y[1] (numeric) = -0.0023807919104828244316843793787923
absolute error = 1.1842389059342373707949554629339e-19
relative error = 4.9741386499170091064897886505030e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.652
y[1] (closed_form) = -0.0023772384903546499273416380354912
y[1] (numeric) = -0.002377238490354649808740050510073
absolute error = 1.1860158752541828638220281927436e-19
relative error = 4.9890487642123205133232103381053e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.651
y[1] (closed_form) = -0.0023736914326604755595241000236963
y[1] (numeric) = -0.0023736914326604754407453984900588
absolute error = 1.1877870153363742920126068079609e-19
relative error = 5.0039655491576741615027377306395e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (closed_form) = -0.0023701507241135987555559175302411
y[1] (numeric) = -0.0023701507241135986366006828266962
absolute error = 1.1895523470354489565742338173838e-19
relative error = 5.0188890306979270477744555816821e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.649
y[1] (closed_form) = -0.0023666163514590178661301718928015
y[1] (numeric) = -0.0023666163514590177469989827802774
absolute error = 1.1913118911252414108973389359766e-19
relative error = 5.0338192347517509167047184980800e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.648
y[1] (closed_form) = -0.0023630883014733472183506888941384
y[1] (numeric) = -0.0023630883014733470990441220642263
absolute error = 1.1930656682991205187193891759927e-19
relative error = 5.0487561872117238711031951253728e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.647
y[1] (closed_form) = -0.0023595665609647323038979644279502
y[1] (numeric) = -0.0023595665609647321844165945109177
absolute error = 1.1948136991703250063153542060182e-19
relative error = 5.0636999139444217157095224674849e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.646
y[1] (closed_form) = -0.0023560511167727652199120342112661
y[1] (numeric) = -0.0023560511167727651002564337840363
absolute error = 1.1965560042722975158896085667798e-19
relative error = 5.0786504407905090350180069994578e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.645
y[1] (closed_form) = -0.0023525419557684003617642013365896
y[1] (numeric) = -0.0023525419557684002419349409306879
absolute error = 1.1982926040590171673080811201241e-19
relative error = 5.0936077935648300061116829109796e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.644
y[1] (closed_form) = -0.0023490390648538703668924946680387
y[1] (numeric) = -0.0023490390648538702468901427775056
absolute error = 1.2000235189053306352733454071997e-19
relative error = 5.1085719980564989473739236026459e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.643
y[1] (closed_form) = -0.002345542430962602308878678844029
y[1] (numeric) = -0.0023455424309626021887038019333009
absolute error = 1.2017487691072817490094213040257e-19
relative error = 5.1235430800289906039427003957878e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.642
y[1] (closed_form) = -0.0023420520410591341409475730023399
y[1] (numeric) = -0.0023420520410591340206007355140959
absolute error = 1.2034683748824396214873273943382e-19
relative error = 5.1385210652202301707694922600887e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.641
y[1] (closed_form) = -0.0023385678821390313880723603391846
y[1] (numeric) = -0.002338567882139031267554124702162
absolute error = 1.2051823563702253151868837443774e-19
relative error = 5.1535059793426830541417721610777e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (closed_form) = -0.0023350899412288040868724842994823
y[1] (numeric) = -0.0023350899412288039661834109362586
absolute error = 1.2068907336322370513549151820960e-19
relative error = 5.1684978480834443725249293321383e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.639
y[1] (closed_form) = -0.0023316182053858239724936296179744
y[1] (numeric) = -0.002331618205385823851634276952717
absolute error = 1.2085935266525739696848446805304e-19
relative error = 5.1834966971043281975764323333377e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.638
y[1] (closed_form) = -0.00232815266169824191166217763702
y[1] (numeric) = -0.0023281526616982417906331021032042
absolute error = 1.2102907553381584453076939545453e-19
relative error = 5.1985025520419565361819951228260e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.637
y[1] (closed_form) = -0.002324693297284905581109405363513
y[1] (numeric) = -0.0023246932972849054599111614116073
absolute error = 1.2119824395190569699497228409638e-19
relative error = 5.2135154385078480543604774866440e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.636
y[1] (closed_form) = -0.0023212400992952773905635666408317
y[1] (numeric) = -0.0023212400992952772691967067459518
absolute error = 1.2136685989487996040773393896356e-19
relative error = 5.2285353820885065438812320006056e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.635
y[1] (closed_form) = -0.0023177930549093526495108516483294
y[1] (numeric) = -0.0023177930549093525279759263178596
absolute error = 1.2153492533046980068154977989436e-19
relative error = 5.2435624083455091324346021847997e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.634
y[1] (closed_form) = -0.0023143521513375779769290677466222
y[1] (numeric) = -0.002314352151337577855226625527806
absolute error = 1.2170244221881620503915703415119e-19
relative error = 5.2585965428155942381932806087137e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.633
y[1] (closed_form) = -0.0023109173758207699532007205076937
y[1] (numeric) = -0.0023109173758207698313313079951922
absolute error = 1.2186941251250150258226312085140e-19
relative error = 5.2736378110107492695992513647606e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.632
y[1] (closed_form) = -0.0023074887156300340134149986502203
y[1] (numeric) = -0.0023074887156300338913791604936395
absolute error = 1.2203583815658074465302237242234e-19
relative error = 5.2886862384182980712080685020463e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.631
y[1] (closed_form) = -0.0023040661580666835812709805879909
y[1] (numeric) = -0.0023040661580666834590692594993779
absolute error = 1.2220172108861294565329966226171e-19
relative error = 5.3037418505009881164192606527271e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (closed_form) = -0.0023006496904621594427971834380461
y[1] (numeric) = -0.0023006496904621593204301201993539
absolute error = 1.2236706323869218498340890173336e-19
relative error = 5.3188046726970774479187021426539e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.629
y[1] (closed_form) = -0.0022972393001779493591053676702548
y[1] (numeric) = -0.0022972393001779492365735011407762
absolute error = 1.2253186652947857075868163235202e-19
relative error = 5.3338747304204213666558523087777e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.628
y[1] (closed_form) = -0.0022938349746055079173992921562834
y[1] (numeric) = -0.0022938349746055077947031592800543
absolute error = 1.2269613287622906595890596994976e-19
relative error = 5.3489520490605588701758375008168e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.627
y[1] (closed_form) = -0.0022904367011661766194618852379436
y[1] (numeric) = -0.0022904367011661764966020210511154
absolute error = 1.2285986418682817766237885680952e-19
relative error = 5.3640366539827988411234342769616e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.626
y[1] (closed_form) = -0.0022870444673111042068470576271441
y[1] (numeric) = -0.0022870444673111040838239952653256
absolute error = 1.2302306236181851001303484582489e-19
relative error = 5.3791285705283059867331075661619e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.625
y[1] (closed_form) = -0.0022836582605211672220051325163652
y[1] (numeric) = -0.002283658260521167098819403221934
absolute error = 1.2318572929443118156585237891884e-19
relative error = 5.3942278240141865301163640162206e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.624
y[1] (closed_form) = -0.0022802780683068908045736072637541
y[1] (numeric) = -0.002280278068306890681225740393138
absolute error = 1.2334786687061610765249363202733e-19
relative error = 5.4093344397335736541547983311612e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.623
y[1] (closed_form) = -0.0022769038782083697220676894644441
y[1] (numeric) = -0.0022769038782083695985582124953719
absolute error = 1.2350947696907214840590638330981e-19
relative error = 5.4244484429557126988043390769839e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.622
y[1] (closed_form) = -0.0022735356777951896342077681731843
y[1] (numeric) = -0.0022735356777951895105372067119072
absolute error = 1.2367056146127712307940592284718e-19
relative error = 5.4395698589260461126133401560272e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.621
y[1] (closed_form) = -0.002270173454666348590123688546278
y[1] (numeric) = -0.0022701734546663484662925663347603
absolute error = 1.2383112221151769129256166446152e-19
relative error = 5.4546987128662981592543148709703e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (closed_form) = -0.0022668171964501787576783952664261
y[1] (numeric) = -0.002266817196450178633687234189507
absolute error = 1.2399116107691910183303674754462e-19
relative error = 5.4698350299745593798662711744954e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.619
y[1] (closed_form) = -0.0022634668908042683841561968454359
y[1] (numeric) = -0.0022634668908042682600055169379611
absolute error = 1.2415067990747480964036943358379e-19
relative error = 5.4849788354253708120017792844472e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.618
y[1] (closed_form) = -0.0022601225254153839875635793097473
y[1] (numeric) = -0.0022601225254153838632538987636714
absolute error = 1.2430968054607596159454241365617e-19
relative error = 5.5001301543698079659700862918342e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.617
y[1] (closed_form) = -0.0022567840879993927777931639050527
y[1] (numeric) = -0.0022567840879993926533249990765119
absolute error = 1.2446816482854075172906015532026e-19
relative error = 5.5152890119355645593647866552771e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.616
y[1] (closed_form) = -0.0022534515663011853069040593514286
y[1] (numeric) = -0.0022534515663011851822779247677849
absolute error = 1.2462613458364364648514503641295e-19
relative error = 5.5304554332270360105617625157837e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.615
y[1] (closed_form) = -0.00225012494809459834777450488168
y[1] (numeric) = -0.0022501249480945982229909132485355
absolute error = 1.2478359163314448062057014616415e-19
relative error = 5.5456294433254026919703235354739e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.614
y[1] (closed_form) = -0.0022468042211823380003853358451307
y[1] (numeric) = -0.0022468042211823378754447980533133
absolute error = 1.2494053779181742438357018821953e-19
relative error = 5.5608110672887129438177024187534e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.613
y[1] (closed_form) = -0.0022434893733959030249954290988273
y[1] (numeric) = -0.0022434893733959028998984542313475
absolute error = 1.2509697486747982255921180361024e-19
relative error = 5.5760003301519658492442993702825e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.612
y[1] (closed_form) = -0.0022401803925955084014729007798024
y[1] (numeric) = -0.0022401803925955082762199961187815
absolute error = 1.2525290466102090599256075296726e-19
relative error = 5.5911972569271937714843164369694e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
memory used=328.0MB, alloc=44.3MB, time=4.84
TOP MAIN SOLVE Loop
x[1] = 2.611
y[1] (closed_form) = -0.0022368772666700091140484343972305
y[1] (numeric) = -0.0022368772666700089886401054308001
absolute error = 1.2540832896643037618995566542283e-19
relative error = 5.6064018726035446539036809273602e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (closed_form) = -0.0022335799835368241607597125433998
y[1] (numeric) = -0.0022335799835368240351964629725729
absolute error = 1.2556324957082686359668638628792e-19
relative error = 5.6216142021473640836644258576520e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.609
y[1] (closed_form) = -0.0022302885311418607868585109386017
y[1] (numeric) = -0.0022302885311418606611408426841155
absolute error = 1.2571766825448626014637924688717e-19
relative error = 5.6368342705022771197819745957360e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.608
y[1] (closed_form) = -0.0022270028974594389414545890383376
y[1] (numeric) = -0.0022270028974594388155830022474677
absolute error = 1.2587158679086992667441174854731e-19
relative error = 5.6520621025892698863390665200142e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.607
y[1] (closed_form) = -0.0022237230704922159566730770824867
y[1] (numeric) = -0.0022237230704922158306480701358339
absolute error = 1.2602500694665277578471510987261e-19
relative error = 5.6672977233067709316173605352285e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.606
y[1] (closed_form) = -0.0022204490382711114486046152959313
y[1] (numeric) = -0.00222044903827111132242668481418
absolute error = 1.2617793048175123075637478382434e-19
relative error = 5.6825411575307323539050636504024e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.605
y[1] (closed_form) = -0.0022171807888552324393300469990711
y[1] (numeric) = -0.00221718078885523231299968784972
absolute error = 1.2633035914935106107350632099461e-19
relative error = 5.6977924301147106947362524816054e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.604
y[1] (closed_form) = -0.0022139183103317986993040036949735
y[1] (numeric) = -0.0022139183103317985728217089990384
absolute error = 1.2648229469593509515896675058653e-19
relative error = 5.7130515658899476003148864521952e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.603
y[1] (closed_form) = -0.0022106615908160683093842468077253
y[1] (numeric) = -0.0022106615908160681827505079464145
absolute error = 1.2663373886131081088955988425543e-19
relative error = 5.7283185896654502518738525832259e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.602
y[1] (closed_form) = -0.0022074106184512634417961476938134
y[1] (numeric) = -0.0022074106184512633150114543151756
absolute error = 1.2678469337863780446750753391077e-19
relative error = 5.7435935262280715657167330547966e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.601
y[1] (closed_form) = -0.0022041653814084963593241948748356
y[1] (numeric) = -0.0022041653814084962323890349003805
absolute error = 1.2693515997445513822008748711584e-19
relative error = 5.7588764003425901636873481333775e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (closed_form) = -0.0022009258678866956320249151851208
y[1] (numeric) = -0.0022009258678866955049397748164122
absolute error = 1.2708514036870856789648311764236e-19
relative error = 5.7741672367517901148094985589227e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.599
y[1] (closed_form) = -0.0021976920661125325707580837313333
y[1] (numeric) = -0.0021976920661125324435234474565556
absolute error = 1.2723463627477765002804863933479e-19
relative error = 5.7894660601765404488367130273547e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.598
y[1] (closed_form) = -0.0021944639643403478768355762621021
y[1] (numeric) = -0.0021944639643403477494519268625994
absolute error = 1.2738364939950272991536815450250e-19
relative error = 5.8047728953158744424491979474854e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.597
y[1] (closed_form) = -0.0021912415508520785070896867832073
y[1] (numeric) = -0.0021912415508520783795575053399955
absolute error = 1.2753218144321181080267571987298e-19
relative error = 5.8200877668470686788325881554771e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.596
y[1] (closed_form) = -0.0021880248139571847536651930667894
y[1] (numeric) = -0.0021880248139571846259849589670421
absolute error = 1.2768023409974730479740757048050e-19
relative error = 5.8354106994257218813705086936126e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.595
y[1] (closed_form) = -0.0021848137419925775378419031301363
y[1] (numeric) = -0.0021848137419925774100140940736436
absolute error = 1.2782780905649266608987632199643e-19
relative error = 5.8507417176858335221803790626502e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.594
y[1] (closed_form) = -0.0021816083233225459171968568394091
y[1] (numeric) = -0.0021816083233225457892219488450102
absolute error = 1.2797490799439890702529033267943e-19
relative error = 5.8660808462398822062193224978159e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.593
y[1] (closed_form) = -0.0021784085463386848054177885645823
y[1] (numeric) = -0.0021784085463386846772962559765713
absolute error = 1.2812153258801099757758936556557e-19
relative error = 5.8814281096789038316844837571034e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.592
y[1] (closed_form) = -0.0021752143994598229040818793121052
y[1] (numeric) = -0.0021752143994598227758141948066111
absolute error = 1.2826768450549414877183016844332e-19
relative error = 5.8967835325725695274295096067939e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.591
y[1] (closed_form) = -0.002172025871131950845716240029404
y[1] (numeric) = -0.002172025871131950717302874620744
absolute error = 1.2841336540865998059913250275037e-19
relative error = 5.9121471394692633681164066029086e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (closed_form) = -0.0021688429498281495474589718482034
y[1] (numeric) = -0.0021688429498281494189003948952108
absolute error = 1.2855857695299257496548742245138e-19
relative error = 5.9275189548961598678194608587927e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.589
y[1] (closed_form) = -0.0021656656240485187746420439494868
y[1] (numeric) = -0.0021656656240485186459387231618124
absolute error = 1.2870332078767441421303515033653e-19
relative error = 5.9428990033593012527953842184883e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.588
y[1] (closed_form) = -0.0021624938823201059136196155292708
y[1] (numeric) = -0.0021624938823201057847720169736586
absolute error = 1.2884759855561220574973964262057e-19
relative error = 5.9582873093436745141313405834688e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.587
y[1] (closed_form) = -0.0021593277131968349531678050586421
y[1] (numeric) = -0.0021593277131968348241763931651795
absolute error = 1.2899141189346259332072079428224e-19
relative error = 5.9736838973132882409800050273043e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.586
y[1] (closed_form) = -0.0021561671052594356737842777009013
y[1] (numeric) = -0.0021561671052594355446495152692436
absolute error = 1.2913476243165775545185313879093e-19
relative error = 5.9890887917112492350883167397454e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.585
y[1] (closed_form) = -0.0021530120471153730442183804102509
y[1] (numeric) = -0.00215301204711537291494072861582
absolute error = 1.2927765179443089159360175870444e-19
relative error = 6.0045020169598389073241047295171e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.584
y[1] (closed_form) = -0.0021498625273987768245649039271336
y[1] (numeric) = -0.002149862527398776695144822327292
absolute error = 1.2942008159984159649044187052891e-19
relative error = 6.0199235974605894569022925449829e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.583
y[1] (closed_form) = -0.0021467185347703713752568916418247
y[1] (numeric) = -0.0021467185347703712456948381820235
absolute error = 1.2956205345980112329859810110365e-19
relative error = 6.0353535575943598340099250050970e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.582
y[1] (closed_form) = -0.0021435800579174056712952471567604
y[1] (numeric) = -0.0021435800579174055415916781766628
absolute error = 1.2970356898009753597224275695290e-19
relative error = 6.0507919217214114865268060312004e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.581
y[1] (closed_form) = -0.0021404470855535835210552153757756
y[1] (numeric) = -0.0021404470855535833912105856153549
absolute error = 1.2984462976042075143570932632696e-19
relative error = 6.0662387141814838915360920949216e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (closed_form) = -0.002137319606418993989012126121163
y[1] (numeric) = -0.0021373196064189938590268887267755
absolute error = 1.2998523739438747205670797027252e-19
relative error = 6.0816939592938698723167505105347e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.579
y[1] (closed_form) = -0.0021341976092800420217310946633619
y[1] (numeric) = -0.0021341976092800418916057011937959
absolute error = 1.3012539346956600893297377870661e-19
relative error = 6.0971576813574907015073657636195e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.578
y[1] (closed_form) = -0.0021310810829293792764676701790618
y[1] (numeric) = -0.0021310810829293791462025706115608
absolute error = 1.3026509956750099650223601524000e-19
relative error = 6.1126299046509709911283602439308e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.577
y[1] (closed_form) = -0.0021279700161858351517287110673486
y[1] (numeric) = -0.0021279700161858350213243538036106
absolute error = 1.3040435726373799898286737595959e-19
relative error = 6.1281106534327133701472881013493e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.576
y[1] (closed_form) = -0.0021248643978943480191450452858509
y[1] (numeric) = -0.0021248643978943478886018771580029
absolute error = 1.3054316812784800915005636852616e-19
relative error = 6.1435999519409729502694624321606e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.575
y[1] (closed_form) = -0.0021217642169258966560097444551203
y[1] (numeric) = -0.0021217642169258965253282107316685
absolute error = 1.3068153372345183994984320519644e-19
relative error = 6.1590978243939315806337865913520e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.574
y[1] (closed_form) = -0.0021186694621774318778381024550261
y[1] (numeric) = -0.0021186694621774317470186468467817
absolute error = 1.3081945560824440945087002358734e-19
relative error = 6.1746042949897718920912800779645e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.573
y[1] (closed_form) = -0.0021155801225718083703076626368992
y[1] (numeric) = -0.0021155801225718082393507273028803
absolute error = 1.3095693533401891963121972944296e-19
relative error = 6.1901193879067511317414181177746e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.572
y[1] (closed_form) = -0.0021124961870577167199388826345447
y[1] (numeric) = -0.0021124961870577165888449081878538
absolute error = 1.3109397444669092949525422404392e-19
relative error = 6.2056431273032747883990417338648e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.571
