|\^/| Maple 18 (X86 64 WINDOWS)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014
\ 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
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
# End Function number 7
# Begin Function number 8
> 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 8
# Begin Function number 9
> 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 9
# Begin Function number 10
> 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 10
# Begin Function number 11
> 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 11
# Begin Function number 12
> 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 12
# Begin Function number 13
> 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 13
# Begin Function number 14
> 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 14
# Begin Function number 15
> 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 15
# Begin Function number 16
> 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 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> 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 18
# Begin Function number 19
> 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 19
# Begin Function number 20
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 20
# Begin Function number 21
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 21
# Begin Function number 22
> 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 22
# Begin Function number 23
> 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 23
# Begin Function number 24
> 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 24
# Begin Function number 25
> 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 25
# Begin Function number 26
> 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 26
# Begin Function number 27
> 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 27
# Begin Function number 28
> 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 28
# Begin Function number 29
> 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 29
# Begin Function number 30
> 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 30
# Begin Function number 31
> 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 31
# Begin Function number 32
> 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 32
# Begin Function number 33
> 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 33
# Begin Function number 34
> 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 34
# Begin Function number 35
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 35
# Begin Function number 36
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 36
# Begin Function number 37
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 37
# Begin Function number 38
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 38
# Begin Function number 39
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 39
# Begin Function number 40
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 40
# Begin Function number 41
> 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 41
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(2.0) - cos(c(x)));
> end;
exact_soln_y := proc(x) return c(2.0) - cos(c(x)) end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]);
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if (rad_given < glob_least_given_sing) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> 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,
#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_g,
> array_tmp1,
> array_tmp2,
> 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_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_g, array_tmp1, array_tmp2, 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,
#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_g,
> array_tmp1,
> array_tmp2,
> 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_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_g, array_tmp1, array_tmp2, 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,
#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_g,
> array_tmp1,
> array_tmp2,
> 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_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_g, array_tmp1, array_tmp2, 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,
#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_g,
> array_tmp1,
> array_tmp2,
> 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_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_g, array_tmp1, array_tmp2, 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,
#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_g,
> array_tmp1,
> array_tmp2,
> 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)*17*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_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_g, array_tmp1, array_tmp2, 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)*17*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,
#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_g,
> array_tmp1,
> array_tmp2,