y[1] (closed_form) = -0.0021094176446096156428792621108897
y[1] (numeric) = -0.0021094176446096155116486876245674
absolute error = 1.3123057448632232301291216333442e-19
relative error = 6.2211755373179700096622417142857e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (closed_form) = -0.0021063444842276644111559866596517
y[1] (numeric) = -0.0021063444842276642797892496725065
absolute error = 1.3136673698714517237148862487817e-19
relative error = 6.2367166420697588112492754204924e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.569
y[1] (closed_form) = -0.00210327669493765547576436052754
y[1] (numeric) = -0.0021032766949376553442618970499545
absolute error = 1.3150246347758549702749406134566e-19
relative error = 6.2522664656579310792702397941870e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.568
y[1] (closed_form) = -0.00210021426579094728596151186654
y[1] (numeric) = -0.002100214265790947154323756386253
absolute error = 1.3163775548028691904377762475348e-19
relative error = 6.2678250321622173660968971774094e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.567
y[1] (closed_form) = -0.0020971571858643973041370569020165
y[1] (numeric) = -0.0020971571858643971723644423898823
absolute error = 1.3177261451213421519470028390301e-19
relative error = 6.2833923656428614804917326251484e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.566
y[1] (closed_form) = -0.0020941054442602952156346037448046
y[1] (numeric) = -0.0020941054442602950837275616605279
absolute error = 1.3190704208427676631975605859071e-19
relative error = 6.2989684901406928726550122254896e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.565
y[1] (closed_form) = -0.0020910590301062963329001626180817
y[1] (numeric) = -0.0020910590301062962008591229159298
absolute error = 1.3204103970215190440366508878160e-19
relative error = 6.3145534296771988148463115136603e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.564
y[1] (closed_form) = -0.0020880179325553551933357070464287
y[1] (numeric) = -0.0020880179325553550611610981809205
absolute error = 1.3217460886550815785860007605069e-19
relative error = 6.3301472082545963782346913376775e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.563
y[1] (closed_form) = -0.0020849821407856593502383000987434
y[1] (numeric) = -0.002084982140785659217930549030315
absolute error = 1.3230775106842839548185780960471e-19
relative error = 6.3457498498559042066294154692406e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.562
y[1] (closed_form) = -0.0020819516440005633562073611220682
y[1] (numeric) = -0.0020819516440005632237668933227153
absolute error = 1.3244046779935286955994995189778e-19
relative error = 6.3613613784450140877408298187670e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.561
y[1] (closed_form) = -0.0020789264314285229384048015832942
y[1] (numeric) = -0.002078926431428522805832041042192
absolute error = 1.3257276054110215858776194144441e-19
relative error = 6.3769818179667623226187572729233e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (closed_form) = -0.0020759064923230293650549036833211
y[1] (numeric) = -0.0020759064923230292323502729124211
absolute error = 1.3270463077090001006911570550079e-19
relative error = 6.3926111923470008939135048917051e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.559
y[1] (closed_form) = -0.002072891815962544002572952356646
y[1] (numeric) = -0.0020728918159625438697368723962499
absolute error = 1.3283607996039608386277079581114e-19
relative error = 6.4082495254926684336023314452468e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.558
y[1] (closed_form) = -0.0020698823916504330627137601514601
y[1] (numeric) = -0.0020698823916504329297466505757715
absolute error = 1.3296710957568859653560949996882e-19
relative error = 6.4238968412918609908219830034482e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.557
y[1] (closed_form) = -0.0020668782087149025391333453339184
y[1] (numeric) = -0.0020668782087149024060356242565715
absolute error = 1.3309772107734686718247437287784e-19
relative error = 6.4395531636139026004456724796722e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.556
y[1] (closed_form) = -0.0020638792565089333327591364079596
y[1] (numeric) = -0.0020638792565089331995312204875259
memory used=374.7MB, alloc=44.3MB, time=5.52
absolute error = 1.3322791592043376516986141146001e-19
relative error = 6.4552185163094156530406556388492e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.555
y[1] (closed_form) = -0.002060885524410216565366181121385
y[1] (numeric) = -0.002060885524410216432008485566857
absolute error = 1.3335769555452806025841869565695e-19
relative error = 6.4708929232103910668403410761039e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.554
y[1] (closed_form) = -0.0020578970018210890807589349722074
y[1] (numeric) = -0.0020578970018210889472718735484607
absolute error = 1.3348706142374667555695867482777e-19
relative error = 6.4865764081302582623626650204470e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.553
y[1] (closed_form) = -0.0020549136781684691329602932687728
y[1] (numeric) = -0.002054913678168468999344278302006
absolute error = 1.3361601496676684375846232611919e-19
relative error = 6.5022689948639549403042634852330e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.552
y[1] (closed_form) = -0.0020519355429037922608116119649085
y[1] (numeric) = -0.0020519355429037921270670543480603
absolute error = 1.3374455761684816710633508594074e-19
relative error = 6.5179707071879966633377842392119e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.551
y[1] (closed_form) = -0.0020489625855029473483895358192934
y[1] (numeric) = -0.0020489625855029472145168450174388
absolute error = 1.3387269080185458153696769333841e-19
relative error = 6.5336815688605462424374992754919e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (closed_form) = -0.002045994795466212870647517948184
y[1] (numeric) = -0.0020459947954662127366471020039078
absolute error = 1.3400041594427622544245982122379e-19
relative error = 6.5494016036214829283562048770919e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.549
y[1] (closed_form) = -0.0020430321623181933236919725842069
y[1] (numeric) = -0.0020430321623181931895642381229557
absolute error = 1.3412773446125121349518054484568e-19
relative error = 6.5651308351924714088742309836975e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.548
y[1] (closed_form) = -0.0020400746756077558391050528526769
y[1] (numeric) = -0.0020400746756077557048504050880896
absolute error = 1.3425464776458731597366724372023e-19
relative error = 6.5808692872770306124392243215358e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.547
y[1] (closed_form) = -0.0020371223249079669817280876621957
y[1] (numeric) = -0.0020371223249079668473469304014122
absolute error = 1.3438115726078354402720339095657e-19
relative error = 6.5966169835606023188132206339422e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.546
y[1] (closed_form) = -0.0020341750998160297303217464093766
y[1] (numeric) = -0.0020341750998160295958144820583249
absolute error = 1.3450726435105164131426579038486e-19
relative error = 6.6123739477106195773413803112948e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.545
y[1] (closed_form) = -0.0020312329899532206405210271495378
y[1] (numeric) = -0.0020312329899532205058880567182004
absolute error = 1.3463297043133748244789311532782e-19
relative error = 6.6281402033765749334546287327966e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.544
y[1] (closed_form) = -0.002028295984964827189505183217091
y[1] (numeric) = -0.0020282959849648270547469063247487
absolute error = 1.3475827689234237867890002182700e-19
relative error = 6.6439157741900884640163176664923e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.543
y[1] (closed_form) = -0.0020253640745200853018047150219514
y[1] (numeric) = -0.0020253640745200851669215299024071
absolute error = 1.3488318511954429124574459256991e-19
relative error = 6.6597006837649756221209070954309e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.542
y[1] (closed_form) = -0.0020224372483121170556695579323379
y[1] (numeric) = -0.002022437248312116920661861439119
absolute error = 1.3500769649321895281775135494230e-19
relative error = 6.6754949556973148919505578147253e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.541
y[1] (closed_form) = -0.0020195154960578685694245938103749
y[1] (numeric) = -0.002019515496057868434292781421914
absolute error = 1.3513181238846089745629754718377e-19
relative error = 6.6912986135655152542934240442061e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (closed_form) = -0.0020165988074980480672406029254004
y[1] (numeric) = -0.002016598807498047931985068750196
absolute error = 1.3525553417520439951648662053288e-19
relative error = 6.7071116809303834633253420923952e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.539
y[1] (closed_form) = -0.0020136871723970641237507546611434
y[1] (numeric) = -0.0020136871723970639883718914428991
absolute error = 1.3537886321824432190976010283607e-19
relative error = 6.7229341813351911352545257577141e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.538
y[1] (closed_form) = -0.0020107805805429640869447096871279
y[1] (numeric) = -0.002010780580542963951442908809871
absolute error = 1.3550180087725687414583685103355e-19
relative error = 6.7387661383057416494268016304269e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.537
y[1] (closed_form) = -0.0020078790217473726787743731118419
y[1] (numeric) = -0.0020078790217473725431500246050216
absolute error = 1.3562434850682028057031732723633e-19
relative error = 6.7546075753504368624868477321729e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.536
y[1] (closed_form) = -0.0020049824858454307729072976053048
y[1] (numeric) = -0.0020049824858454306371607901488694
absolute error = 1.3574650745643535921224978712566e-19
relative error = 6.7704585159603436361888369675667e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.535
y[1] (closed_form) = -0.0020020909626957343490656876014519
y[1] (numeric) = -0.0020020909626957342131974085309059
absolute error = 1.3586827907054601165392511182820e-19
relative error = 6.7863189836092601794478326328807e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.534
y[1] (closed_form) = -0.0019992044421802736233909004958984
y[1] (numeric) = -0.0019992044421802734874012358073388
absolute error = 1.3598966468855962433314738727555e-19
relative error = 6.8021890017537822052212366990561e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.533
y[1] (closed_form) = -0.0019963229142043723542752782716812
y[1] (numeric) = -0.0019963229142043722181646126268138
absolute error = 1.3611066564486738168621818070532e-19
relative error = 6.8180685938333689028075527291174e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.532
y[1] (closed_form) = -0.0019934463686966273231050732439007
y[1] (numeric) = -0.0019934463686966271868737899750362
absolute error = 1.3623128326886449153787372509489e-19
relative error = 6.8339577832704087261476940725541e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.531
y[1] (closed_form) = -0.0019905747956088479893601546430853
y[1] (numeric) = -0.001990574795608847853008635758115
absolute error = 1.3635151888497032314242584196257e-19
relative error = 6.8498565934702849987120443705444e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (closed_form) = -0.0019877081849159963195180985857177
y[1] (numeric) = -0.0019877081849159961830467247730693
absolute error = 1.3647137381264845827837935447306e-19
relative error = 6.8657650478214413355544613753610e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.529
y[1] (closed_form) = -0.0019848465266161267892121726377327
y[1] (numeric) = -0.0019848465266161266526213232713061
absolute error = 1.3659084936642665579683090982316e-19
relative error = 6.8816831696954468831124066043523e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.528
y[1] (closed_form) = -0.0019819898107303265580946276918034
y[1] (numeric) = -0.0019819898107303264213846808358866
absolute error = 1.3670994685591673002199648645891e-19
relative error = 6.8976109824470613773303823831183e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.527
y[1] (closed_form) = -0.001979138027302655816858604280672
y[1] (numeric) = -0.0019791380273026556800299366948376
absolute error = 1.3682866758583434340026735211125e-19
relative error = 6.9135485094143000206818643536074e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.526
y[1] (closed_form) = -0.0019762911664000883058738477652853
y[1] (numeric) = -0.0019762911664000881689268349092666
absolute error = 1.3694701285601871379225680757517e-19
relative error = 6.9294957739184981786629315006903e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.525
y[1] (closed_form) = -0.0019734492181124520048933070966002
y[1] (numeric) = -0.0019734492181124518678283231351479
absolute error = 1.3706498396145223680037264356003e-19
relative error = 6.9454527992643758963288171552878e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.524
y[1] (closed_form) = -0.0019706121725523699932895650820348
y[1] (numeric) = -0.0019706121725523698561069828897547
absolute error = 1.3718258219228002352253279908250e-19
relative error = 6.9614196087401022354426332334438e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.523
y[1] (closed_form) = -0.0019677800198552014802819143199354
y[1] (numeric) = -0.001967780019855201342982105486106
absolute error = 1.3729980883382935412073418535104e-19
relative error = 6.9773962256173594328035561390734e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.522
y[1] (closed_form) = -0.0019649527501789830046167522262672
y[1] (numeric) = -0.0019649527501789828672000870596381
absolute error = 1.3741666516662904759128697480649e-19
relative error = 6.9933826731514068803198062638294e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.521
y[1] (closed_form) = -0.0019621303537043698031658208950602
y[1] (numeric) = -0.0019621303537043696656326684286314
absolute error = 1.3753315246642874812163879715150e-19
relative error = 7.0093789745811449273898038311166e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (closed_form) = -0.0019593128206345773479086629358654
y[1] (numeric) = -0.0019593128206345772102593909316473
absolute error = 1.3764927200421812841683517934665e-19
relative error = 7.0253851531291785061529419233389e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.519
y[1] (closed_form) = -0.0019565001411953230507675029453978
y[1] (numeric) = -0.0019565001411953229130024778991518
absolute error = 1.3776502504624601037679416150361e-19
relative error = 7.0414012320018805801694828727425e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.518
y[1] (closed_form) = -0.0019536923056347681357645959243397
y[1] (numeric) = -0.0019536923056347679978841830703003
absolute error = 1.3788041285403940350371426250116e-19
relative error = 7.0574272343894554170871567575777e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.517
y[1] (closed_form) = -0.0019508893042234596779739087715124
y[1] (numeric) = -0.00195088930422345953997847208709
absolute error = 1.3799543668442246141708580542680e-19
relative error = 7.0734631834660016858501204977290e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.516
y[1] (closed_form) = -0.00194809112725427280874081900373
y[1] (numeric) = -0.0019480911272542726706307212141946
absolute error = 1.3811009778953535685193599134640e-19
relative error = 7.0895091023895753790040229585861e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.515
y[1] (closed_form) = -0.0019452977650423530866453260879525
y[1] (numeric) = -0.0019452977650423529484209286710994
absolute error = 1.3822439741685307551410797846516e-19
relative error = 7.1055650143022525606490155199708e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.514
y[1] (closed_form) = -0.0019425092079250590336860752600627
y[1] (numeric) = -0.0019425092079250588953477384508585
absolute error = 1.3833833680920412916455353080358e-19
relative error = 7.1216309423301919405906487197729e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.513
y[1] (closed_form) = -0.0019397254462619048361642914687817
y[1] (numeric) = -0.0019397254462619046977123742639926
absolute error = 1.3845191720478918830280749470537e-19
relative error = 7.1377069095836972752367038110624e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.512
y[1] (closed_form) = -0.0019369464704345032097485121508945
y[1] (numeric) = -0.0019369464704345030711833723136949
absolute error = 1.3856513983719963481801039174777e-19
relative error = 7.1537929391572795957861233484452e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.511
y[1] (closed_form) = -0.0019341722708465084282027919419218
y[1] (numeric) = -0.0019341722708465082895247860064858
absolute error = 1.3867800593543603497405273215899e-19
relative error = 7.1698890541297192642543272160464e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (closed_form) = -0.0019314028379235595152628301814016
y[1] (numeric) = -0.0019314028379235593764723134574751
absolute error = 1.3879051672392653309363120317231e-19
relative error = 7.1859952775641278578773297975947e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.509
y[1] (closed_form) = -0.0019286381621132235991462432106426
y[1] (numeric) = -0.0019286381621132234602435697880974
absolute error = 1.3890267342254516630423262166295e-19
relative error = 7.2021116325080098824352102406102e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.508
y[1] (closed_form) = -0.0019258782338849394291849680097074
y[1] (numeric) = -0.0019258782338849392901704907630773
absolute error = 1.3901447724663010070729641000692e-19
relative error = 7.2182381419933243150336309537675e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.507
y[1] (closed_form) = -0.0019231230437299610540695417058645
y[1] (numeric) = -0.0019231230437299609149436122988627
absolute error = 1.3912592940700178933005030874480e-19
relative error = 7.2343748290365459768802495713233e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.506
y[1] (closed_form) = -0.0019203725821613016611967529340975
y[1] (numeric) = -0.0019203725821613015219597218241164
absolute error = 1.3923703110998105221776702998223e-19
relative error = 7.2505217166387267365910265934007e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.505
y[1] (closed_form) = -0.0019176268397136775766139059676579
y[1] (numeric) = -0.0019176268397136774372661224102509
absolute error = 1.3934778355740707902245153245201e-19
relative error = 7.2666788277855565445595947383577e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.504
y[1] (closed_form) = -0.0019148858069434524250546769891387
y[1] (numeric) = -0.0019148858069434522855964890424834
absolute error = 1.3945818794665535444223951401740e-19
relative error = 7.2828461854474242989210266960107e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.503
y[1] (closed_form) = -0.001912149474428581449563273866091
y[1] (numeric) = -0.0019121494744285813099950283954355
absolute error = 1.3956824547065550686406752161024e-19
relative error = 7.2990238125794785436395154208139e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.502
y[1] (closed_form) = -0.001909417832768555990205336355632
y[1] (numeric) = -0.0019094178327685558505273790377229
absolute error = 1.3967795731790908056046372394459e-19
relative error = 7.3152117321216879992476653250278e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.501
y[1] (closed_form) = -0.0019066908725843481213657328155264
y[1] (numeric) = -0.0019066908725843479815784081430191
absolute error = 1.3978732467250723178960583087559e-19
relative error = 7.3314099669989019267632836963530e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
memory used=421.3MB, alloc=44.3MB, time=6.22
x[1] = 2.5
y[1] (closed_form) = -0.0019039685845183554471351222704825
y[1] (numeric) = -0.0019039685845183553072387735563342
absolute error = 1.3989634871414834914609882730778e-19
relative error = 7.3476185401209103253077593455060e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.499
y[1] (closed_form) = -0.0019012509592343460542888570973922
y[1] (numeric) = -0.0019012509592343459142838264792366
absolute error = 1.4000503061815559850824007169222e-19
relative error = 7.3638374743825039639483198599207e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.498
y[1] (closed_form) = -0.0018985379874174036223635016773537
y[1] (numeric) = -0.0018985379874174034822501301218593
absolute error = 1.4011337155549439292586284225142e-19
relative error = 7.3800667926635342482846698734354e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.497
y[1] (closed_form) = -0.0018958296597738726903379361408452
y[1] (numeric) = -0.0018958296597738725501165634480554
absolute error = 1.4022137269278978779118155127231e-19
relative error = 7.3963065178289729222987304318626e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.496
y[1] (closed_form) = -0.0018931259670313040794277018305271
y[1] (numeric) = -0.0018931259670313039390986666381833
absolute error = 1.4032903519234380163340254250788e-19
relative error = 7.4125566727289716059844238142203e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.495
y[1] (closed_form) = -0.0018904268999384004715029263489359
y[1] (numeric) = -0.0018904268999384003310665661367832
absolute error = 1.4043636021215266287621359259885e-19
relative error = 7.4288172801989211692726790327506e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.494
y[1] (closed_form) = -0.0018877324492649621426418410707327
y[1] (numeric) = -0.0018877324492649620020984921648088
absolute error = 1.4054334890592398289562290839443e-19
relative error = 7.4450883630595109427650706553750e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.493
y[1] (closed_form) = -0.0018850426058018328513335728060659
y[1] (numeric) = -0.001885042605801832710683570382972
absolute error = 1.4065000242309385571398450231338e-19
relative error = 7.4613699441167877657877475457802e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.492
y[1] (closed_form) = -0.0018823573603608458808455539277283
y[1] (numeric) = -0.0018823573603608457400892320188844
absolute error = 1.4075632190884388466442129189365e-19
relative error = 7.4776620461622148722755585728272e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.491
y[1] (closed_form) = -0.001879676703774770235272551744804
y[1] (numeric) = -0.0018796767037747700944102432406859
absolute error = 1.4086230850411813635824006214734e-19
relative error = 7.4939646919727306149945392765055e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (closed_form) = -0.0018770006268972569887859682439247
y[1] (numeric) = -0.0018770006268972568478180048982847
absolute error = 1.4096796334564002228632350523679e-19
relative error = 7.5102779043108070286091868663567e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.489
y[1] (closed_form) = -0.0018743291206027857876037055505471
y[1] (numeric) = -0.001874329120602785646530417984618
absolute error = 1.4107328756592910838388386654573e-19
relative error = 7.5266017059245082320992207444737e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.488
y[1] (closed_form) = -0.0018716621757866115042025306111397
y[1] (numeric) = -0.0018716621757866113630242483178218
absolute error = 1.4117828229331785288637023491813e-19
relative error = 7.5429361195475486710288019632080e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.487
y[1] (closed_form) = -0.0018689997833647110432965046870568
y[1] (numeric) = -0.0018689997833647109020135560350885
absolute error = 1.4128294865196827280273717341232e-19
relative error = 7.5592811678993512001694676221010e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.486
y[1] (closed_form) = -0.001866341934273730299106669306316
y[1] (numeric) = -0.0018663419342737301577193815444275
absolute error = 1.4138728776188853933070615135555e-19
relative error = 7.5756368736851050069763251538939e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.485
y[1] (closed_form) = -0.0018636886194709312634488003644851
y[1] (numeric) = -0.0018636886194709311219574996255356
absolute error = 1.4149130073894950253708306502168e-19
relative error = 7.5920032595958233764153467204863e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.484
y[1] (closed_form) = -0.0018610398299341392841676561243624
y[1] (numeric) = -0.0018610398299341391425726674294612
absolute error = 1.4159498869490114562463497937747e-19
relative error = 7.6083803483084012976379055112179e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.483
y[1] (closed_form) = -0.0018583955566616904734477529599043
y[1] (numeric) = -0.0018583955566616903317494002225153
absolute error = 1.4169835273738896910547704378431e-19
relative error = 7.6247681624856729129970035827886e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.482
y[1] (closed_form) = -0.0018557557906723792655323048466387
y[1] (numeric) = -0.0018557557906723791237309108766684
absolute error = 1.4180139396997030519937628727962e-19
relative error = 7.6411667247764688098979549775214e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.481
y[1] (closed_form) = -0.0018531205230054061233835588422121
y[1] (numeric) = -0.0018531205230054059814794453500816
absolute error = 1.4190411349213056277384264131947e-19
relative error = 7.6575760578156731559746081796812e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (closed_form) = -0.0018504897447203253938193491502692
y[1] (numeric) = -0.0018504897447203252518128367509698
absolute error = 1.4200651239929940314134902710563e-19
relative error = 7.6739961842242806780805184934165e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.479
y[1] (closed_form) = -0.0018478634468969933106622768419672
y[1] (numeric) = -0.0018478634468969931685536850591003
absolute error = 1.4210859178286684702750163855349e-19
relative error = 7.6904271266094534855828136259563e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.478
y[1] (closed_form) = -0.0018452416206355161454395009454003
y[1] (numeric) = -0.001845241620635516003229148215201
absolute error = 1.4221035273019931302246860852870e-19
relative error = 7.7068689075645777384448346114312e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.477
y[1] (closed_form) = -0.0018426242570561985051726994272611
y[1] (numeric) = -0.0018426242570561983628609031026055
absolute error = 1.4231179632465558782647002337494e-19
relative error = 7.7233215496693201605819791896521e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.476
y[1] (closed_form) = -0.0018400113472994917767993256063188
y[1] (numeric) = -0.0018400113472994916343864019607161
absolute error = 1.4241292364560272859863470739496e-19
relative error = 7.7397850754896843989735258360473e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.475
y[1] (closed_form) = -0.0018374028825259427177678467777648
y[1] (numeric) = -0.0018374028825259425752541110093329
absolute error = 1.4251373576843189771703929348990e-19
relative error = 7.7562595075780672290115737994978e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.474
y[1] (closed_form) = -0.0018347988539161421923512073140745
y[1] (numeric) = -0.0018347988539161420497369735495003
absolute error = 1.4261423376457413025626278749976e-19
relative error = 7.7727448684733146065665977198905e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.473
y[1] (closed_form) = -0.0018321992526706740532243082646004
y[1] (numeric) = -0.0018321992526706739105098895630844
absolute error = 1.4271441870151603448731508104529e-19
relative error = 7.7892411807007775672474846428190e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.472
y[1] (closed_form) = -0.0018296040700100641678528395253554
y[1] (numeric) = -0.0018296040700100640250385478825399
absolute error = 1.4281429164281542570333063020513e-19
relative error = 7.8057484667723679733322965010669e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.471
y[1] (closed_form) = -0.0018270132971747295892423390149999
y[1] (numeric) = -0.001827013297174729446328485366883
absolute error = 1.4291385364811689367295875475772e-19
relative error = 7.8222667491866141088443823674964e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (closed_form) = -0.0018244269254249278705978859954526
y[1] (numeric) = -0.0018244269254249277275847802222853
absolute error = 1.4301310577316730402192968479039e-19
relative error = 7.8387960504287161232468519780217e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.469
y[1] (closed_form) = -0.0018218449460407065234463627382253
y[1] (numeric) = -0.0018218449460407063803343136683941
absolute error = 1.4311204906983123384183054827058e-19
relative error = 7.8553363929706013242268151528424e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.468
y[1] (closed_form) = -0.0018192673503218526187747401828916
y[1] (numeric) = -0.0018192673503218524755640555967853
absolute error = 1.4321068458610634182368791495448e-19
relative error = 7.8718877992709793200391907855436e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.467
y[1] (closed_form) = -0.0018166941295878425307393590842785
y[1] (numeric) = -0.0018166941295878423874303457181398
absolute error = 1.4330901336613867321252324926942e-19
relative error = 7.8884502917753970118782939996067e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.466
y[1] (closed_form) = -0.0018141252751777918225026884221702
y[1] (numeric) = -0.0018141252751777916790956519719323
absolute error = 1.4340703645023789987762463826471e-19
relative error = 7.9050238929162934367438208670116e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.465
y[1] (closed_form) = -0.0018115607784504052737555475736003
y[1] (numeric) = -0.0018115607784504051302507926987078
absolute error = 1.4350475487489249579186241131941e-19
relative error = 7.9216086251130544612662667207159e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.464
y[1] (closed_form) = -0.0018090006307839270494842779451382
y[1] (numeric) = -0.0018090006307839269058821082723534
absolute error = 1.4360216967278484821196771718322e-19
relative error = 7.9382045107720673269552365487617e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.463
y[1] (closed_form) = -0.0018064448235760910095438434528283
y[1] (numeric) = -0.001806444823576090865844561580022
absolute error = 1.4369928187280630485029173248755e-19
relative error = 7.9548115722867750473325342095493e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.462
y[1] (closed_form) = -0.0018038933482440711585993274423883
y[1] (numeric) = -0.0018038933482440710148032349423161
absolute error = 1.4379609250007215732716890569347e-19
relative error = 7.9714298320377306574103512325208e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.461
y[1] (closed_form) = -0.0018013461962244322359997763836137
y[1] (numeric) = -0.0018013461962244320921071738076771
absolute error = 1.4389260257593656119162045335495e-19
relative error = 7.9880593123926513159733157432663e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (closed_form) = -0.0017988033589730804451498179722466
y[1] (numeric) = -0.0017988033589730803011610048542392
absolute error = 1.4398881311800739279675418359870e-19
relative error = 8.0047000357064722611216075541960e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.459
y[1] (closed_form) = -0.0017962648279652143219459531513755
y[1] (numeric) = -0.0017962648279652141778612280112145
absolute error = 1.4408472514016104331484358709809e-19
relative error = 8.0213520243214006195307966687474e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.458
y[1] (closed_form) = -0.0017937305946952757418458880441292
y[1] (numeric) = -0.001793730594695275597665548391572
absolute error = 1.4418033965255715017570297100443e-19
relative error = 8.0380153005669690698825193361114e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.457
y[1] (closed_form) = -0.0017912006506769010651407328913508
y[1] (numeric) = -0.0017912006506769009208650752296975
absolute error = 1.4427565766165326621061617896196e-19
relative error = 8.0546898867600893609185683421889e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.456
y[1] (closed_form) = -0.0017886749874428724200013508333118
y[1] (numeric) = -0.0017886749874428722756306706630923
absolute error = 1.4437068017021946678272410335007e-19
relative error = 8.0713758052051056845694424086090e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.455
y[1] (closed_form) = -0.001786153596545069122871589784492
y[1] (numeric) = -0.0017861535965450689784061816071391
absolute error = 1.4446540817735289518343071735623e-19
relative error = 8.0880730781938479046068733728762e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.454
y[1] (closed_form) = -0.0017836364695544192357825757460675
y[1] (numeric) = -0.0017836364695544190912227330675753
absolute error = 1.4455984267849224657304869767967e-19
relative error = 8.1047817280056846412683292169193e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.453
y[1] (closed_form) = -0.0017811235980608512601636857029778
y[1] (numeric) = -0.0017811235980608511155097010375457
absolute error = 1.4465398466543219074257383710082e-19
relative error = 8.1215017769075762122999759764164e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.452
y[1] (closed_form) = -0.001778614973673245966727252782153
y[1] (numeric) = -0.0017786149736732458219794176558153
absolute error = 1.4474783512633773397215232353344e-19
relative error = 8.1382332471541274308630720772990e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.451
y[1] (closed_form) = -0.0017761105880193883610054856264729
y[1] (numeric) = -0.0017761105880193882161640905807143
absolute error = 1.4484139504575852026048655241484e-19
relative error = 8.1549761609876402607472646869082e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (closed_form) = -0.0017736104327459197841195079859889
y[1] (numeric) = -0.0017736104327459196391848425813458
absolute error = 1.4493466540464307219811340650079e-19
relative error = 8.1717305406381663293327592136039e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.449
y[1] (closed_form) = -0.0017711144995182901483618433644869
y[1] (numeric) = -0.0017711144995182900033341961841339
absolute error = 1.4502764718035297175618384563155e-19
relative error = 8.1884964083235592987418401185181e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.448
y[1] (closed_form) = -0.0017686227800207103071750832061238
y[1] (numeric) = -0.0017686227800207101620547418594468
absolute error = 1.4512034134667698126107416334078e-19
relative error = 8.2052737862495270956187336949840e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.447
y[1] (closed_form) = -0.0017661352659561045591108855840778
y[1] (numeric) = -0.0017661352659561044138981367102327
absolute error = 1.4521274887384510482386735200725e-19
relative error = 8.2220626966096839999753214034605e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.446
y[1] (closed_form) = -0.0017636519490460632853548546812552
y[1] (numeric) = -0.0017636519490460631400499839527126
absolute error = 1.4530487072854259049245763851474e-19
relative error = 8.2388631615856025935387357010777e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.445
y[1] (closed_form) = -0.0017611728210307957204042495523727
y[1] (numeric) = -0.0017611728210307955750075416784488
absolute error = 1.4539670787392387339275237320054e-19
relative error = 8.2556752033468655680353990539214e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
memory used=468.0MB, alloc=44.3MB, time=6.91
x[1] = 2.444
y[1] (closed_form) = -0.0017586978736690828554868637473516
y[1] (numeric) = -0.0017586978736690827099986024777251
absolute error = 1.4548826126962646012417304154573e-19
relative error = 8.2724988440511173938446009456128e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.443
y[1] (closed_form) = -0.0017562270987382304743108053780273
y[1] (numeric) = -0.0017562270987382303287312735062425
absolute error = 1.4557953187178475467339118609429e-19
relative error = 8.2893341058441158494532471764737e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.442
y[1] (closed_form) = -0.0017537604880340223207362901436958
y[1] (numeric) = -0.0017537604880340221750657695106519
absolute error = 1.4567052063304382610897544117835e-19
relative error = 8.3061810108597834121419605625235e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.441
y[1] (closed_form) = -0.0017512980333706733979619377159208
y[1] (numeric) = -0.0017512980333706732522007092133477
absolute error = 1.4576122850257311831837266106481e-19
relative error = 8.3230395812202585103312622717716e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (closed_form) = -0.0017488397265807833988194347391519
y[1] (numeric) = -0.0017488397265807832529677783130718
absolute error = 1.4585165642608010204739922920262e-19
relative error = 8.3399098390359466380151184558509e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.439
y[1] (closed_form) = -0.0017463855595152902667717955508132
y[1] (numeric) = -0.0017463855595152901208299902049893
absolute error = 1.4594180534582386950117803861272e-19
relative error = 8.3567918064055713317076975271860e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.438
y[1] (closed_form) = -0.0017439355240434238872118145822954
y[1] (numeric) = -0.0017439355240434237411801383816667
absolute error = 1.4603167620062867176422229758281e-19
relative error = 8.3736855054162250103277493749038e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.437
y[1] (closed_form) = -0.0017414896120526599086586622903066
y[1] (numeric) = -0.0017414896120526597625373923644092
absolute error = 1.4612126992589739929613920735587e-19
relative error = 8.3905909581434196784435889859319e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.436
y[1] (closed_form) = -0.0017390478154486736934519294058302
y[1] (numeric) = -0.0017390478154486735472413419522052
absolute error = 1.4621058745362500575820464626867e-19
relative error = 8.4075081866511374933002433206765e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.435
y[1] (closed_form) = -0.0017366101261552943975437722949197
y[1] (numeric) = -0.0017366101261552942512441425825078
absolute error = 1.4629962971241187542484424482637e-19
relative error = 8.4244372129918811960489018648538e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.434
y[1] (closed_form) = -0.0017341765361144591789911553210874
y[1] (numeric) = -0.0017341765361144590326027576936103
absolute error = 1.4638839762747713443284661569603e-19
relative error = 8.4413780592067244075973980201196e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.433
y[1] (closed_form) = -0.0017317470372861675347515243023774
y[1] (numeric) = -0.0017317470372861673882746321817055
absolute error = 1.4647689212067190611993097895597e-19
relative error = 8.4583307473253617894990403858144e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.432
y[1] (closed_form) = -0.0017293216216484357653865784865367
y[1] (numeric) = -0.0017293216216484356188214643760442
absolute error = 1.4656511411049251070309396372022e-19
relative error = 8.4752952993661590702957100022186e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.431
y[1] (closed_form) = -0.0017269002811972515672801369441231
y[1] (numeric) = -0.0017269002811972514206270724320295
absolute error = 1.4665306451209360954596894022206e-19
relative error = 8.4922717373362029377297417520941e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (closed_form) = -0.0017244830079465287519774189209293
y[1] (numeric) = -0.001724483007946528605236674683628
absolute error = 1.4674074423730129426324580952052e-19
relative error = 8.5092600832313507972377153319437e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.429
y[1] (closed_form) = -0.0017220697939280620922543765167155
y[1] (numeric) = -0.0017220697939280619454262223220893
absolute error = 1.4682815419462612090901971930323e-19
relative error = 8.5262603590362803971378934874076e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.428
y[1] (closed_form) = -0.0017196606311914822945270320857769
y[1] (numeric) = -0.0017196606311914821476117367965008
absolute error = 1.4691529528927608949476365208848e-19
relative error = 8.5432725867245393209216625386841e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.427
y[1] (closed_form) = -0.0017172555118042110972120820051352
y[1] (numeric) = -0.0017172555118042109502099135819656
absolute error = 1.4700216842316956908145221494809e-19
relative error = 8.5602967882585943470579525820355e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.426
y[1] (closed_form) = -0.0017148544278514164946513329468138
y[1] (numeric) = -0.0017148544278514163475625584518657
absolute error = 1.4708877449494816868920221632591e-19
relative error = 8.5773329855898806767182421226203e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.425
y[1] (closed_form) = -0.0017124573714359680862138365403951
y[1] (numeric) = -0.0017124573714359679390387221404055
absolute error = 1.4717511439998955426663971443416e-19
relative error = 8.5943812006588510298283842524899e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.424
y[1] (closed_form) = -0.0017100643346783925501908833393826
y[1] (numeric) = -0.0017100643346783924029296943089624
absolute error = 1.4726118903042021196105313206602e-19
relative error = 8.6114414553950246098521288160545e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.423
y[1] (closed_form) = -0.0017076753097168292421003073283039
y[1] (numeric) = -0.0017076753097168290947533080531758
absolute error = 1.4734699927512815792924772363588e-19
relative error = 8.6285137717170359377098572842327e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.422
y[1] (closed_form) = -0.0017052902887069859170178378453628
y[1] (numeric) = -0.0017052902887069857695852918255873
absolute error = 1.4743254601977559492787812118711e-19
relative error = 8.6455981715326835552346942684805e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.421
y[1] (closed_form) = -0.0017029092638220945755545167661148
y[1] (numeric) = -0.0017029092638220944280366866193033
absolute error = 1.4751783014681151592090284650330e-19
relative error = 8.6626946767389785985668117276678e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (closed_form) = -0.0017005322272528674331004751153346
y[1] (numeric) = -0.0017005322272528672854976225798503
absolute error = 1.4760285253548425494067752600234e-19
relative error = 8.6798033092221932418853989351377e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.419
y[1] (closed_form) = -0.0016981591712074530119566349651324
y[1] (numeric) = -0.0016981591712074528642690209032784
absolute error = 1.4768761406185398543808205363423e-19
relative error = 8.6969240908579090118764331611218e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.418
y[1] (closed_form) = -0.0016957900879113923559771695555473
y[1] (numeric) = -0.0016957900879113922082050539567421
absolute error = 1.4777211559880516635596108456167e-19
relative error = 8.7140570435110649733330527679526e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.417
y[1] (closed_form) = -0.0016934249696075753673468170573151
y[1] (numeric) = -0.0016934249696075752194904590412562
absolute error = 1.4785635801605893615904697916167e-19
relative error = 8.7312021890360057862840059932565e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.416
y[1] (closed_form) = -0.0016910638085561972651184013032144
y[1] (numeric) = -0.001691063808556197117178059123029
absolute error = 1.4794034218018545505242962319897e-19
relative error = 8.7483595492765296350443250906420e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.415
y[1] (closed_form) = -0.0016887065970347151651371661621926
y[1] (numeric) = -0.0016887065970347150171130972075764
absolute error = 1.4802406895461619561953839640518e-19
relative error = 8.7655291460659360295810566895170e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.414
y[1] (closed_form) = -0.0016863533273378047809797790371663
y[1] (numeric) = -0.0016863533273378046328722398375101
absolute error = 1.4810753919965618210950791883059e-19
relative error = 8.7827110012270734795855652068526e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.413
y[1] (closed_form) = -0.0016840039917773172455371032506782
y[1] (numeric) = -0.001684003991777317097346349478182
absolute error = 1.4819075377249617860271104306511e-19
relative error = 8.7999051365723870416426168753154e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.412
y[1] (closed_form) = -0.0016816585826822360528710788601198
y[1] (numeric) = -0.001681658582682235904597365332895
absolute error = 1.4827371352722482628215985175539e-19
relative error = 8.8171115739039657398851474256452e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.411
y[1] (closed_form) = -0.0016793170923986341199772867335698
y[1] (numeric) = -0.0016793170923986339716208674187291
absolute error = 1.4835641931484073003739813494632e-19
relative error = 8.8343303350135898605223166579744e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (closed_form) = -0.0016769795132896309680860015359303
y[1] (numeric) = -0.0016769795132896308196471295526658
absolute error = 1.4843887198326449462643693197435e-19
relative error = 8.8515614416827781206271580385506e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.409
y[1] (closed_form) = -0.0016746458377353500231357656403996
y[1] (numeric) = -0.0016746458377353498746146932630489
absolute error = 1.4852107237735071062021819942603e-19
relative error = 8.8688049156828347115688410467106e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.408
y[1] (closed_form) = -0.0016723160581328760350547379097437
y[1] (numeric) = -0.0016723160581328758864517165708438
absolute error = 1.4860302133889989035303048169341e-19