> 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_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_g, array_tmp1, array_tmp2, 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,
#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_g,
> array_tmp1,
> array_tmp2,
> 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_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_g, array_tmp1, array_tmp2, 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,
#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_g,
> array_tmp1,
> array_tmp2,
> 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 sin 1 $eq_no = 1
> array_tmp1[1] := sin(array_x[1]);
> array_tmp1_g[1] := cos(array_x[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_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 sin ID_LINEAR iii = 2 $eq_no = 1
> array_tmp1[2] := array_tmp1_g[1] * array_x[2] / c(1);
> array_tmp1_g[2] := neg(array_tmp1[1]) * array_x[2] / c(1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sin ID_LINEAR iii = 3 $eq_no = 1
> array_tmp1[3] := array_tmp1_g[2] * array_x[2] / c(2);
> array_tmp1_g[3] := neg(array_tmp1[2]) * array_x[2] / c(2);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sin ID_LINEAR iii = 4 $eq_no = 1
> array_tmp1[4] := array_tmp1_g[3] * array_x[2] / c(3);
> array_tmp1_g[4] := neg(array_tmp1[3]) * array_x[2] / c(3);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sin ID_LINEAR iii = 5 $eq_no = 1
> array_tmp1[5] := array_tmp1_g[4] * array_x[2] / c(4);
> array_tmp1_g[5] := neg(array_tmp1[4]) * array_x[2] / c(4);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit sin LINEAR $eq_no = 1
> array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / c(kkk - 1);
> array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1]) * array_x[2] / c(kkk - 1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp2[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_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_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_g, array_tmp1, array_tmp2, 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] := sin(array_x[1]);
array_tmp1_g[1] := cos(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_tmp1_g[1]*array_x[2]/c(1);
array_tmp1_g[2] := neg(array_tmp1[1])*array_x[2]/c(1);
array_tmp2[2] := array_tmp1[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp1[3] := array_tmp1_g[2]*array_x[2]/c(2);
array_tmp1_g[3] := neg(array_tmp1[2])*array_x[2]/c(2);
array_tmp2[3] := array_tmp1[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp1[4] := array_tmp1_g[3]*array_x[2]/c(3);
array_tmp1_g[4] := neg(array_tmp1[3])*array_x[2]/c(3);
array_tmp2[4] := array_tmp1[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp1[5] := array_tmp1_g[4]*array_x[2]/c(4);
array_tmp1_g[5] := neg(array_tmp1[4])*array_x[2]/c(4);
array_tmp2[5] := array_tmp1[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/c(kkk - 1);
array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1])*array_x[2]/c(kkk - 1)
;
array_tmp2[kkk] := array_tmp1[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_tmp2[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,
> #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_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 40;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=16;
> max_terms:=40;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(40),[]);
> array_norms:= Array(0..(40),[]);
> array_fact_1:= Array(0..(40),[]);
> array_1st_rel_error:= Array(0..(2),[]);
> array_last_rel_error:= Array(0..(2),[]);
> array_est_rel_error:= Array(0..(2),[]);
> array_max_est_error:= Array(0..(2),[]);
> array_type_pole:= Array(0..(2),[]);
> array_type_real_pole:= Array(0..(2),[]);
> array_type_complex_pole:= Array(0..(2),[]);
> array_est_digits:= Array(0..(2),[]);
> array_y:= Array(0..(40),[]);
> array_x:= Array(0..(40),[]);
> array_tmp0:= Array(0..(40),[]);
> array_tmp1_g:= Array(0..(40),[]);
> array_tmp1:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_m1:= Array(0..(40),[]);
> array_y_higher := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..40+ 1),[]);
> array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(40) ,(0..40+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 40) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp1_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=40) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1_g);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> 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_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_h := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 1000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> array_y_set_initial[1,31] := false;
> array_y_set_initial[1,32] := false;
> array_y_set_initial[1,33] := false;
> array_y_set_initial[1,34] := false;
> array_y_set_initial[1,35] := false;
> array_y_set_initial[1,36] := false;
> array_y_set_initial[1,37] := false;
> array_y_set_initial[1,38] := false;
> array_y_set_initial[1,39] := false;
> array_y_set_initial[1,40] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 40;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/sin_lg_hpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( x ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"Digits:=16;");