relative error = 8.8860607787748962174732782536856e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.407
y[1] (closed_form) = -0.0016699901668962126154862888025911
y[1] (numeric) = -0.0016699901668962124668015690959208
absolute error = 1.4868471970667035410124458571430e-19
relative error = 8.9033290527099784090945280217323e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.406
y[1] (closed_form) = -0.0016676681564562398935965263692842
y[1] (numeric) = -0.0016676681564562397448303580528941
absolute error = 1.4876616831639006671168666853841e-19
relative error = 8.9206097592290229134781672510552e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.405
y[1] (closed_form) = -0.0016653500192606722896026464268054
y[1] (numeric) = -0.0016653500192606721407552784260369
absolute error = 1.4884736800076842489992080752922e-19
relative error = 8.9379029200629437597965367549967e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.404
y[1] (closed_form) = -0.001663035747774016405662204560014
y[1] (numeric) = -0.001663035747774016256733884970506
absolute error = 1.4892831958950799543767301056561e-19
relative error = 8.9552085569326738017344945930545e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.403
y[1] (closed_form) = -0.0016607253344775290337646076038731
y[1] (numeric) = -0.0016607253344775288847555836945569
absolute error = 1.4900902390931620444759370997386e-19
relative error = 8.9725266915492110168030500185684e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.402
y[1] (closed_form) = -0.001658418771869175280267317935429
y[1] (numeric) = -0.001658418771869175131177836151512
absolute error = 1.4908948178391697802252604167717e-19
relative error = 8.9898573456136646829569925855903e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.401
y[1] (closed_form) = -0.001656116052463586806720455261879
y[1] (numeric) = -0.0016561160524635866575507612278166
absolute error = 1.4916969403406233438542261292839e-19
relative error = 9.0072005408173014328913773897740e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (closed_form) = -0.0016538171687920201866246676489018
y[1] (numeric) = -0.0016538171687920200373750061713578
absolute error = 1.4924966147754392780503398087299e-19
relative error = 9.0245562988415911863904783734471e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.399
y[1] (closed_form) = -0.0016515221134023153777683263082347
y[1] (numeric) = -0.0016515221134023152284389413790302
absolute error = 1.4932938492920454448147767310751e-19
relative error = 9.0419246413582529611015770877619e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.398
y[1] (closed_form) = -0.0016492308788588543097912771719058
y[1] (numeric) = -0.0016492308788588541603824119709562
absolute error = 1.4940886520094955061478725353494e-19
relative error = 9.0593055900293005621047142574574e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.397
y[1] (closed_form) = -0.0016469434577425195866235565391276
y[1] (numeric) = -0.0016469434577425194371354534373693
absolute error = 1.4948810310175829286853664550414e-19
relative error = 9.0766991665070881506482959188556e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.396
y[1] (closed_form) = -0.0016446598426506533034486481071431
y[1] (numeric) = -0.0016446598426506531538815486694477
absolute error = 1.4956709943769545143963564293405e-19
relative error = 9.0941053924343556924192147819100e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.395
y[1] (closed_form) = -0.0016423800261970159778420245056994
y[1] (numeric) = -0.001642380026197015828196169493777
absolute error = 1.4964585501192234594439824249070e-19
relative error = 9.1115242894442742857149207851037e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.394
y[1] (closed_form) = -0.0016401040010117455947368780626903
y[1] (numeric) = -0.0016401040010117454450125074379821
absolute error = 1.4972437062470819432999608967766e-19
relative error = 9.1289558791604913698836525505642e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.393
y[1] (closed_form) = -0.0016378317597413167648701029521375
y[1] (numeric) = -0.0016378317597413166150674558786961
absolute error = 1.4980264707344132501942492283627e-19
relative error = 9.1464001831971758143978235887465e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.392
y[1] (closed_form) = -0.0016355632950484999963627441313009
y[1] (numeric) = -0.0016355632950484998464820589786605
absolute error = 1.4988068515264034249713239559061e-19
relative error = 9.1638572231590628889243436303724e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.391
y[1] (closed_form) = -0.0016332985996123210790902775774885
y[1] (numeric) = -0.0016332985996123209291317919235232
absolute error = 1.4995848565396524654148103442090e-19
relative error = 9.1813270206414991147544463609823e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (closed_form) = -0.0016310376661280205814992313031562
y[1] (numeric) = -0.0016310376661280204314631819369277
absolute error = 1.5003604936622850530925031815395e-19
relative error = 9.1988095972304869979543900835290e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.389
y[1] (closed_form) = -0.001628780487307013459527797476183
y[1] (numeric) = -0.0016287804873070133094144204007769
absolute error = 1.5011337707540608247641692471052e-19
relative error = 9.2163049745027296445971974200391e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
memory used=514.7MB, alloc=44.3MB, time=7.61
x[1] = 2.388
y[1] (closed_form) = -0.0016265270558768487772892227167319
y[1] (numeric) = -0.0016265270558768486270987531520835
absolute error = 1.5019046956464841863849205207865e-19
relative error = 9.2338131740256752584344040677031e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.387
y[1] (closed_form) = -0.0016242773645811695391778962987541
y[1] (numeric) = -0.0016242773645811693889105686844627
absolute error = 1.5026732761429136717273935995880e-19
relative error = 9.2513342173575615213655948310924e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.386
y[1] (closed_form) = -0.0016220314061796726330591845687937
y[1] (numeric) = -0.0016220314061796724827152325669266
absolute error = 1.5034395200186708476364647076258e-19
relative error = 9.2688681260474598570623176438865e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.385
y[1] (closed_form) = -0.0016197891734480688842051844230599
y[1] (numeric) = -0.0016197891734480687337848409209451
absolute error = 1.5042034350211487679207708869091e-19
relative error = 9.2864149216353195781017830539338e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.384
y[1] (closed_form) = -0.0016175506591780432196396891714518
y[1] (numeric) = -0.0016175506591780430691431862844598
absolute error = 1.5049650288699199778758961865604e-19
relative error = 9.3039746256520119169645776581455e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.383
y[1] (closed_form) = -0.0016153158561772149425567765799775
y[1] (numeric) = -0.0016153158561772147919843456542931
absolute error = 1.5057243092568440714247166816983e-19
relative error = 9.3215472596193739412494452221851e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.382
y[1] (closed_form) = -0.0016130847572690981164785413363723
y[1] (numeric) = -0.0016130847572690979658304129517548
absolute error = 1.5064812838461748028510797045778e-19
relative error = 9.3391328450502523534570186877723e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.381
y[1] (closed_form) = -0.0016108573552930620588186026431858
y[1] (numeric) = -0.0016108573552930619080950066157191
absolute error = 1.5072359602746667550937205157043e-19
relative error = 9.3567314034485471756932199413659e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (closed_form) = -0.0016086336431042919435191221236229
y[1] (numeric) = -0.0016086336431042917927202875084547
absolute error = 1.5079883461516815665580935388134e-19
relative error = 9.3743429563092553196418820757665e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.379
y[1] (closed_form) = -0.0016064136135737495124301677433502
y[1] (numeric) = -0.0016064136135737493615563228374209
absolute error = 1.5087384490592937183946149894807e-19
relative error = 9.3919675251185140421549909046101e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.378
y[1] (closed_form) = -0.0016041972595881338951013560216391
y[1] (numeric) = -0.0016041972595881337441527283663995
absolute error = 1.5094862765523958841826790026742e-19
relative error = 9.4096051313536442868077886726951e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.377
y[1] (closed_form) = -0.0016019845740498425366567974428435
y[1] (numeric) = -0.0016019845740498423856336138269631
absolute error = 1.5102318361588038439507199710710e-19
relative error = 9.4272557964831939117648332265439e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.376
y[1] (closed_form) = -0.0015997755498769322334254586995032
y[1] (numeric) = -0.0015997755498769320823279451615671
absolute error = 1.5109751353793609644535495060635e-19
relative error = 9.4449195419669808043019603535723e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.375
y[1] (closed_form) = -0.0015975701800030802760001402164257
y[1] (numeric) = -0.0015975701800030801248285220476215
absolute error = 1.5117161816880422476191969909787e-19
relative error = 9.4625963892561358823279555488027e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.374
y[1] (closed_form) = -0.0015953684573775456993993483360042
y[1] (numeric) = -0.0015953684573775455481538500827984
absolute error = 1.5124549825320579490685278763653e-19
relative error = 9.4802863597931459832486041093717e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.373
y[1] (closed_form) = -0.001593170374965130640007418603764
y[1] (numeric) = -0.0015931703749651304886882640705684
absolute error = 1.5131915453319567686020034367751e-19
relative error = 9.4979894750118966405146551733500e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.372
y[1] (closed_form) = -0.001590975925746141798969319794631
y[1] (numeric) = -0.0015909759257461416475767320464582
absolute error = 1.5139258774817286145390794350827e-19
relative error = 9.5157057563377147481941060949088e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.371
y[1] (closed_form) = -0.0015887851027163520117176376795532
y[1] (numeric) = -0.0015887851027163518602518390446625
absolute error = 1.5146579863489069437869187931251e-19
relative error = 9.5334352251874111139080883669720e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (closed_form) = -0.001586597898886961923310303063699
y[1] (numeric) = -0.0015865978988869617717715151362319
absolute error = 1.5153878792746706795063147166562e-19
relative error = 9.5511779029693229004685151495949e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.369
y[1] (closed_form) = -0.0015844143072845617692586903462403
y[1] (numeric) = -0.0015844143072845616176471339888457
absolute error = 1.5161155635739457082339855399104e-19
relative error = 9.5689338110833559565545333218903e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.368
y[1] (closed_form) = -0.0015822343209510932615267707724068
y[1] (numeric) = -0.0015822343209510931098426661188562
absolute error = 1.5168410465355059583117106133271e-19
relative error = 9.5867029709210270367637098319167e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.367
y[1] (closed_form) = -0.001580057932943811579383058685689
y[1] (numeric) = -0.0015800579329438114276266251434816
absolute error = 1.5175643354220740614641276313161e-19
relative error = 9.6044854038655059113727729571566e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.366
y[1] (closed_form) = -0.001577885136335247464788139456343
y[1] (numeric) = -0.0015778851363352473129595957093008
absolute error = 1.5182854374704215993584056607155e-19
relative error = 9.6222811312916573661416238927065e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.365
y[1] (closed_form) = -0.001575715924213169422001614376219
y[1] (numeric) = -0.0015757159242131692701011783870721
absolute error = 1.5190043598914689369704445613898e-19
relative error = 9.6400901745660830924932328398176e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.364
y[1] (closed_form) = -0.0015735502896805460210933406838426
y[1] (numeric) = -0.0015735502896805458691212296968041
absolute error = 1.5197211098703846445737302660658e-19
relative error = 9.6579125550471634684009364587404e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.363
y[1] (closed_form) = -0.0015713882258555083050448840320121
y[1] (numeric) = -0.0015713882258555081530013145753437
absolute error = 1.5204356945666845101584962860560e-19
relative error = 9.6757482940850992303135601618146e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.362
y[1] (closed_form) = -0.0015692297258713123001281361472714
y[1] (numeric) = -0.0015692297258713121480133240358384
absolute error = 1.5211481211143301440804046132135e-19
relative error = 9.6935974130219530364476992403077e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.361
y[1] (closed_form) = -0.0015670747828763016292490821707338
y[1] (numeric) = -0.0015670747828763014770632425085511
absolute error = 1.5218583966218271777295636777811e-19
relative error = 9.7114599331916909217754072266353e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (closed_form) = -0.001564923390033870227945730227095
y[1] (numeric) = -0.0015649233900338700756890774098627
absolute error = 1.5225665281723230580023469793841e-19
relative error = 9.7293358759202236450344581773270e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.359
y[1] (closed_form) = -0.0015627755405224251627302401574211
y[1] (numeric) = -0.0015627755405224250104029878750506
absolute error = 1.5232725228237044393501632181392e-19
relative error = 9.7472252625254479280872717065390e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.358
y[1] (closed_form) = -0.0015606312275353495514663090855353
y[1] (numeric) = -0.0015606312275353493990686703246658
absolute error = 1.5239763876086941751710569997418e-19
relative error = 9.7651281143172875879535155902317e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.357
y[1] (closed_form) = -0.0015584904442809655854738885815853
y[1] (numeric) = -0.0015584904442809654330060756280905
absolute error = 1.5246781295349479103017882586751e-19
relative error = 9.7830444525977345618403305825353e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.356
y[1] (closed_form) = -0.0015563531839824976530543216536329
y[1] (numeric) = -0.0015563531839824975005165460951179
absolute error = 1.5253777555851502763598482247424e-19
relative error = 9.8009742986608898254930557236305e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.355
y[1] (closed_form) = -0.0015542194398780355641299976527919
y[1] (numeric) = -0.0015542194398780354115224703810808
absolute error = 1.5260752727171106916767198385182e-19
relative error = 9.8189176737930042051882698579960e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.354
y[1] (closed_form) = -0.001552089205220497875693629433407
y[1] (numeric) = -0.0015520892052204977230165606470211
absolute error = 1.5267706878638587675555807907602e-19
relative error = 9.8368745992725190836899063085503e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.353
y[1] (closed_form) = -0.0015499624732775953177632597808333
y[1] (numeric) = -0.0015499624732775951650168589874594
absolute error = 1.5274640079337393225785776101812e-19
relative error = 9.8548450963701070004881426514936e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.352
y[1] (closed_form) = -0.0015478392373317943195401032192785
y[1] (numeric) = -0.0015478392373317941667245792382278
absolute error = 1.5281552398105070066807692452669e-19
relative error = 9.8728291863487121466397162940726e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.351
y[1] (closed_form) = -0.00154571949068028063546732485462
y[1] (numeric) = -0.001545719490680280482582885819278
absolute error = 1.5288443903534205366998481721928e-19
relative error = 9.8908268904635907545272690586315e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (closed_form) = -0.0015436032266349230708888499057254
y[1] (numeric) = -0.0015436032266349229179357032659917
absolute error = 1.5295314663973365451027960066124e-19
relative error = 9.9088382299623513828542802068186e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.349
y[1] (closed_form) = -0.0015414904385222373070082860461843
y[1] (numeric) = -0.001541490438522237153986638570904
absolute error = 1.5302164747528030435827186975822e-19
relative error = 9.9268632260849950971911072834042e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.348
y[1] (closed_form) = -0.0015393811196833498248490256300212
y[1] (numeric) = -0.0015393811196833496717590834094059
absolute error = 1.5308994222061525032112334336751e-19
relative error = 9.9449019000639555463866178055829e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.347
y[1] (closed_form) = -0.0015372752634739619279175763233681
y[1] (numeric) = -0.0015372752634739617747595447714086
absolute error = 1.5315803155195945528239451920490e-19
relative error = 9.9629542731241389351588621567176e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.346
y[1] (closed_form) = -0.0015351728632643138632731466226642
y[1] (numeric) = -0.0015351728632643137100472304795333
absolute error = 1.5322591614313082973087552096397e-19
relative error = 9.9810203664829638931772090490988e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.345
y[1] (closed_form) = -0.0015330739124391490407074872220527
y[1] (numeric) = -0.0015330739124391488874138905564993
absolute error = 1.5329359666555342574589863515704e-19
relative error = 9.9991002013504012409473395843989e-15 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 17
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.344
y[1] (closed_form) = -0.001530978404397678349739960211595
y[1] (numeric) = -0.0015309784043976781963788864233284
absolute error = 1.5336107378826659330455911962612e-19
relative error = 1.0017193798929013652809474249070e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.343
y[1] (closed_form) = -0.001528886332553544574133775656945
y[1] (numeric) = -0.0015288863325535444207054274790109
absolute error = 1.5342834817793409907550274516043e-19
relative error = 1.0035301180413995217359189121040e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.342
y[1] (closed_form) = -0.0015267976903347869036402992434387
y[1] (numeric) = -0.0015267976903347867501448787445855
absolute error = 1.5349542049885320786317418650560e-19
relative error = 1.0053422366993210895599163119798e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.341
y[1] (closed_form) = -0.0015247124711838055426792953762835
y[1] (numeric) = -0.0015247124711838053891170039633197
absolute error = 1.5356229141296372686565978967650e-19
relative error = 1.0071557379847235877129187290518e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (closed_form) = -0.0015226306685573264156639274267743
y[1] (numeric) = -0.0015226306685573262620349658469173
absolute error = 1.5362896157985701290850138941592e-19
relative error = 1.0089706240149394834680759860427e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.339
y[1] (closed_form) = -0.0015205522759263659686802907152544
y[1] (numeric) = -0.0015205522759263658149848590584695
absolute error = 1.5369543165678494281610471450732e-19
relative error = 1.0107868969065801077301587128531e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.338
y[1] (closed_form) = -0.0015184772867761960672322043378541
y[1] (numeric) = -0.0015184772867761959134705020391853
absolute error = 1.5376170229866884708161648018711e-19
relative error = 1.0126045587755395602494310134343e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.337
y[1] (closed_form) = -0.0015164056946063089897629350888139
y[1] (numeric) = -0.0015164056946063088359351609307055
absolute error = 1.5382777415810840699539850695458e-19
relative error = 1.0144236117369986047612780483816e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.336
y[1] (closed_form) = -0.0015143374929303825166664705163057
y[1] (numeric) = -0.0015143374929303823627728226309152
absolute error = 1.5389364788539051539148510459081e-19
relative error = 1.0162440579054285540818215677766e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.335
y[1] (closed_form) = -0.0015122726752762451145018985899217
y[1] (numeric) = -0.0015122726752762449605425744614236
absolute error = 1.5395932412849810117067150022226e-19
relative error = 1.0180658993945951451896574776122e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.334
y[1] (closed_form) = -0.0015102112351858412151253885651889
y[1] (numeric) = -0.00151021123518584106110058503207
absolute error = 1.5402480353311891775814625095563e-19
relative error = 1.0198891383175624043237509226933e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
memory used=561.2MB, alloc=44.3MB, time=8.30
x[1] = 2.333
y[1] (closed_form) = -0.0015081531662151965894552014172917
y[1] (numeric) = -0.0015081531662151964353651146746374
absolute error = 1.5409008674265429565284934622153e-19
relative error = 1.0217137767866965021274261178851e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.332
y[1] (closed_form) = -0.0015060984619343838155860886953255
y[1] (numeric) = -0.0015060984619343836614309142970976
absolute error = 1.5415517439822785922501005385745e-19
relative error = 1.0235398169136695988682902566393e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.331
y[1] (closed_form) = -0.0015040471159274878409703658324611
y[1] (numeric) = -0.0015040471159274876867502986937669
absolute error = 1.5422006713869420791759447859198e-19
relative error = 1.0253672608094636797638332695472e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (closed_form) = -0.0015019991217925716383838698489519
y[1] (numeric) = -0.0015019991217925714840991042483043
absolute error = 1.5428476560064756200667226352654e-19
relative error = 1.0271961105843743804423479949154e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.329
y[1] (closed_form) = -0.0014999544731416419553959320164584
y[1] (numeric) = -0.001499954473141641801046661598028
absolute error = 1.5434927041843037307499485610610e-19
relative error = 1.0290263683480148025687184567283e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.328
y[1] (closed_form) = -0.0014979131636006151570634134261721
y[1] (numeric) = -0.0014979131636006150026498312020302
absolute error = 1.5441358222414189935236426169028e-19
relative error = 1.0308580362093193196645274215313e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.327
y[1] (closed_form) = -0.0014958751868092831615697655320922
y[1] (numeric) = -0.0014958751868092830070920638844454
absolute error = 1.5447770164764674607566120203905e-19
relative error = 1.0326911162765473731518382234384e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.326
y[1] (closed_form) = -0.0014938405364212794685309886369121
y[1] (numeric) = -0.0014938405364212793139893593203287
absolute error = 1.5454162931658337102069506477325e-19
relative error = 1.0345256106572872586499100043378e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.325
y[1] (closed_form) = -0.0014918092061040452796912689636089
y[1] (numeric) = -0.0014918092061040451250859031072364
absolute error = 1.5460536585637255535733495521504e-19
relative error = 1.0363615214584599025540100131384e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.324
y[1] (closed_form) = -0.0014897811895387957117319794232607
y[1] (numeric) = -0.0014897811895387955570630675330349
absolute error = 1.5466891189022583997868152611315e-19
relative error = 1.0381988507863226289253914422836e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.323
y[1] (closed_form) = -0.0014877564804204861009186304610533
y[1] (numeric) = -0.0014877564804204859461863624218994
absolute error = 1.5473226803915392745434304586202e-19
relative error = 1.0400376007464729167214104504696e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.322
y[1] (closed_form) = -0.0014857350724577783993112554500341
y[1] (numeric) = -0.0014857350724577782445158205280591
absolute error = 1.5479543492197504975718635428212e-19
relative error = 1.0418777734438521473946615262646e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.321
y[1] (closed_form) = -0.0014837169593730076622646100180387
y[1] (numeric) = -0.0014837169593730075074061968627154
absolute error = 1.5485841315532330191224392928339e-19
relative error = 1.0437193709827493428899161868564e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (closed_form) = -0.0014817021349021486269454564494155
y[1] (numeric) = -0.0014817021349021484720242530957585
absolute error = 1.5492120335365694171577223032434e-19
relative error = 1.0455623954668048940675561781906e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.319
y[1] (closed_form) = -0.0014796905927947823815950929117118
y[1] (numeric) = -0.0014796905927947822266112867824451
absolute error = 1.5498380612926665567177377813969e-19
relative error = 1.0474068489990142795820988460403e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.318
y[1] (closed_form) = -0.0014776823268140631252661727303316
y[1] (numeric) = -0.0014776823268140629702199506380478
absolute error = 1.5504622209228379129261605746716e-19
relative error = 1.0492527336817317752443191808010e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.317
y[1] (closed_form) = -0.0014756773307366850177637412832299
y[1] (numeric) = -0.0014756773307366848626552894325414
absolute error = 1.5510845185068855590970427328075e-19
relative error = 1.0511000516166741538953802007902e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.316
y[1] (closed_form) = -0.0014736755983528491195212973248544
y[1] (numeric) = -0.0014736755983528489643508013145363
absolute error = 1.5517049601031818213949223424916e-19
relative error = 1.0529488049049243758212908282925e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.315
y[1] (closed_form) = -0.0014716771234662304211435616855786
y[1] (numeric) = -0.0014716771234662302659112065107035
absolute error = 1.5523235517487506014944616278990e-19
relative error = 1.0547989956469352697359182282870e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.314
y[1] (closed_form) = -0.0014696818998939449623485093415759
y[1] (numeric) = -0.0014696818998939448070544793956411
absolute error = 1.5529402994593483686791002228319e-19
relative error = 1.0566506259425332043606897204855e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.313
y[1] (closed_form) = -0.0014676899214665170400420908221742
y[1] (numeric) = -0.0014676899214665168846865698992197
absolute error = 1.5535552092295448228115799193476e-19
relative error = 1.0585036978909217506290278397666e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.312
y[1] (closed_form) = -0.0014657011820278465052599358288746
y[1] (numeric) = -0.0014657011820278463498431071255943
absolute error = 1.5541682870328032296025999171604e-19
relative error = 1.0603582135906853345434709070767e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.311
y[1] (closed_form) = -0.0014637156754351761487111957940556
y[1] (numeric) = -0.0014637156754351759932332419118996
absolute error = 1.5547795388215604295972964713640e-19
relative error = 1.0622141751397928807133405811697e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (closed_form) = -0.0014617333955590591746605429194726
y[1] (numeric) = -0.0014617333955590590191216458667419
absolute error = 1.5553889705273065222927076977761e-19
relative error = 1.0640715846356014466007272899470e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.309
y[1] (closed_form) = -0.0014597543362833267628852010165539
y[1] (numeric) = -0.0014597543362833266072855422104875
absolute error = 1.5559965880606642267928829809815e-19
relative error = 1.0659304441748598475024741874276e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.308
y[1] (closed_form) = -0.0014577784915050557184447382336585
y[1] (numeric) = -0.0014577784915050555627844985025117
absolute error = 1.5566023973114679204018267763476e-19
relative error = 1.0677907558537122722957503473157e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.307
y[1] (closed_form) = -0.0014558058551345362090022035113395
y[1] (numeric) = -0.0014558058551345360532815630964552
absolute error = 1.5572064041488423565480284412180e-19
relative error = 1.0696525217677018899747142855375e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.306
y[1] (closed_form) = -0.0014538364210952395894360373666464
y[1] (numeric) = -0.0014538364210952394336551759245183
absolute error = 1.5578086144212810634279229103143e-19
relative error = 1.0715157440117744470056796007876e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.305
y[1] (closed_form) = -0.0014518701833237863134830333829356
y[1] (numeric) = -0.0014518701833237861576421299872631
absolute error = 1.5584090339567244247492513851610e-19
relative error = 1.0733804246802818555281055328681e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.304
y[1] (closed_form) = -0.0014499071357699139321534695838475
y[1] (numeric) = -0.0014499071357699137762527027275838
absolute error = 1.5590076685626374439489465770066e-19
relative error = 1.0752465658669857724286465622303e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.303
y[1] (closed_form) = -0.0014479472723964451786603687103015
y[1] (numeric) = -0.0014479472723964450226999163076928
absolute error = 1.5596045240260871932538532680337e-19
relative error = 1.0771141696650611693154068094507e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.302
y[1] (closed_form) = -0.0014459905871792561396056833087613
y[1] (numeric) = -0.0014459905871792559835857226973793
absolute error = 1.5601996061138199489463118782783e-19
relative error = 1.0789832381670998934194569392212e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.301
y[1] (closed_form) = -0.001444037074107244512167035488803
y[1] (numeric) = -0.0014440370741072443560877434315692
absolute error = 1.5607929205723380141903801881213e-19
relative error = 1.0808537734651142194505835286170e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (closed_form) = -0.0014420867271822979470294722292816
y[1] (numeric) = -0.001442086727182297790891024916484
absolute error = 1.5613844731279762307682462118123e-19
relative error = 1.0827257776505403924341534227733e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.299
y[1] (closed_form) = -0.0014401395404192624768075252162216
y[1] (numeric) = -0.0014401395404192623206100982675237
absolute error = 1.5619742694869781810701932904533e-19
relative error = 1.0845992528142421615558884714694e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.298
y[1] (closed_form) = -0.0014381955078459110297036893929762
y[1] (numeric) = -0.001438195507845910873447457859419
absolute error = 1.5625623153355720816753166182295e-19
relative error = 1.0864742010465143050412592163452e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.297
y[1] (closed_form) = -0.0014362546235029120281502567051883
y[1] (numeric) = -0.0014362546235029118718353950711836
absolute error = 1.5631486163400463698540584793096e-19
relative error = 1.0883506244370861460961195793820e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.296
y[1] (closed_form) = -0.0014343168814437980721822609405825
y[1] (numeric) = -0.0014343168814437979158089431259
absolute error = 1.5637331781468249843175273014566e-19
relative error = 1.0902285250751250599351183877396e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.295
y[1] (closed_form) = -0.0014323822757349347072901061075249
y[1] (numeric) = -0.0014323822757349345508585054692706
absolute error = 1.5643160063825423415324930735147e-19
relative error = 1.0921079050492399719243376568904e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.294
y[1] (closed_form) = -0.0014304508004554892765012644774342
y[1] (numeric) = -0.0014304508004554891200115538120224
absolute error = 1.5648971066541180089149085759336e-19
relative error = 1.0939887664474848468645219420913e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.293
y[1] (closed_form) = -0.0014285224496973998564412412453484
y[1] (numeric) = -0.0014285224496973996998935927904653
absolute error = 1.5654764845488310762087920855240e-19
relative error = 1.0958711113573621694411777564576e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.292
y[1] (closed_form) = -0.0014265972175653442771248107509772
y[1] (numeric) = -0.0014265972175653441205193961875378
absolute error = 1.5660541456343942263513225876919e-19
relative error = 1.0977549418658264158677370411009e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.291
y[1] (closed_form) = -0.0014246750981767092252293343601478
y[1] (numeric) = -0.001424675098176709068566324814245
absolute error = 1.5666300954590275071190429122668e-19
relative error = 1.0996402600592875167478939578522e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (closed_form) = -0.0014227560856615594306027724443357
y[1] (numeric) = -0.0014227560856615592738823384891825
absolute error = 1.5672043395515318048441394543200e-19
relative error = 1.1015270680236143111831398568781e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.289
y[1] (closed_form) = -0.0014208401741626069357598024246049
y[1] (numeric) = -0.0014208401741626067789821140824687
absolute error = 1.5677768834213620214838691014482e-19
relative error = 1.1034153678441379921514371488999e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.288
y[1] (closed_form) = -0.00141892735783518044812025157635
y[1] (numeric) = -0.00141892735783518029128547832048
absolute error = 1.5683477325586999563203345170770e-19
relative error = 1.1053051616056555431828889836232e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.287
y[1] (closed_form) = -0.0014170176308471947747448472332839
y[1] (numeric) = -0.0014170176308471946178531579898312
absolute error = 1.5689168924345268935619678793849e-19
relative error = 1.1071964513924331663581781012708e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.286
y[1] (closed_form) = -0.0014151109873791203393240781936488
y[1] (numeric) = -0.0014151109873791201823756413435793
absolute error = 1.5694843685006958971122704022322e-19
relative error = 1.1090892392882097016554649816832e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.285
y[1] (closed_form) = -0.0014132074216239527811767495291126
y[1] (numeric) = -0.0014132074216239526241717329101122
absolute error = 1.5700501661900038137655703235461e-19
relative error = 1.1109835273762000376713524641993e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.284
y[1] (closed_form) = -0.0014113069277871826360155986376595
y[1] (numeric) = -0.0014113069277871824789541695460332
absolute error = 1.5706142909162629860838053942809e-19
relative error = 1.1128793177390985137414413503648e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.283
y[1] (closed_form) = -0.0014094095000867650982381232763806
y[1] (numeric) = -0.0014094095000867649411204484689433
absolute error = 1.5711767480743726762026070944391e-19
relative error = 1.1147766124590823134859191293433e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.282
y[1] (closed_form) = -0.0014075151327530898645015524687373
y[1] (numeric) = -0.0014075151327530897073277981646983
absolute error = 1.5717375430403902018092626995630e-19
relative error = 1.1166754136178148498055418816397e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.281
y[1] (closed_form) = -0.0014056238200289510583416686139181
y[1] (numeric) = -0.0014056238200289509011120004967579
absolute error = 1.5722966811716017855294577802177e-19
relative error = 1.1185757232964491413532876192943e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (closed_form) = -0.0014037355561695172355959638435772
y[1] (numeric) = -0.0014037355561695170783105470629179
absolute error = 1.5728541678065931189540555976635e-19
relative error = 1.1204775435756311805068778090087e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.279
y[1] (closed_form) = -0.0014018503354423014703923856837489
y[1] (numeric) = -0.0014018503354423013130513848572169
absolute error = 1.5734100082653196425315510213057e-19
relative error = 1.1223808765355032928672825976209e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.278
y[1] (closed_form) = -0.001399968152127131521465696397242
y[1] (numeric) = -0.0013999681521271313640692756123244
absolute error = 1.5739642078491765425462448984923e-19
relative error = 1.1242857242557074883082443159150e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
memory used=607.8MB, alloc=44.3MB, time=8.98
x[1] = 2.277
y[1] (closed_form) = -0.0013980890005161200785642370144647
y[1] (numeric) = -0.0013980890005161199211125598303579
absolute error = 1.5745167718410684663966201164577e-19
relative error = 1.1261920888153888036017731758389e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.276
y[1] (closed_form) = -0.0013962128749136350887106510184959
y[1] (numeric) = -0.001396212874913634931203880467948
absolute error = 1.5750677055054789573828627720411e-19
relative error = 1.1280999722931986366444886967670e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.275
y[1] (closed_form) = -0.0013943397696362701620808839433593
y[1] (numeric) = -0.0013943397696362700045191825345053
absolute error = 1.5756170140885396102069607703826e-19
relative error = 1.1300093767672980723096002974193e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.274
y[1] (closed_form) = -0.0013924696790128150572665337828683
y[1] (numeric) = -0.0013924696790128148996500635010584
absolute error = 1.5761647028180989483833276729466e-19
relative error = 1.1319203043153611999492406703809e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.273
y[1] (closed_form) = -0.0013906025973842262456863831010701
y[1] (numeric) = -0.001390602597384226088015305410691
absolute error = 1.5767107769037910247524415725382e-19
relative error = 1.1338327570145784225717860148085e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.272
y[1] (closed_form) = -0.0013887385191035975549136970941451
y[1] (numeric) = -0.0013887385191035973971881729404347
absolute error = 1.5772552415371037462845570537630e-19
relative error = 1.1357467369416597577187179388194e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.271
y[1] (closed_form) = -0.0013868774385361308906866225875032
y[1] (numeric) = -0.0013868774385361307329068123983585
absolute error = 1.5777981018914469243551427676597e-19
relative error = 1.1376622461728381300655028551916e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (closed_form) = -0.0013850193500591070373697710706107
y[1] (numeric) = -0.0013850193500591068795358347583887
absolute error = 1.5783393631222200516683176757627e-19
relative error = 1.1395792867838726557708859813222e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.269
y[1] (closed_form) = -0.0013831642480618565366358143855807
y[1] (numeric) = -0.0013831642480618563787479113488927
absolute error = 1.5788790303668798069992054690774e-19
relative error = 1.1414978608500519185989186158712e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.268
y[1] (closed_form) = -0.0013813121269457306441366646035442
y[1] (numeric) = -0.0013813121269457304861949537290434
absolute error = 1.5794171087450072889207989095480e-19
relative error = 1.1434179704461972378379591991218e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.267
y[1] (closed_form) = -0.0013794629811240723639345499550081
y[1] (numeric) = -0.0013794629811240722059391896191706
absolute error = 1.5799536033583749796756237444424e-19
relative error = 1.1453396176466659280408107707952e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.266
y[1] (closed_form) = -0.0013776168050221875604640364364963
y[1] (numeric) = -0.0013776168050221874024151845073949
absolute error = 1.5804885192910134403472152772401e-19
relative error = 1.1472628045253545506100798168548e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.265
y[1] (closed_form) = -0.0013757735930773161477967799054063
y[1] (numeric) = -0.0013757735930773159896945937444786
absolute error = 1.5810218616092777384811695123660e-19
relative error = 1.1491875331557021572527641446929e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.264
y[1] (closed_form) = -0.0013739333397386033559815261078181
y[1] (numeric) = -0.0013739333397386031978261625716267
absolute error = 1.5815536353619136093003048964307e-19
relative error = 1.1511138056106935253280003430137e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.263
y[1] (closed_form) = -0.0013720960394670710742326061695208
y[1] (numeric) = -0.0013720960394670709160242216115085
absolute error = 1.5820838455801233516532699271711e-19
relative error = 1.1530416239628623851118245676932e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.262
y[1] (closed_form) = -0.0013702616867355892707409026283351
y[1] (numeric) = -0.001370261686735589112479652900572
absolute error = 1.5826124972776314598307561653803e-19
relative error = 1.1549709902842946390027238469098e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.261
y[1] (closed_form) = -0.0013684302760288474888819861053758
y[1] (numeric) = -0.0013684302760288473305680265603008
absolute error = 1.5831395954507499923783253377924e-19
relative error = 1.1569019066466315726916788168999e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (closed_form) = -0.001366601801843326419596845213703
y[1] (numeric) = -0.0013666018018433262612303307058586
absolute error = 1.5836651450784436790297331338547e-19
relative error = 1.1588343751210730583203227828020e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.259
y[1] (closed_form) = -0.001364776258687269549721352294253
y[1] (numeric) = -0.0013647762586872693913024371820136
absolute error = 1.5841891511223947668795308509494e-19
relative error = 1.1607683977783807496507662462229e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.258
y[1] (closed_form) = -0.0013629536410806548860413250604209
y[1] (numeric) = -0.0013629536410806547275701632077141
absolute error = 1.5847116185270676069086491059699e-19
relative error = 1.1627039766888812692705605513997e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.257
y[1] (closed_form) = -0.0013611339435551667548507592335142
y[1] (numeric) = -0.0013611339435551665963275040115369
absolute error = 1.5852325522197729819716152819265e-19
relative error = 1.1646411139224693878561990741613e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.256
y[1] (closed_form) = -0.0013593171606541676767915197708419
y[1] (numeric) = -0.0013593171606541675182163240597687
absolute error = 1.5857519571107321773490280928326e-19
relative error = 1.1665798115486111955184794113296e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.255
y[1] (closed_form) = -0.0013575032869326703167534883356888
y[1] (numeric) = -0.0013575032869326701581265045263747
absolute error = 1.5862698380931407949639085055440e-19
relative error = 1.1685200716363472652529753217692e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.254
y[1] (closed_form) = -0.0013556923169573095086148722431132
y[1] (numeric) = -0.00135569231695730934993625223879
absolute error = 1.5867862000432323123555661311745e-19
relative error = 1.1704618962542958085187927230285e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.253
y[1] (closed_form) = -0.0013538842453063143546030852465718
y[1] (numeric) = -0.0013538842453063141958729804645377
absolute error = 1.5873010478203413874996639695544e-19
relative error = 1.1724052874706558229687098584333e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.252
y[1] (closed_form) = -0.0013520790665694803990573132169903
y[1] (numeric) = -0.0013520790665694802402758745902936
absolute error = 1.5878143862669669105582319369084e-19
relative error = 1.1743502473532102323537278176508e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.251
y[1] (closed_form) = -0.0013502767753481418763745780171861
y[1] (numeric) = -0.0013502767753481417175419559963026
absolute error = 1.5883262202088348036384708091588e-19
relative error = 1.1762967779693290186249839181596e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (closed_form) = -0.0013484773662551440329218106995885
y[1] (numeric) = -0.0013484773662551438740381552540924
absolute error = 1.5888365544549605696343029512816e-19
relative error = 1.1782448813859723462559070347944e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.249
y[1] (closed_form) = -0.0013466808339148155226971405630536
y[1] (numeric) = -0.0013466808339148153637626011832824
absolute error = 1.5893453937977115912197643578771e-19
relative error = 1.1801945596696936788074207986280e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.248
y[1] (closed_form) = -0.0013448871729629408765242996042421
y[1] (numeric) = -0.0013448871729629407175390253029552
absolute error = 1.5898527430128691810584939831152e-19
relative error = 1.1821458148866428877589276739536e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.247
y[1] (closed_form) = -0.0013430963780467330445647324995023
y[1] (numeric) = -0.0013430963780467328855288718135332
absolute error = 1.5903586068596903842887609716567e-19
relative error = 1.1840986491025693536277342621019e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.246
y[1] (closed_form) = -0.0013413084438248060119326904634156
y[1] (numeric) = -0.0013413084438248058528463914553187
absolute error = 1.5908629900809695343386780988499e-19
relative error = 1.1860530643828250593995057723207e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.245
y[1] (closed_form) = -0.0013395233649671474871992731590314
y[1] (numeric) = -0.0013395233649671473280626834187215
absolute error = 1.5913658974030995631214803718876e-19
relative error = 1.1880090627923676762922654420240e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.244