> omniout_str(ALWAYS,"max_terms:=40;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"x_start := c(0.0);");
> omniout_str(ALWAYS,"x_end := c(5.0);");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := false;");
> omniout_str(ALWAYS,"glob_max_h := c(1.0);");
> omniout_str(ALWAYS,"glob_min_h := c(1.0);");
> omniout_str(ALWAYS,"glob_display_interval:= c(1.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 3;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=100000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=false;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"return(c(2.0) - cos(c(x)));");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := c(0.0);
> x_end := c(5.0);
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := false;
> glob_max_h := c(1.0);
> glob_min_h := c(1.0);
> glob_display_interval:= c(1.0);
> glob_type_given_pole := 3;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=100000;
> glob_upper_ratio_limit:=c(1.000001);
> glob_lower_ratio_limit:=c(0.999999);
> glob_look_poles:=false;
> glob_h:=c(0.001);
> glob_display_interval:=c(0.01);
> #END OVERRIDE BLOCK
> #END BLOCK 2
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
> # after second input block
> glob_check_sign := c(my_check_sign(x_start,x_end));
> glob__pi := arccos(glob__m1);
> glob_prec = expt(10.0,c(-Digits));
> if (glob_optimize) then # if number 9
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> found_h := false;
> glob_min_pole_est := glob_larger_float;
> last_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> glob_min_h := float_abs(glob_min_h) * glob_check_sign;
> glob_max_h := float_abs(glob_max_h) * glob_check_sign;
> glob_h := float_abs(glob_min_h) * glob_check_sign;
> glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign));
> display_max := c(x_end) - c(x_start)/glob__10;
> if ((glob_display_interval) > (display_max)) then # if number 10
> glob_display_interval := c(display_max);
> fi;# end if 10;
> chk_data();
> min_value := glob_larger_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := glob_small_float;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> atomall();
> if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> glob_h := glob_check_sign * float_abs(glob_min_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
> glob_h_reason := 2;
> glob_h := glob_display_interval;
> found_h := true;
> fi;# end if 10;
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if ( not found_h) then # if number 10
> est_answer := est_size_answer();
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := test_suggested_h();
> omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
> if (estimated_step_error < est_needed_step_err) then # if number 11
> omniout_str(ALWAYS,"Double H and LOOP");
> glob_h := glob_h*glob__2;
> else
> omniout_str(ALWAYS,"Found H for OPTIMAL");
> found_h := true;
> glob_h_reason := 3;
> glob_h := glob_h/glob__2;
> fi;# end if 11;
> fi;# end if 10;
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 10
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 10;
> if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MAX H");
> glob_h := glob_check_sign * float_abs(glob_max_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> else
> found_h := true;
> glob_h := glob_h * glob_check_sign;
> fi;# end if 9;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 9
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 9;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 9
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> glob_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and (glob_check_sign * array_x[1] < glob_check_sign * x_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1
> #left paren 0001C
> if (reached_interval()) then # if number 10
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 10;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> track_estimated_error();
> atomall();
> track_estimated_error();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if (reached_interval()) then # if number 10
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 10;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 10
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 10;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 10;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = sin ( x ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2015-04-24T20:35:54-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sin_lg_h")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( x ) ; ")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 308.maple.seems.ok | ")
> ;
> logitem_str(html_log_file,"sin_lg_h diffeq.mxt")
> ;
> logitem_str(html_log_file,"sin_lg_h 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_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_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
ATS_MAX_TERMS := 40;
Digits := 16;
max_terms := 40;
glob_html_log := true;
array_y_init := Array(0 .. 40, []);
array_norms := Array(0 .. 40, []);
array_fact_1 := Array(0 .. 40, []);