y[1] (closed_form) = -0.0013377411361550916635720662912041
y[1] (numeric) = -0.0013377411361550915043853329375908
absolute error = 1.5918673335361330666560012177298e-19
relative error = 1.1899666463957636418763827804545e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.243
y[1] (closed_form) = -0.0013359617520812920525377036071951
y[1] (numeric) = -0.0013359617520812918933009732898108
absolute error = 1.5923673031738431271527548731337e-19
relative error = 1.1919258172571912305729228502612e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.242
y[1] (closed_form) = -0.001334185207449694389755360766608
y[1] (numeric) = -0.0013341852074496942304687796672296
absolute error = 1.5928658109937838926013323823537e-19
relative error = 1.1938865774404436165526573897478e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.241
y[1] (closed_form) = -0.0013324114969755096129898649345525
y[1] (numeric) = -0.0013324114969755094536535787688174
absolute error = 1.5933628616573509148901398848795e-19
relative error = 1.1958489290089319290579674136808e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (closed_form) = -0.0013306406153851869118737780064251
y[1] (numeric) = -0.0013306406153851867524879320254409
absolute error = 1.5938584598098412474848515254690e-19
relative error = 1.1978128740256883001697960116311e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.239
y[1] (closed_form) = -0.0013288725574163868492884830985238
y[1] (numeric) = -0.0013288725574163866898532220904724
absolute error = 1.5943526100805133036873152287994e-19
relative error = 1.1997784145533689050417393889505e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.238
y[1] (closed_form) = -0.0013271073178179545541549733445697
y[1] (numeric) = -0.0013271073178179543946704416363051
absolute error = 1.5948453170826464764920376390118e-19
relative error = 1.2017455526542569946232937657420e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.237
y[1] (closed_form) = -0.0013253448913498929854257091326939
y[1] (numeric) = -0.0013253448913498928258920505913338
absolute error = 1.5953365854136005210527846185538e-19
relative error = 1.2037142903902659208942055626599e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.236
y[1] (closed_form) = -0.0013235852727833362670695747091687
y[1] (numeric) = -0.0013235852727833361074869327436812
absolute error = 1.5958264196548747007672657199251e-19
relative error = 1.2056846298229421546318023581708e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.235
y[1] (closed_form) = -0.001321828456900523093842627572675
y[1] (numeric) = -0.0013218284569005229342111451354584
absolute error = 1.5963148243721666979833248776753e-19
relative error = 1.2076565730134682957331123991182e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.234
y[1] (closed_form) = -0.0013200744384947702076379942947182
y[1] (numeric) = -0.0013200744384947700479578138831751
absolute error = 1.5968018041154312903255351063672e-19
relative error = 1.2096301220226660761135109841638e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.233
y[1] (closed_form) = -0.0013183232123704459442089243364361
y[1] (numeric) = -0.0013183232123704457844801879945422
absolute error = 1.5972873634189387936365921238382e-19
relative error = 1.2116052789109993552035628170351e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.232
y[1] (closed_form) = -0.0013165747733429438500596690979316
y[1] (numeric) = -0.0013165747733429436902825184177982
absolute error = 1.5977715068013332725234204392065e-19
relative error = 1.2135820457385771080656604425987e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.231
y[1] (closed_form) = -0.0013148291162386563692995068418337
y[1] (numeric) = -0.0013148291162386562094740829652646
absolute error = 1.5982542387656905194934454434769e-19
relative error = 1.2155604245651564061519901327224e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (closed_form) = -0.0013130862358949486002558852864376
y[1] (numeric) = -0.00131308623589494844038232890648
absolute error = 1.5987355637995758036620463096830e-19
relative error = 1.2175404174501453907252880797950e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.229
y[1] (closed_form) = -0.0013113461271601321216433025738476
y[1] (numeric) = -0.0013113461271601319617217539363374
absolute error = 1.5992154863751013900077869422030e-19
relative error = 1.2195220264526062389637814827657e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.228
y[1] (closed_form) = -0.0013096087848934388880851939933724
y[1] (numeric) = -0.001309608784893438728115792898474
absolute error = 1.5996940109489838301476257047293e-19
relative error = 1.2215052536312581227716410727717e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.227
y[1] (closed_form) = -0.0013078742039649951947867362882886
y[1] (numeric) = -0.0013078742039649950347696220920285
absolute error = 1.6001711419626010255999290974260e-19
relative error = 1.2234901010444801603162038219656e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.226
y[1] (closed_form) = -0.0013061423792557957111571236032534
y[1] (numeric) = -0.0013061423792557955510924352190484
absolute error = 1.6006468838420490644987598407215e-19
relative error = 1.2254765707503143603131570091662e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.225
y[1] (closed_form) = -0.0013044133056576775831805091483313
y[1] (numeric) = -0.0013044133056576774230683850485114
absolute error = 1.6011212409981988327185758511476e-19
relative error = 1.2274646648064685590808074785735e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.224
y[1] (closed_form) = -0.0013026869780732946043354444720028
y[1] (numeric) = -0.0013026869780732944441760226893275
absolute error = 1.6015942178267524003641632594068e-19
relative error = 1.2294543852703193503844928221493e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.223
y[1] (closed_form) = -0.0013009633914160914548632838577879
y[1] (numeric) = -0.001300963391416091294656701986958
absolute error = 1.6020658187082991845763338187311e-19
relative error = 1.2314457341989150080921243415034e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.222
y[1] (closed_form) = -0.0012992425406102780091866547953935
y[1] (numeric) = -0.0012992425406102778489330499945563
absolute error = 1.6025360480083718895996446794286e-19
relative error = 1.2334387136489784016617850003987e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
memory used=654.5MB, alloc=44.3MB, time=9.66
x[1] = 2.221
y[1] (closed_form) = -0.0012975244205908037112797267356481
y[1] (numeric) = -0.0012975244205908035509792357278979
absolute error = 1.6030049100775022250541464607178e-19
relative error = 1.2354333256769099044822391634329e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (closed_form) = -0.0012958090263033320177926394270087
y[1] (numeric) = -0.0012958090263033318574453985018811
absolute error = 1.6034724092512764033489337314337e-19
relative error = 1.2374295723387902950871447292285e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.219
y[1] (closed_form) = -0.0012940963527042149087330790581218
y[1] (numeric) = -0.0012940963527042147483392240730828
absolute error = 1.6039385498503904171710603154634e-19
relative error = 1.2394274556903836512636923067195e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.218
y[1] (closed_form) = -0.0012923863947604674655086152038045
y[1] (numeric) = -0.001292386394760467305068281585734
absolute error = 1.6044033361807050979791901648194e-19
relative error = 1.2414269777871402370763303500198e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.217
y[1] (closed_form) = -0.0012906791474497425161340341988443
y[1] (numeric) = -0.0012906791474497423556473569455143
absolute error = 1.6048667725333009564271827926560e-19
relative error = 1.2434281406841993828261696600580e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.216
y[1] (closed_form) = -0.0012889746057603053474085250531329
y[1] (numeric) = -0.0012889746057603051868756387346796
absolute error = 1.6053288631845328056386603303402e-19
relative error = 1.2454309464363923579665953788298e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.215
y[1] (closed_form) = -0.001287272764691008483868192380753
y[1] (numeric) = -0.0012872727646910083232892311411446
absolute error = 1.6057896123960841682494710675225e-19
relative error = 1.2474353970982452369955495439209e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.214
y[1] (closed_form) = -0.0012855736192512665333199870526034
y[1] (numeric) = -0.0012855736192512663726950846111012
absolute error = 1.6062490244150214681308517531309e-19
relative error = 1.2494414947239817583448824360632e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.213
y[1] (closed_form) = -0.0012838771644610310987637594048127
y[1] (numeric) = -0.0012838771644610309380930490574279
absolute error = 1.6067071034738480077019978800002e-19
relative error = 1.2514492413675261762871063400756e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.212
y[1] (closed_form) = -0.0012821833953507657565097518513687
y[1] (numeric) = -0.0012821833953507655957933664723129
absolute error = 1.6071638537905577317366775486070e-19
relative error = 1.2534586390825061058798209487942e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.211
y[1] (closed_form) = -0.00128049230696142110029945766686
y[1] (numeric) = -0.0012804923069614209395375297099912
absolute error = 1.6076192795686887785644702088008e-19
relative error = 1.2554696899222553609680154696848e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (closed_form) = -0.0012788038943444098512383805317325
y[1] (numeric) = -0.0012788038943444096904310420319948
absolute error = 1.6080733849973768195631765156999e-19
relative error = 1.2574823959398167852643885439493e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.209
y[1] (closed_form) = -0.0012771181525615820333498351757245
y[1] (numeric) = -0.0012771181525615818724972177505837
absolute error = 1.6085261742514081878349296107716e-19
relative error = 1.2594967591879450765277633572683e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.208
y[1] (closed_form) = -0.0012754350766852002145595331228571
y[1] (numeric) = -0.0012754350766852000536617679737298
absolute error = 1.6089776514912727969545412557456e-19
relative error = 1.2615127817191096038596118090547e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.207
y[1] (closed_form) = -0.0012737546617979148129212991411569
y[1] (numeric) = -0.0012737546617979146519785170548352
absolute error = 1.6094278208632168506746383101553e-19
relative error = 1.2635304655854972181386383124279e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.206
y[1] (closed_form) = -0.001272076902992739467894863539831
y[1] (numeric) = -0.0012720769029927393069071948899014
absolute error = 1.6098766864992953444681859581666e-19
relative error = 1.2655498128390150556133107192466e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.205
y[1] (closed_form) = -0.0012704017953730264764872729434676
y[1] (numeric) = -0.0012704017953730263154548476917252
absolute error = 1.6103242525174243597850537626794e-19
relative error = 1.2675708255312933346721630026617e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.204
y[1] (closed_form) = -0.0012687293340524422940700576145894
y[1] (numeric) = -0.0012687293340524421329930053124461
absolute error = 1.6107705230214331518953589606751e-19
relative error = 1.2695935057136881458116316829793e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.203
y[1] (closed_form) = -0.0012670595141549430996848868000589
y[1] (numeric) = -0.0012670595141549429385633365899473
absolute error = 1.6112155021011160321884183201563e-19
relative error = 1.2716178554372842348211255503513e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.202
y[1] (closed_form) = -0.0012653923308147504256510349509508
y[1] (numeric) = -0.0012653923308147502644851155677224
absolute error = 1.6116591938322840457922552629800e-19
relative error = 1.2736438767528977792049660191639e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.201
y[1] (closed_form) = -0.0012637277791763268512885710170206
y[1] (numeric) = -0.001263727779176326690078410789339
absolute error = 1.6121016022768164453747427271114e-19
relative error = 1.2756715717110791578607734431713e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (closed_form) = -0.0012620658543943517605717703532856
y[1] (numeric) = -0.0012620658543943515993174972050144
absolute error = 1.6125427314827119619836143045032e-19
relative error = 1.2777009423621157140338129266451e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.199
y[1] (closed_form) = -0.0012604065516336971635278341048846
y[1] (numeric) = -0.0012604065516336970022295755564706
absolute error = 1.6129825854841398737787464555879e-19
relative error = 1.2797319907560345115667515843029e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.198
y[1] (closed_form) = -0.0012587498660694035811965842647117
y[1] (numeric) = -0.0012587498660694034198544674345626
absolute error = 1.6134211683014908735063029773952e-19
relative error = 1.2817647189426050844642178307552e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.197
y[1] (closed_form) = -0.0012570957928866559939673839336629
y[1] (numeric) = -0.0012570957928866558325815355395201
absolute error = 1.6138584839414277355605392991974e-19
relative error = 1.2837991289713421797914921179009e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.196
y[1] (closed_form) = -0.0012554443272807598531101116630448
y[1] (numeric) = -0.0012554443272807596916806580233512
absolute error = 1.6142945363969357834752885074184e-19
relative error = 1.2858352228915084939265975853354e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.195
y[1] (closed_form) = -0.0012537954644571171553175961300575
y[1] (numeric) = -0.0012537954644571169938446631653202
absolute error = 1.6147293296473731586833931708936e-19
relative error = 1.2878730027521174021849983436383e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.194
y[1] (closed_form) = -0.0012521491996312025800774927975612
y[1] (numeric) = -0.0012521491996312024185612060317091
absolute error = 1.6151628676585208913786069594578e-19
relative error = 1.2899124706019356818360525726238e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.193
y[1] (closed_form) = -0.001250505528028539689692157645813
y[1] (numeric) = -0.0012505055280285395281326422075497
absolute error = 1.6155951543826327743107676347743e-19
relative error = 1.2919536284894862285303072854928e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.192
y[1] (closed_form) = -0.0012488644448846771917656445437247
y[1] (numeric) = -0.0012488644448846770301630251678762
absolute error = 1.6160261937584850403413381542533e-19
relative error = 1.2939964784630507661566614845712e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.191
y[1] (closed_form) = -0.0012472259454451652639775223576457
y[1] (numeric) = -0.0012472259454451651023319233865031
absolute error = 1.6164559897114258445827252792793e-19
relative error = 1.2960410225706725501483645141914e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (closed_form) = -0.0012455900249655319409637754838593
y[1] (numeric) = -0.0012455900249655317792753208685168
absolute error = 1.6168845461534245519411151306439e-19
relative error = 1.2980872628601590642567567005249e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.189
y[1] (closed_form) = -0.0012439566787112595631256171440473
y[1] (numeric) = -0.0012439566787112594013944304457352
absolute error = 1.6173118669831208308789125004160e-19
relative error = 1.3001352013790847108115998560455e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.188
y[1] (closed_form) = -0.0012423259019577612871876085080092
y[1] (numeric) = -0.0012423259019577611254138128994219
absolute error = 1.6177379560858735542092353242591e-19
relative error = 1.3021848401747934944867859170576e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.187
y[1] (closed_form) = -0.0012406976899903576583270385120112
y[1] (numeric) = -0.0012406976899903574965107567786302
absolute error = 1.6181628173338095077312974556833e-19
relative error = 1.3042361812944016995901528756086e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.186
y[1] (closed_form) = -0.0012390720381042532436970791313232
y[1] (numeric) = -0.001239072038104253081838433672736
absolute error = 1.6185864545858719075119116785815e-19
relative error = 1.3062892267848005608960782613802e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.185
y[1] (closed_form) = -0.0012374489416045133271667888488056
y[1] (numeric) = -0.0012374489416045131652659016800188
absolute error = 1.6190088716878687266147606617916e-19
relative error = 1.3083439786926589280394617240844e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.184
y[1] (closed_form) = -0.0012358283958060406651015931448161
y[1] (numeric) = -0.001235828395806040503158585897564
absolute error = 1.6194300724725208320755162149446e-19
relative error = 1.3104004390644259234896497617364e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.183
y[1] (closed_form) = -0.0012342103960335523030084250241959
y[1] (numeric) = -0.0012342103960335521410234189482449
absolute error = 1.6198500607595099329173366645099e-19
relative error = 1.3124586099463335941227973342042e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.182
y[1] (closed_form) = -0.0012325949376215564528702609005917
y[1] (numeric) = -0.0012325949376215562908433768650391
absolute error = 1.6202688403555263399977383492247e-19
relative error = 1.3145184933843995564111029939224e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.181
y[1] (closed_form) = -0.0012309820159143294309953375837906
y[1] (numeric) = -0.0012309820159143292689266960783589
absolute error = 1.6206864150543165384743200518813e-19
relative error = 1.3165800914244296352472962558640e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (closed_form) = -0.00122937162626589265620688466897
y[1] (numeric) = -0.001229371626265892494096605805297
absolute error = 1.6211027886367305736733185570925e-19
relative error = 1.3186434061120204964226982160798e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.179
y[1] (closed_form) = -0.0012277637640399897081997533146541
y[1] (numeric) = -0.0012277637640399895460479568275771
absolute error = 1.6215179648707692511414893699288e-19
relative error = 1.3207084394925622727771189116055e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.178
y[1] (closed_form) = -0.0012261584246100634458908672255422
y[1] (numeric) = -0.0012261584246100632836976724743791
absolute error = 1.6219319475116311516583388664235e-19
relative error = 1.3227751936112411840387975935926e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.177
y[1] (closed_form) = -0.0012245556033592331855909646340497
y[1] (numeric) = -0.0012245556033592330233564906038738
absolute error = 1.6223447403017594619822826925047e-19
relative error = 1.3248436705130421503725349594186e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.176
y[1] (closed_form) = -0.0012229552956802719388256412071371
y[1] (numeric) = -0.0012229552956802717765500065100482
absolute error = 1.6227563469708886221008700019827e-19
relative error = 1.3269138722427513996541094575680e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.175
y[1] (closed_form) = -0.001221357496975583709634243099562
y[1] (numeric) = -0.0012213574969755835473175659759529
absolute error = 1.6231667712360907897517940462828e-19
relative error = 1.3289858008449590684890130405286e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.174
y[1] (closed_form) = -0.0012197622026571808511756968377864
y[1] (numeric) = -0.0012197622026571806888180951576042
absolute error = 1.6235760168018221229780066185600e-19
relative error = 1.3310594583640617969934851951208e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.173
y[1] (closed_form) = -0.0012181694081466614814708983571043
y[1] (numeric) = -0.0012181694081466613190724896211074
absolute error = 1.6239840873599688814768668329730e-19
relative error = 1.3331348468442653173557677258591e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.172
y[1] (closed_form) = -0.0012165791088751869581118173347979
y[1] (numeric) = -0.0012165791088751867956727186758086
absolute error = 1.6243909865898933474998836069758e-19
relative error = 1.3352119683295870361954466044331e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.171
y[1] (closed_form) = -0.0012149913002834594117680049709222
y[1] (numeric) = -0.0012149913002834592492883331550742
absolute error = 1.6247967181584795670562559316311e-19
relative error = 1.3372908248638586107386912264966e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (closed_form) = -0.0012134059778216993383217235722777
y[1] (numeric) = -0.0012134059778216991758015950002598
absolute error = 1.6252012857201789121700754837364e-19
relative error = 1.3393714184907285188271456349642e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.169
y[1] (closed_form) = -0.0012118231369496232494634447008577
y[1] (numeric) = -0.0012118231369496230869029754091521
absolute error = 1.6256046929170554649377322759312e-19
relative error = 1.3414537512536646227781706762430e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.168
y[1] (closed_form) = -0.001210242773136421381579989262102
y[1] (numeric) = -0.0012102427731364212189792949242189
absolute error = 1.6260069433788312241287557792977e-19
relative error = 1.3435378251959567271140806515909e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.167
y[1] (closed_form) = -0.0012086648818607354627681077372105
y[1] (numeric) = -0.0012086648818607353001273036649174
absolute error = 1.6264080407229311350700312100631e-19
relative error = 1.3456236423607191301779628093839e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.166
y[1] (closed_form) = -0.0012070894586106365378068218140707
y[1] (numeric) = -0.001207089458610636375126022958618
absolute error = 1.6268079885545279435500533710221e-19
relative error = 1.3477112047908931696536129948332e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
memory used=701.2MB, alloc=44.3MB, time=10.33
x[1] = 2.165
y[1] (closed_form) = -0.0012055164988836028509223699495279
y[1] (numeric) = -0.0012055164988836026882016909028692
absolute error = 1.6272067904665868744766185028161e-19
relative error = 1.3498005145292497620070659309100e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.164
y[1] (closed_form) = -0.001203945998186497786180118908238
y[1] (numeric) = -0.001203945998186497623419673904247
absolute error = 1.6276044500399101360181079542013e-19
relative error = 1.3518915736183919358671439472533e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.163
y[1] (closed_form) = -0.0012023779520355478653383210766318
y[1] (numeric) = -0.0012023779520355477025382239923136
absolute error = 1.6280009708431812499552860482848e-19
relative error = 1.3539843841007573593623935019601e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.162
y[1] (closed_form) = -0.0012008123559563208029991133509957
y[1] (numeric) = -0.0012008123559563206401594777076948
absolute error = 1.6283963564330092089673182281724e-19
relative error = 1.3560789480186208614317245537205e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.161
y[1] (closed_form) = -0.0011992492054837036188926676527321
y[1] (numeric) = -0.0011992492054837034560136066173349
absolute error = 1.6287906103539724615725143357173e-19
relative error = 1.3581752674140969471260137380940e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (closed_form) = -0.0011976884961618808071309156378601
y[1] (numeric) = -0.0011976884961618806442125420239938
absolute error = 1.6291837361386627254411156366207e-19
relative error = 1.3602733443291423069178783811430e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.159
y[1] (closed_form) = -0.0011961302235443125622677809480984
y[1] (numeric) = -0.0011961302235443123993102072173255
absolute error = 1.6295757373077286297942728799619e-19
relative error = 1.3623731808055583200367746454997e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.158
y[1] (closed_form) = -0.00119457438319371306200336140375
y[1] (numeric) = -0.001194574383193712899006699666758
absolute error = 1.6299666173699191876002061966370e-19
relative error = 1.3644747788849935518465195475568e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.157
y[1] (closed_form) = -0.0011930209706820288063700108703672
y[1] (numeric) = -0.0011930209706820286433343728881545
absolute error = 1.6303563798221270982753959258688e-19
relative error = 1.3665781406089462452822832091956e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.156
y[1] (closed_form) = -0.0011914699815904170132387761480921
y[1] (numeric) = -0.0011914699815904168501642733331489
absolute error = 1.6307450281494318815955264389971e-19
relative error = 1.3686832680187668063640445126284e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.155
y[1] (closed_form) = -0.0011899214115092240699851481408665
y[1] (numeric) = -0.0011899214115092239068718915583523
absolute error = 1.6311325658251428435177926326334e-19
relative error = 1.3707901631556602838034503118815e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.154
y[1] (closed_form) = -0.0011883752560379640411535887686229
y[1] (numeric) = -0.0011883752560379638780016891375387
absolute error = 1.6315189963108418746130809168072e-19
relative error = 1.3728988280606888427209655185283e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.153
y[1] (closed_form) = -0.0011868315107852972319607955952724
y[1] (numeric) = -0.0011868315107852970687703632896298
absolute error = 1.6319043230564260818034531561490e-19
relative error = 1.3750092647747742324901487218434e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.152
y[1] (closed_form) = -0.0011852901713690088074781649649905
y[1] (numeric) = -0.0011852901713690086442493100149754
absolute error = 1.6322885495001502540972930620487e-19
relative error = 1.3771214753387002487258355239434e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.151
y[1] (closed_form) = -0.0011837512334159874673344115750883
y[1] (numeric) = -0.0011837512334159873040672436682214
absolute error = 1.6326716790686691630114199100380e-19
relative error = 1.3792354617931151894329594680562e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (closed_form) = -0.0011822146925622041757797978717813
y[1] (numeric) = -0.0011822146925622040124744263540734
absolute error = 1.6330537151770796983664340987143e-19
relative error = 1.3813512261785343053326883121826e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.149
y[1] (closed_form) = -0.0011806805444526909469539204415161
y[1] (numeric) = -0.0011806805444526907836104543186198
absolute error = 1.6334346612289628401385329040293e-19
relative error = 1.3834687705353422443825014504289e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.148
y[1] (closed_form) = -0.0011791487847415196851994926912693
y[1] (numeric) = -0.0011791487847415195218180406296268
absolute error = 1.6338145206164254670480227457777e-19
relative error = 1.3855880969037954905067825095689e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.147
y[1] (closed_form) = -0.0011776194090917810802650535724309
y[1] (numeric) = -0.0011776194090917809168457239004167
absolute error = 1.6341932967201420025617563020526e-19
relative error = 1.3877092073240247965544495482933e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.146
y[1] (closed_form) = -0.001176092413175563557240020910559
y[1] (numeric) = -0.0011760924131755633937829216196194
absolute error = 1.6345709929093958989837388130663e-19
relative error = 1.3898321038360376115000938604973e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.145
y[1] (closed_form) = -0.0011745677926739322810659950634458
y[1] (numeric) = -0.0011745677926739321175712338092337
absolute error = 1.6349476125421209603051778392123e-19
relative error = 1.3919567884797205019050471312016e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.144
y[1] (closed_form) = -0.0011730455432769082154687041485416
y[1] (numeric) = -0.0011730455432769080519363882520473
absolute error = 1.6353231589649425044822945110552e-19
relative error = 1.3940832632948415676547456136828e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.143
y[1] (closed_form) = -0.001171525660683447236155465963798
y[1] (numeric) = -0.0011715256606834470725857024124762
absolute error = 1.6356976355132183658072718629386e-19
relative error = 1.3962115303210528519887090884631e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.142
y[1] (closed_form) = -0.0011700081406014192981235239793551
y[1] (numeric) = -0.0011700081406014191345164194282471
absolute error = 1.6360710455110797380347871092943e-19
relative error = 1.3983415915978927458394016283685e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.141
y[1] (closed_form) = -0.0011684929787475876569250954071059
y[1] (numeric) = -0.0011684929787475874932807561799588
absolute error = 1.6364433922714718589236596360792e-19
relative error = 1.4004734491647883864961906282729e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (closed_form) = -0.0011669801708475881437354483669233
y[1] (numeric) = -0.0011669801708475879800539804573039
absolute error = 1.6368146790961945368502449719603e-19
relative error = 1.4026071050610580506105701627954e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.139
y[1] (closed_form) = -0.0011654697126359084940708025680838
y[1] (numeric) = -0.0011654697126359083303523116404896
absolute error = 1.6371849092759425201473170081665e-19
relative error = 1.4047425613259135415587645094814e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.138
y[1] (closed_form) = -0.0011639615998558677300033237180177
y[1] (numeric) = -0.0011639615998558675662479151089831
absolute error = 1.6375540860903457098193061859202e-19
relative error = 1.4068798199984625711777776182717e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.137
y[1] (closed_form) = -0.001162455828259595595720956063765
y[1] (numeric) = -0.0011624558282595954319287347829641
absolute error = 1.6379222128080092162819002000024e-19
relative error = 1.4090188831177111358909044197243e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.136
y[1] (closed_form) = -0.0011609523936080120462803100702283
y[1] (numeric) = -0.001160952393608011882451380801573
absolute error = 1.6382892926865532607711659105579e-19
relative error = 1.4111597527225658872386701439006e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.135
y[1] (closed_form) = -0.0011594512916708067894012932492445
y[1] (numeric) = -0.0011594512916708066255357603519792
absolute error = 1.6386553289726529220645165473508e-19
relative error = 1.4133024308518364968311142684447e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.134
y[1] (closed_form) = -0.0011579525182264188801526415804182
y[1] (numeric) = -0.0011579525182264187162506090902105
absolute error = 1.6390203249020777291530268662784e-19
relative error = 1.4154469195442380157372863275767e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.133
y[1] (closed_form) = -0.0011564560690620163683779768142744
y[1] (numeric) = -0.0011564560690620162044395484443013
absolute error = 1.6393842836997311005017906123518e-19
relative error = 1.4175932208383932283277715928746e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.132
y[1] (closed_form) = -0.0011549619399734759987124812263255
y[1] (numeric) = -0.0011549619399734758347377603683566
absolute error = 1.6397472085796896305322193921708e-19
relative error = 1.4197413367728350005860155812433e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.131
y[1] (closed_form) = -0.0011534701267653629630407461027783
y[1] (numeric) = -0.001153470126765362799029835828254
absolute error = 1.6401091027452422239573997981346e-19
relative error = 1.4218912693860086229041674547566e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (closed_form) = -0.0011519806252509107052468133904904
y[1] (numeric) = -0.0011519806252509105411998164515975
absolute error = 1.6404699693889290785988562925164e-19
relative error = 1.4240430207162741473791136505244e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.129
y[1] (closed_form) = -0.0011504934312520007781078915410795
y[1] (numeric) = -0.0011504934312520006140249103718214
absolute error = 1.6408298116925805173103108887214e-19
relative error = 1.4261965928019087196243245157750e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.128
y[1] (closed_form) = -0.0011490085405991427521836866273846
y[1] (numeric) = -0.001149008540599142588064823344649
absolute error = 1.6411886328273556696312869964856e-19
relative error = 1.4283519876811089051130883233724e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.127
y[1] (closed_form) = -0.0011475259491314541765537483153991
y[1] (numeric) = -0.001147525949131454012399104720021
absolute error = 1.6415464359537810037906738647345e-19
relative error = 1.4305092073919930100686588054159e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.126
y[1] (closed_form) = -0.0011460456526966405912556872418959
y[1] (numeric) = -0.001146045652696640427065364819717
absolute error = 1.6419032242217887096776497978989e-19
relative error = 1.4326682539726033969167942668065e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.125
y[1] (closed_form) = -0.0011445676471509755912775757828096
y[1] (numeric) = -0.0011445676471509754270516757057341
absolute error = 1.6422590007707549333946566766001e-19
relative error = 1.4348291294609087943161184261335e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.124
y[1] (closed_form) = -0.0011430919283592809419582981055544
y[1] (numeric) = -0.0011430919283592807776969212326006
absolute error = 1.6426137687295378640044252200126e-19
relative error = 1.4369918358948066017816853773429e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.123
y[1] (closed_form) = -0.0011416184921949067456500677853553
y[1] (numeric) = -0.0011416184921949065813533146637038
absolute error = 1.6429675312165156730803698234322e-19
relative error = 1.4391563753121251889170834718300e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.122
y[1] (closed_form) = -0.0011401473345397116594977821368392
y[1] (numeric) = -0.0011401473345397114951657530028768
absolute error = 1.6433202913396243076670036295101e-19
relative error = 1.4413227497506261892703654862595e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.121
y[1] (closed_form) = -0.001138678451284043164190331773038
y[1] (numeric) = -0.0011386784512840429998231265533985
absolute error = 1.6436720521963951372543686844380e-19
relative error = 1.4434909612480067888290451659973e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (closed_form) = -0.0011372118383267178835394317600521
y[1] (numeric) = -0.0011372118383267177191371500726529
absolute error = 1.6440228168739924553678325305850e-19
relative error = 1.4456610118419020091693531169513e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.119
y[1] (closed_form) = -0.0011357474915750019547419870923237
y[1] (numeric) = -0.0011357474915750017903047282473986
absolute error = 1.6443725884492508363719713345186e-19
relative error = 1.4478329035698869852748980593047e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.118
y[1] (closed_form) = -0.0011342854069445914491824500761907
y[1] (numeric) = -0.0011342854069445912847103130773195
absolute error = 1.6447213699887123480846405840940e-19
relative error = 1.4500066384694792380398326545098e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.117
y[1] (closed_form) = -0.0011328255803595928436320705835124
y[1] (numeric) = -0.0011328255803595926791251541286461
absolute error = 1.6450691645486636207947274508182e-19
relative error = 1.4521822185781409414715764714252e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.116
y[1] (closed_form) = -0.0011313680077525035417023820280351
y[1] (numeric) = -0.0011313680077525033771607845105178
absolute error = 1.6454159751751727732744840447065e-19
relative error = 1.4543596459332811846081021680660e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.115
y[1] (closed_form) = -0.0011299126850641924454107063301572
y[1] (numeric) = -0.0011299126850641922808345258397446
absolute error = 1.6457618049041261963747579294075e-19
relative error = 1.4565389225722582281647446315283e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.114
y[1] (closed_form) = -0.0011284596082438805767159000761616
y[1] (numeric) = -0.001128459608243880412105234400035
absolute error = 1.6461066567612651947888653568071e-19
relative error = 1.4587200505323817559254466396866e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.113
y[1] (closed_form) = -0.0011270087732491217488830015511236
y[1] (numeric) = -0.0011270087732491215842379481749013
absolute error = 1.6464505337622224875682936642953e-19
relative error = 1.4609030318509151208933085836886e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.112
y[1] (closed_form) = -0.0011255601760457832875358743358505
y[1] (numeric) = -0.0011255601760457831228565304445947
absolute error = 1.6467934389125585679708720963205e-19
relative error = 1.4630878685650775862152639195324e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.111
y[1] (closed_form) = -0.0011241138126080268012573777126239
y[1] (numeric) = -0.0011241138126080266365438401918441
absolute error = 1.6471353752077979232195149070261e-19
relative error = 1.4652745627120465608956562995464e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (closed_form) = -0.0011226696789182890015970272274391
y[1] (numeric) = -0.0011226696789182888368493926640926
memory used=747.8MB, alloc=44.3MB, time=11.00
absolute error = 1.6474763456334651147471169151883e-19
relative error = 1.4674631163289598303134487698613e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.109
y[1] (closed_form) = -0.001121227770967262572346540413091
y[1] (numeric) = -0.0011212277709672624075649050965789
absolute error = 1.6478163531651207195006696592023e-19
relative error = 1.4696535314529177815577500074030e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.108
y[1] (closed_form) = -0.0011197880847538770879440928930303
y[1] (numeric) = -0.0011197880847538769231285528161906
absolute error = 1.6481554007683971328751658816144e-19
relative error = 1.4718458101209856235962973090158e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.107
y[1] (closed_form) = -0.0011183506162852799808685388656082
y[1] (numeric) = -0.0011183506162852798160191897257047
absolute error = 1.6484934913990342338453712031007e-19
relative error = 1.4740399543701956022914909354806e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.106
y[1] (closed_form) = -0.0011169153615768175578852773172763
y[1] (numeric) = -0.0011169153615768173930022145169848
absolute error = 1.6488306280029149128610644685504e-19
relative error = 1.4762359662375492102785294539008e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.105
y[1] (closed_form) = -0.0011154823166520160650058712366759
y[1] (numeric) = -0.0011154823166520159000891898850658
absolute error = 1.6491668135161004630688823070366e-19
relative error = 1.4784338477600193917201509126333e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.104
y[1] (closed_form) = -0.001114051477542562801023951604437
y[1] (numeric) = -0.0011140514775425626360737465179504
absolute error = 1.6495020508648658354214488872236e-19
relative error = 1.4806336009745527419524400231112e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.103
y[1] (closed_form) = -0.0011126228402882872794903610210271
y[1] (numeric) = -0.0011126228402882871145067267244536
absolute error = 1.6498363429657347582320286147481e-19
relative error = 1.4828352279180717020361170120005e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.102
y[1] (closed_form) = -0.0011111964009371424389909135122146
y[1] (numeric) = -0.0011111964009371422739739442396631
absolute error = 1.6501696927255147217305075531828e-19
relative error = 1.4850387306274767482276794446234e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.101
y[1] (closed_form) = -0.0011097721555451859015905673237103
y[1] (numeric) = -0.0011097721555451857365403570195771
absolute error = 1.6505021030413318281740886004692e-19
relative error = 1.4872441111396485763847241059223e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (closed_form) = -0.0011083501001765612793082263883551
y[1] (numeric) = -0.0011083501001765611142248687082885
absolute error = 1.6508335768006655080636758636347e-19
relative error = 1.4894513714914502813197319579207e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.099
y[1] (closed_form) = -0.0011069302309034795284868036258679
y[1] (numeric) = -0.0011069302309034793633703919377296
absolute error = 1.6511641168813831030145251918662e-19
relative error = 1.4916605137197295311165552721083e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.098
y[1] (closed_form) = -0.001105512543806200351923595321646
y[1] (numeric) = -0.0011055125438062001867742227064686
absolute error = 1.6514937261517743158273503975916e-19
relative error = 1.4938715398613207364238022609275e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.097
y[1] (closed_form) = -0.0011040970349730136486264305324102
y[1] (numeric) = -0.0011040970349730134834441897853517
absolute error = 1.6518224074705855283036982633697e-19
relative error = 1.4960844519530472147392709040394e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.096
y[1] (closed_form) = -0.0011026837005002210110614727875774
y[1] (numeric) = -0.001102683700500220845846456418872
absolute error = 1.6521501636870539873470399456374e-19
relative error = 1.4982992520317233496995401817683e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.095
y[1] (closed_form) = -0.0011012725364921172697589633010592
y[1] (numeric) = -0.001101272536492117104511263536965
absolute error = 1.6524769976409418598886717915207e-19
relative error = 1.5005159421341567453887835895582e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.094
y[1] (closed_form) = -0.0010998635390609720851436054836663
y[1] (numeric) = -0.0010998635390609719198633142674093
absolute error = 1.6528029121625701571751748290471e-19
relative error = 1.5027345242971503756808266128909e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.093
y[1] (closed_form) = -0.0010984567043270115864566997563392
y[1] (numeric) = -0.0010984567043270114211439087490539
absolute error = 1.6531279100728525289518492215615e-19
relative error = 1.5049550005575047286284267914070e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.092
y[1] (closed_form) = -0.001097052028418400057637545513929
y[1] (numeric) = -0.0010970520284183998922923460955961
absolute error = 1.6534519941833289280742177415470e-19
relative error = 1.5071773729520199459137120934165e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.091
y[1] (closed_form) = -0.0010956495074712216700320335830761
y[1] (numeric) = -0.0010956495074712215046545168534562
absolute error = 1.6537751672961991460773807652796e-19
relative error = 1.5094016435174979573736705570767e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (closed_form) = -0.0010942491376294622617967576607378
y[1] (numeric) = -0.0010942491376294620963870144403022
absolute error = 1.6540974322043562202307043659466e-19
relative error = 1.5116278142907446106145415317381e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.089
y[1] (closed_form) = -0.0010928509150449911638673770169288
y[1] (numeric) = -0.0010928509150449909984254978477868
absolute error = 1.6544187916914197126030327374458e-19
relative error = 1.5138558873085717957289163718120e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.088
y[1] (closed_form) = -0.0010914548358775430723603652010781
y[1] (numeric) = -0.0010914548358775429068864403479012
absolute error = 1.6547392485317688616613363627349e-19
relative error = 1.5160858646077995651293140954752e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.087
y[1] (closed_form) = -0.0010900608962946999672776806108648
y[1] (numeric) = -0.0010900608962946998017718000618073
absolute error = 1.6550588054905756069234379982621e-19
relative error = 1.5183177482252582485119553211136e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.086
y[1] (closed_form) = -0.0010886690924718730773842945702504
y[1] (numeric) = -0.0010886690924718729118465480378667
absolute error = 1.6553774653238374871831996288689e-19
relative error = 1.5205515401977905629644157350959e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.085
y[1] (closed_form) = -0.0010872794205922848911289110244447
y[1] (numeric) = -0.0010872794205922847255593879466037
absolute error = 1.6556952307784104128243050050880e-19
relative error = 1.5227872425622537182307984247704e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.084
y[1] (closed_form) = -0.0010858918768469512134786090984545
y[1] (numeric) = -0.0010858918768469510478773986392503
absolute error = 1.6560121045920413127365341566681e-19
relative error = 1.5250248573555215171480226299919e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.083
y[1] (closed_form) = -0.0010845064574346632685385355874001
y[1] (numeric) = -0.00108450645743466310290572663806
absolute error = 1.6563280894934006563461983324237e-19
relative error = 1.5272643866144864512667848245128e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.082
y[1] (closed_form) = -0.0010831231585619698478281689556519
y[1] (numeric) = -0.0010831231585619696821638501354404
absolute error = 1.6566431882021148512701860973637e-19
relative error = 1.5295058323760617916707065347167e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.081
y[1] (closed_form) = -0.0010817419764431595040860696227115
y[1] (numeric) = -0.0010817419764431593383903292798317
absolute error = 1.6569574034287985171008637739654e-19