array_1st_rel_error := Array(0 .. 2, []);
array_last_rel_error := Array(0 .. 2, []);
array_est_rel_error := Array(0 .. 2, []);
array_max_est_error := Array(0 .. 2, []);
array_type_pole := Array(0 .. 2, []);
array_type_real_pole := Array(0 .. 2, []);
array_type_complex_pole := Array(0 .. 2, []);
array_est_digits := Array(0 .. 2, []);
array_y := Array(0 .. 40, []);
array_x := Array(0 .. 40, []);
array_tmp0 := Array(0 .. 40, []);
array_tmp1_g := Array(0 .. 40, []);
array_tmp1 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_m1 := Array(0 .. 40, []);
array_y_higher := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 41, []);
array_y_set_initial := Array(0 .. 2, 0 .. 41, []);
array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
array_fact_2 := Array(0 .. 40, 0 .. 41, []);
term := 1;
while term <= 40 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 40 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp1_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 40 do
term := 1;
while term <= 40 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1_g);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
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_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_h := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 1000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
array_y_set_initial[1, 31] := false;
array_y_set_initial[1, 32] := false;
array_y_set_initial[1, 33] := false;
array_y_set_initial[1, 34] := false;
array_y_set_initial[1, 35] := false;
array_y_set_initial[1, 36] := false;
array_y_set_initial[1, 37] := false;
array_y_set_initial[1, 38] := false;
array_y_set_initial[1, 39] := false;
array_y_set_initial[1, 40] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 40;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/sin_lg_hpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) ; ")
;
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "Digits:=16;");
omniout_str(ALWAYS, "max_terms:=40;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "x_start := c(0.0);");
omniout_str(ALWAYS, "x_end := c(5.0);");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := false;");
omniout_str(ALWAYS, "glob_max_h := c(1.0);");
omniout_str(ALWAYS, "glob_min_h := c(1.0);");
omniout_str(ALWAYS, "glob_display_interval:= c(1.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 3;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=100000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=false;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "return(c(2.0) - cos(c(x)));");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := c(0.);
x_end := c(5.0);
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := false;
glob_max_h := c(1.0);
glob_min_h := c(1.0);
glob_display_interval := c(1.0);
glob_type_given_pole := 3;
glob_desired_digits_correct := 8;
glob_max_minutes := 3.0;
glob_subiter_method := 3;
glob_max_iter := 100000;
glob_upper_ratio_limit := c(1.000001);
glob_lower_ratio_limit := c(0.999999);
glob_look_poles := false;
glob_h := c(0.001);
glob_display_interval := c(0.01);
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
glob_check_sign := c(my_check_sign(x_start, x_end));
glob__pi := arccos(glob__m1);
glob_prec = expt(10.0, c(-Digits));
if glob_optimize then
omniout_str(ALWAYS, "START of Optimize");
found_h := false;
glob_min_pole_est := glob_larger_float;
last_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
glob_min_h := float_abs(glob_min_h)*glob_check_sign;
glob_max_h := float_abs(glob_max_h)*glob_check_sign;
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_display_interval :=
c(float_abs(c(glob_display_interval))*glob_check_sign);
display_max := c(x_end) - c(x_start)/glob__10;
if display_max < glob_display_interval then
glob_display_interval := c(display_max)
end if;
chk_data();
min_value := glob_larger_float;
est_answer := est_size_answer();
opt_iter := 1;
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
;
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := glob_small_float;
while opt_iter <= 100 and not found_h do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] :=
array_y_init[it]*expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
atomall();
if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if;
if
glob_check_sign*glob_display_interval <= glob_check_sign*glob_h
then
omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL");
glob_h_reason := 2;
glob_h := glob_display_interval;
found_h := true
end if;
if glob_look_poles then check_for_pole() end if;
if not found_h then
est_answer := est_size_answer();
est_needed_step_err := estimated_needed_step_error(x_start,
x_end, glob_h, est_answer);
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := test_suggested_h();
omniout_float(ALWAYS, "estimated_step_error", 32,
estimated_step_error, 32, "");
if estimated_step_error < est_needed_step_err then
omniout_str(ALWAYS, "Double H and LOOP");
glob_h := glob_h*glob__2
else
omniout_str(ALWAYS, "Found H for OPTIMAL");
found_h := true;
glob_h_reason := 3;
glob_h := glob_h/glob__2
end if
end if;
opt_iter := opt_iter + 1
end do;
if not found_h and opt_iter = 1 then
omniout_str(ALWAYS, "Beginning glob_h too large.");
found_h := false
end if;
if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then
omniout_str(ALWAYS, "SETTING H FOR MAX H");
glob_h := float_abs(glob_max_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if
else found_h := true; glob_h := glob_check_sign*glob_h
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
glob_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
glob_clock_sec - glob_orig_start_sec < glob_max_sec do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
track_estimated_error();
atomall();
track_estimated_error();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO,
"diff ( y , x , 1 ) = sin ( x ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2015-04-24T20:35:54-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sin_lg_h");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = sin ( x ) ; ");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 308.maple.seems.ok | ");
logitem_str(html_log_file, "sin_lg_h diffeq.mxt");
logitem_str(html_log_file, "sin_lg_h 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/sin_lg_hpostode.ode#################
diff ( y , x , 1 ) = sin ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=16;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(0.0);
x_end := c(5.0);
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := false;
glob_max_h := c(1.0);
glob_min_h := c(1.0);
glob_display_interval:= c(1.0);
glob_type_given_pole := 3;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=100000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=false;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(2.0) - cos(c(x)));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0
y[1] (closed_form) = 1
y[1] (numeric) = 1
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 0.001
memory used=4.2MB, alloc=40.3MB, time=0.08
TOP MAIN SOLVE Loop
x[1] = 0.01
y[1] (closed_form) = 1.000049999583335
y[1] (numeric) = 1.000049999583334
absolute error = 1e-15
relative error = 9.999500029164983e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.02
y[1] (closed_form) = 1.000199993333422
y[1] (numeric) = 1.000199993333421
absolute error = 1e-15
relative error = 9.998000466559138e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.03
y[1] (closed_form) = 1.000449966251012
y[1] (numeric) = 1.000449966251012
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.04
y[1] (closed_form) = 1.000799893339022
y[1] (numeric) = 1.000799893339022
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.05
y[1] (closed_form) = 1.001249739605034
y[1] (numeric) = 1.001249739605031
absolute error = 3e-15
relative error = 2.996255460883734e-13 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.06
y[1] (closed_form) = 1.001799460064796
y[1] (numeric) = 1.001799460064792
absolute error = 4e-15
relative error = 3.992815088701766e-13 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.07
y[1] (closed_form) = 1.00244899974672
y[1] (numeric) = 1.002448999746717
absolute error = 3e-15
relative error = 2.992670949602407e-13 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.08
y[1] (closed_form) = 1.003198293697381
y[1] (numeric) = 1.003198293697377
absolute error = 4e-15
relative error = 3.987247611095536e-13 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.09
y[1] (closed_form) = 1.004047266988006
y[1] (numeric) = 1.004047266988003
absolute error = 3e-15
relative error = 2.987907142060710e-13 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (closed_form) = 1.004995834721974
y[1] (numeric) = 1.004995834721971
absolute error = 3e-15
relative error = 2.985086998723663e-13 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (closed_form) = 1.006043902043303
y[1] (numeric) = 1.006043902043299
absolute error = 4e-15
relative error = 3.975969629034965e-13 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (closed_form) = 1.007191364146134
y[1] (numeric) = 1.007191364146128
absolute error = 6e-15
relative error = 5.957159893926033e-13 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (closed_form) = 1.008438106285212
y[1] (numeric) = 1.008438106285205
absolute error = 7e-15
relative error = 6.941427497009144e-13 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (closed_form) = 1.009784003787363
y[1] (numeric) = 1.009784003787357
absolute error = 6e-15
relative error = 5.941864772561262e-13 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (closed_form) = 1.011228922063958
y[1] (numeric) = 1.011228922063951
absolute error = 7e-15
relative error = 6.922270365559486e-13 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 0.001
memory used=46.9MB, alloc=44.3MB, time=0.59
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (closed_form) = 1.012772716624373
y[1] (numeric) = 1.012772716624366
absolute error = 7e-15
relative error = 6.911718577225682e-13 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (closed_form) = 1.014415233090439
y[1] (numeric) = 1.014415233090433
absolute error = 6e-15
relative error = 5.914737677707051e-13 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (closed_form) = 1.016156307211879