relative error = 1.5317491966771836750071419369471e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (closed_form) = -0.0010803629073002427904754232113271
y[1] (numeric) = -0.0010803629073002426247483494238184
absolute error = 1.6572707378750866358268759961901e-19
relative error = 1.5339944815548131847430770455869e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.079
y[1] (closed_form) = -0.0010789859473629345450630740322226
y[1] (numeric) = -0.0010789859473629343793047546088559
absolute error = 1.6575831942336665793927048033392e-19
relative error = 1.5362416890459384276595112115969e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.078
y[1] (closed_form) = -0.001077611092868636220445135384686
y[1] (numeric) = -0.001077611092868636054655657865855
absolute error = 1.6578947751883100148976683873913e-19
relative error = 1.5384908211875766055976706949294e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.077
y[1] (closed_form) = -0.0010762383400624182583926512677028
y[1] (numeric) = -0.0010762383400624180925721029263123
absolute error = 1.6582054834139046879328732734995e-19
relative error = 1.5407418800167760824703632536118e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.076
y[1] (closed_form) = -0.001074867685197002509391170826949
y[1] (numeric) = -0.0010748676851970023435396386693004
absolute error = 1.6585153215764860845524763106118e-19
relative error = 1.5429948675706184465517420068628e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.075
y[1] (closed_form) = -0.0010734991245327446969484823133438
y[1] (numeric) = -0.0010734991245327445310660530800169
absolute error = 1.6588242923332689723734653296781e-19
relative error = 1.5452497858862205680587062788766e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.074
y[1] (closed_form) = -0.0010721326543376169265451375035748
y[1] (numeric) = -0.0010721326543376167606318976703069
absolute error = 1.6591323983326788212960296428385e-19
relative error = 1.5475066370007366520371267134097e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.073
y[1] (closed_form) = -0.001070768270887190239102780436588
y[1] (numeric) = -0.0010707682708871900731588162151497
absolute error = 1.6594396422143831043344636608305e-19
relative error = 1.5497654229513602865660416665475e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.072
y[1] (closed_form) = -0.0010694059704646172088456759570184
y[1] (numeric) = -0.0010694059704646170428710732960862
absolute error = 1.6597460266093224790464287502939e-19
relative error = 1.5520261457753264862929317355483e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.071
y[1] (closed_form) = -0.0010680457493606145854312139314214
y[1] (numeric) = -0.0010680457493606144194260585174473
absolute error = 1.6600515541397418500462899906506e-19
relative error = 1.5542888075099137313131392649704e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (closed_form) = -0.0010666876038734459802255441204606
y[1] (numeric) = -0.0010666876038734458141899213785384
absolute error = 1.6603562274192213130861456749776e-19
relative error = 1.5565534101924460014064597869244e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.069
y[1] (closed_form) = -0.0010653315303089045966008745543769
y[1] (numeric) = -0.0010653315303089044305348696491062
absolute error = 1.6606600490527069811860781841892e-19
relative error = 1.5588199558602948056438925997802e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.068
y[1] (closed_form) = -0.0010639775249802960041313428745753
y[1] (numeric) = -0.0010639775249802958380350407109211
absolute error = 1.6609630216365416932930752025725e-19
relative error = 1.5610884465508812073774980685263e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.067
y[1] (closed_form) = -0.0010626255842084209565647454754543
y[1] (numeric) = -0.0010626255842084207904382306996047
absolute error = 1.6612651477584956059460000891604e-19
relative error = 1.5633588843016778446262697397645e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.066
y[1] (closed_form) = -0.0010612757043215582534477834121056
y[1] (numeric) = -0.001061275704321558087291140412326
absolute error = 1.6615664299977966684219295277234e-19
relative error = 1.5656312711502109458708900045569e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.065
y[1] (closed_form) = -0.0010599278816554476452828569356228
y[1] (numeric) = -0.0010599278816554474790961698431067
absolute error = 1.6618668709251609818371253026596e-19
relative error = 1.5679056091340623412701988125600e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.064
y[1] (closed_form) = -0.001058582112553272782094812182879
y[1] (numeric) = -0.0010585821125532726158781648725966
absolute error = 1.6621664731028230426738651433785e-19
relative error = 1.5701819002908714693121658406260e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.063
y[1] (closed_form) = -0.0010572383933656442052864139861423
y[1] (numeric) = -0.0010572383933656440390398900776857
absolute error = 1.6624652390845658712023250007087e-19
relative error = 1.5724601466583373789121175478540e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.062
y[1] (closed_form) = -0.0010558967204505823826616879841383
y[1] (numeric) = -0.0010558967204505822163853708425632
absolute error = 1.6627631714157510252646818204882e-19
relative error = 1.5747403502742207269709317064851e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.061
y[1] (closed_form) = -0.0010545570901735007864966432145015
y[1] (numeric) = -0.0010545570901735006201906159511667
absolute error = 1.6630602726333484998865918170854e-19
relative error = 1.5770225131763457714058732835920e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (closed_form) = -0.0010532194989071890145372531522954
y[1] (numeric) = -0.0010532194989071888482015986256988
absolute error = 1.6633565452659665131791943786648e-19
relative error = 1.5793066374026023596667069617611e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.059
y[1] (closed_form) = -0.0010518839430317959538049387347344
y[1] (numeric) = -0.0010518839430317957874397395513463
absolute error = 1.6636519918338811789927960122868e-19
relative error = 1.5815927249909479127496831274552e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.058
y[1] (closed_form) = -0.0010505504189348129870901612827095
y[1] (numeric) = -0.0010505504189348128206954997978029
absolute error = 1.6639466148490660667814021163737e-19
relative error = 1.5838807779794094047219558230171e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.057
y[1] (closed_form) = -0.0010492189230110572420150963994692
y[1] (numeric) = -0.0010492189230110570755910547179471
absolute error = 1.6642404168152216491352868068670e-19
relative error = 1.5861707984060853377689529518859e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.056
y[1] (closed_form) = -0.0010478894516626548825467219001088
y[1] (numeric) = -0.0010478894516626547160933818773283
absolute error = 1.6645334002278046374368224779435e-19
relative error = 1.5884627883091477127771809460997e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.055
y[1] (closed_form) = -0.0010465620012990244428420136066079
y[1] (numeric) = -0.0010465620012990242763594568492022
absolute error = 1.6648255675740572060928312050841e-19
relative error = 1.5907567497268439954649081500961e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
memory used=794.3MB, alloc=44.3MB, time=11.67
x[1] = 2.054
y[1] (closed_form) = -0.0010452365683368602033073024362657
y[1] (numeric) = -0.0010452365683368600367956103029621
absolute error = 1.6651169213330361057947694544295e-19
relative error = 1.5930526846974990780731333447668e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.053
y[1] (closed_form) = -0.001043913149200115608754204620719
y[1] (numeric) = -0.0010439131492001154422134582231549
absolute error = 1.6654074639756416662561158047880e-19
relative error = 1.5953505952595172366292081302081e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.052
y[1] (closed_form) = -0.0010425917403199867285348941224911
y[1] (numeric) = -0.0010425917403199865619651743260265
absolute error = 1.6656971979646466888743984746499e-19
relative error = 1.5976504834513840837954443042218e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.051
y[1] (closed_form) = -0.001041272338134895758539842370386
y[1] (numeric) = -0.0010412723381348955919412297949135
absolute error = 1.6659861257547252297633753336159e-19
relative error = 1.5999523513116685173149999158925e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (closed_form) = -0.0010399549390904745649415053181806
y[1] (numeric) = -0.0010399549390904743983140803389324
absolute error = 1.6662742497924812735989637234684e-19
relative error = 1.6022562008790246640673003390836e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.049
y[1] (closed_form) = -0.0010386395396395482695677915471189
y[1] (numeric) = -0.0010386395396395481029116342954712
absolute error = 1.6665615725164772987206107766317e-19
relative error = 1.6045620341921938197452134990009e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.048
y[1] (closed_form) = -0.0010373261362421188767894976858155
y[1] (numeric) = -0.0010373261362421187101046880500893
absolute error = 1.6668480963572627339278969571153e-19
relative error = 1.6068698532900063841661612956496e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.047
y[1] (closed_form) = -0.0010360147253653489418062488154433
y[1] (numeric) = -0.001036014725365348775092866441703
absolute error = 1.6671338237374023074102762195701e-19
relative error = 1.6091796602113837922293123006082e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.046
y[1] (closed_form) = -0.0010347053034835452802158317676165
y[1] (numeric) = -0.0010347053034835451134739560604661
absolute error = 1.6674187570715042882459754443544e-19
relative error = 1.6114914569953404405309639576481e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.045
y[1] (closed_form) = -0.0010333978670781427187521583112677
y[1] (numeric) = -0.0010333978670781425519818684346429
absolute error = 1.6677028987662486209042036192936e-19
relative error = 1.6138052456809856096501857928939e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.044
y[1] (closed_form) = -0.0010320924126376878870774431671257
y[1] (numeric) = -0.0010320924126376877202788180450842
absolute error = 1.6679862512204149531829575610848e-19
relative error = 1.6161210283075253821167585360305e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.043
y[1] (closed_form) = -0.0010307889366578230505145285881905
y[1] (numeric) = -0.0010307889366578228836876469056994
absolute error = 1.6682688168249105580128557602384e-19
relative error = 1.6184388069142645560734075700838e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.042
y[1] (closed_form) = -0.0010294874356412699836056329059029
y[1] (numeric) = -0.0010294874356412698167505731096231
absolute error = 1.6685505979627981495555851524498e-19
relative error = 1.6207585835406085546442927631134e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.041
y[1] (closed_form) = -0.0010281879060978138843841449685515
y[1] (numeric) = -0.0010281879060978137175009852676192
absolute error = 1.6688315970093235940237072259557e-19
relative error = 1.6230803602260653310216804903316e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (closed_form) = -0.0010268903445442873292464297948487
y[1] (numeric) = -0.0010268903445442871623352481616543
absolute error = 1.6691118163319435156467398285373e-19
relative error = 1.6254041390102472692826875292805e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.039
y[1] (closed_form) = -0.0010255947475045542683109530355453
y[1] (numeric) = -0.00102559474750455410137182720651
absolute error = 1.6693912582903527982066092994093e-19
relative error = 1.6277299219328730809479505033402e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.038
y[1] (closed_form) = -0.0010243011115094940611523729834066
y[1] (numeric) = -0.0010243011115094938941853804597554
absolute error = 1.6696699252365119825637540804601e-19
relative error = 1.6300577110337696972940386595870e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.037
y[1] (closed_form) = -0.0010230094330969855527985889008112
y[1] (numeric) = -0.0010230094330969853858038069493437
absolute error = 1.6699478195146745605933557186068e-19
relative error = 1.6323875083528741574313919954523e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.036
y[1] (closed_form) = -0.0010217197088118911898790733486079
y[1] (numeric) = -0.0010217197088118910228565790024664
absolute error = 1.6702249434614141659493761169901e-19
relative error = 1.6347193159302354921595310943361e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.035
y[1] (closed_form) = -0.0010204319352060411768131540036012
y[1] (numeric) = -0.001020431935206041009763024063036
absolute error = 1.6705012994056516620722909881695e-19
relative error = 1.6370531358060166036112494928899e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.034
y[1] (closed_form) = -0.0010191461088382176719272471490593
y[1] (numeric) = -0.0010191461088382175048495581821911
absolute error = 1.6707768896686821278546286683828e-19
relative error = 1.6393889700204961406974639816925e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.033
y[1] (closed_form) = -0.0010178622262741390233903806168481
y[1] (numeric) = -0.0010178622262741388562852089604279
absolute error = 1.6710517165642017413766507295017e-19
relative error = 1.6417268206140703703643629360792e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.032
y[1] (closed_form) = -0.0010165802840864440448576784550824
y[1] (numeric) = -0.0010165802840864438777251002152489
absolute error = 1.6713257823983345621227461359445e-19
relative error = 1.6440666896272550446744575845537e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.031
y[1] (closed_form) = -0.0010153002788546763307118129954249
y[1] (numeric) = -0.001015300278854676163551904048459
absolute error = 1.6715990894696592120873539990736e-19
relative error = 1.6464085791006872637231060480947e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (closed_form) = -0.0010140222071652686107927623032123
y[1] (numeric) = -0.0010140222071652684436055982962887
absolute error = 1.6718716400692354561774812432986e-19
relative error = 1.6487524910751273344020450243624e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.029
y[1] (closed_form) = -0.0010127460656115271445065422152959
y[1] (numeric) = -0.0010127460656115269772921985672328
absolute error = 1.6721434364806306823171406781910e-19
relative error = 1.6510984275914606250214291459128e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.028
y[1] (closed_form) = -0.0010114718507936161542039123086774
y[1] (numeric) = -0.0010114718507936159869624642106828
absolute error = 1.6724144809799462816573020315548e-19
relative error = 1.6534463906906994158018433106329e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.027
y[1] (closed_form) = -0.0010101995593185422977203842015157
y[1] (numeric) = -0.0010101995593185421304519066179313
absolute error = 1.6726847758358439292932234019486e-19
relative error = 1.6557963824139847452477186653143e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.026
y[1] (closed_form) = -0.0010089291878001391799691885706836
y[1] (numeric) = -0.0010089291878001390126737562397264
absolute error = 1.6729543233095717658893132981549e-19
relative error = 1.6581484048025882524135484191933e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.025
y[1] (closed_form) = -0.0010076607328590519034791841805464
y[1] (numeric) = -0.0010076607328590517361568716150473
absolute error = 1.6732231256549904806099639102721e-19
relative error = 1.6605024598979140150742652729973e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.024
y[1] (closed_form) = -0.0010063941911227216577700180597924
y[1] (numeric) = -0.0010063941911227214904208995479324
absolute error = 1.6734911851185992957530944653868e-19
relative error = 1.6628585497415003838111079701555e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.023
y[1] (closed_form) = -0.00100512955922537034745717074073
y[1] (numeric) = -0.0010051295592253701800813203467739
absolute error = 1.6737585039395618534814494232685e-19
relative error = 1.6652166763750218120242703099588e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.022
y[1] (closed_form) = -0.0010038668338079852589798441922182
y[1] (numeric) = -0.001003866833807985091577335757245
absolute error = 1.6740250843497320050450098275007e-19
relative error = 1.6675768418402906818835919072039e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.021
y[1] (closed_form) = -0.0010026060115183037658449727370467
y[1] (numeric) = -0.0010026060115183035984158798796787
absolute error = 1.6742909285736795028861973084084e-19
relative error = 1.6699390481792591262285160388215e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (closed_form) = -0.0010013470890107980722809588508551
y[1] (numeric) = -0.0010013470890107979048253549679835
absolute error = 1.6745560388287155960178789997049e-19
relative error = 1.6723032974340208464285060847941e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.019
y[1] (closed_form) = -0.0010000900629466599951950562962618
y[1] (numeric) = -0.00100009006294665982771301456377
absolute error = 1.6748204173249185290625179448060e-19
relative error = 1.6746695916468129262150783479142e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.018
y[1] (closed_form) = -0.00099883492999378578432864255647147
y[1] (numeric) = -0.00099883492999378561682023592995558
absolute error = 1.6750840662651589453391573952717e-19
relative error = 1.6770379328600176414965754242346e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.017
y[1] (closed_form) = -0.0009975816868267609805049410009049
y[1] (numeric) = -0.00099758168682676081297024221639238
absolute error = 1.6753469878451251943832787070289e-19
relative error = 1.6794083231161642661667707930332e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.016
y[1] (closed_form) = -0.00099633033012684531186407064501566
y[1] (numeric) = -0.00099633033012684514430315221968081
absolute error = 1.6756091842533485442829312842860e-19
relative error = 1.6817807644579308739183619013658e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.015
y[1] (closed_form) = -0.00099508085658195762798061776106625
y[1] (numeric) = -0.00099508085658195746039355199394342
absolute error = 1.6758706576712282992128991709361e-19
relative error = 1.6841552589281461360723757334350e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.014
y[1] (closed_form) = -0.00099383326288666087175923895987176
y[1] (numeric) = -0.00099383326288666070414609793256608
absolute error = 1.6761314102730568225470424094886e-19
relative error = 1.6865318085697911154344776786714e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.013
y[1] (closed_form) = -0.00099258754574214708900411969899509
y[1] (numeric) = -0.00099258754574214692136497527639065
absolute error = 1.6763914442260444659273321430888e-19
relative error = 1.6889104154260010561891414442299e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.012
y[1] (closed_form) = -0.00099134370185622247555842548420477
y[1] (numeric) = -0.00099134370185622230789334931517033
absolute error = 1.6766507616903444046664865920707e-19
relative error = 1.6912910815400671698426047971647e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.011
y[1] (closed_form) = -0.00099010172794329246191019532177521
y[1] (numeric) = -0.00099010172794329229421925883986747
absolute error = 1.6769093648190773798595104579995e-19
relative error = 1.6936738089554384172255030684907e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (closed_form) = -0.00098886162072434683516143825299956
y[1] (numeric) = -0.00098886162072434666744471267716393
absolute error = 1.6771672557583563475778429607431e-19
relative error = 1.6960585997157232865660396052788e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.009
y[1] (closed_form) = -0.00098762337692694489825750406266258
y[1] (numeric) = -0.00098762337692694473051506039793148
absolute error = 1.6774244366473110355182295633677e-19
relative error = 1.6984454558646915676445197175041e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.008
y[1] (closed_form) = -0.0009863869932852006663741085037373
y[1] (numeric) = -0.00098638699328520049860601754192606
absolute error = 1.6776809096181124074768494513760e-19
relative error = 1.7008343794462761220400421331901e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.007
y[1] (closed_form) = -0.00098515246653976810035970162476421
y[1] (numeric) = -0.00098515246653976793256603394516451
absolute error = 1.6779366767959970360176549729406e-19
relative error = 1.7032253725045746494801095480921e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.006
y[1] (closed_form) = -0.00098391979343782637713117502777023
y[1] (numeric) = -0.00098391979343782620931200099784109
absolute error = 1.6781917402992913837023104814655e-19
relative error = 1.7056184370838514503038875343805e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.005
y[1] (closed_form) = -0.00098268897073306519692121012669949
y[1] (numeric) = -0.00098268897073306502907659990275589
absolute error = 1.6784461022394359932475563173201e-19
relative error = 1.7080135752285391840498088561330e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.004
y[1] (closed_form) = -0.00098145999518567012727587472265856
y[1] (numeric) = -0.0009814599951856699594058982505576
absolute error = 1.6786997647210095869742689884038e-19
relative error = 1.7104107889832406241781881275743e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.003
y[1] (closed_form) = -0.00098023286356230798370137946631065
y[1] (numeric) = -0.00098023286356230781580610648213535
absolute error = 1.6789527298417530759109409259386e-19
relative error = 1.7128100803927304089394797425270e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.002
y[1] (closed_form) = -0.00097900757263611224685920904296017
y[1] (numeric) = -0.00097900757263611207893870907370082
absolute error = 1.6792049996925934789127624693532e-19
relative error = 1.7152114515019567883987801001099e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
TOP MAIN SOLVE Loop
x[1] = 2.001
y[1] (closed_form) = -0.00097778411918666851620914519571034
y[1] (numeric) = -0.00097778411918666834826348755994357
absolute error = 1.6794565763576677521559549392797e-19
relative error = 1.7176149043560433676271433519637e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = -0.001
Finished!
diff ( y , x , 1 ) = neg ( 5.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ;
Iterations = 1000
Total Elapsed Time = 12 Seconds
Elapsed Time(since restart) = 12 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 12 Seconds
Time to Timeout = 2 Minutes 47 Seconds
Percent Done = 0 %
> quit
memory used=839.3MB, alloc=44.3MB, time=12.30