y[1] (numeric) = 1.016156307211872
absolute error = 7e-15
relative error = 6.888703982172330e-13 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (closed_form) = 1.01799576488273
y[1] (numeric) = 1.017995764882722
absolute error = 8e-15
relative error = 7.858578862478446e-13 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (closed_form) = 1.019933422158758
y[1] (numeric) = 1.019933422158751
absolute error = 7e-15
relative error = 6.863193075077417e-13 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (closed_form) = 1.021969085275852
y[1] (numeric) = 1.021969085275843
absolute error = 9e-15
relative error = 8.806528621725090e-13 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (closed_form) = 1.024102550669394
y[1] (numeric) = 1.024102550669385
absolute error = 9e-15
relative error = 8.788182388684847e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (closed_form) = 1.026333604994625
y[1] (numeric) = 1.026333604994615
absolute error = 1.0e-14
relative error = 9.743420610350541e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (closed_form) = 1.02866202514797
y[1] (numeric) = 1.028662025147959
absolute error = 1.1e-14
relative error = 1.069350256068574e-12 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (closed_form) = 1.031087578289355
y[1] (numeric) = 1.031087578289344
absolute error = 1.1e-14
relative error = 1.066834692960782e-12 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (closed_form) = 1.033610021865487
y[1] (numeric) = 1.033610021865476
absolute error = 1.1e-14
relative error = 1.064231167200460e-12 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (closed_form) = 1.03622910363411
y[1] (numeric) = 1.036229103634099
absolute error = 1.1e-14
relative error = 1.061541309872732e-12 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (closed_form) = 1.038944561689229
y[1] (numeric) = 1.038944561689217
absolute error = 1.2e-14
relative error = 1.155018317867615e-12 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (closed_form) = 1.041756124487303
y[1] (numeric) = 1.04175612448729
absolute error = 1.3e-14
relative error = 1.247892831577823e-12 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (closed_form) = 1.044663510874394
y[1] (numeric) = 1.04466351087438
absolute error = 1.4e-14
relative error = 1.340144444049918e-12 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 0.001
memory used=89.6MB, alloc=44.3MB, time=1.09
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (closed_form) = 1.047666430114287
y[1] (numeric) = 1.047666430114272
absolute error = 1.5e-14
relative error = 1.431753425406949e-12 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (closed_form) = 1.050764581917559
y[1] (numeric) = 1.050764581917544
absolute error = 1.5e-14
relative error = 1.427531937993783e-12 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (closed_form) = 1.053957656471613
y[1] (numeric) = 1.0539576564716
absolute error = 1.3e-14
relative error = 1.233446137060264e-12 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (closed_form) = 1.057245334471654
y[1] (numeric) = 1.057245334471642
absolute error = 1.2e-14
relative error = 1.135025108055630e-12 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (closed_form) = 1.060627287152621
y[1] (numeric) = 1.06062728715261
absolute error = 1.1e-14
relative error = 1.037122100594903e-12 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (closed_form) = 1.064103176322065
y[1] (numeric) = 1.064103176322054
absolute error = 1.1e-14
relative error = 1.033734345011550e-12 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (closed_form) = 1.067672654393966
y[1] (numeric) = 1.067672654393955
absolute error = 1.1e-14
relative error = 1.030278330603479e-12 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (closed_form) = 1.07133536442349
y[1] (numeric) = 1.071335364423479
absolute error = 1.1e-14
relative error = 1.026755987460505e-12 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (closed_form) = 1.075090940142687
y[1] (numeric) = 1.075090940142676
absolute error = 1.1e-14
relative error = 1.023169258457342e-12 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (closed_form) = 1.078939005997115
y[1] (numeric) = 1.078939005997105
absolute error = 1.0e-14
relative error = 9.268364517749893e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (closed_form) = 1.082879177183395
y[1] (numeric) = 1.082879177183385
absolute error = 1.0e-14
relative error = 9.234640586598345e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (closed_form) = 1.086911059687692
y[1] (numeric) = 1.08691105968768
absolute error = 1.2e-14
relative error = 1.104046176827755e-12 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (closed_form) = 1.091034250325115
y[1] (numeric) = 1.091034250325106
absolute error = 9e-15
relative error = 8.249053590497373e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (closed_form) = 1.095248336780037
y[1] (numeric) = 1.095248336780027
absolute error = 1.0e-14
relative error = 9.130349404957224e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (closed_form) = 1.099552897647323
y[1] (numeric) = 1.099552897647313
absolute error = 1.0e-14
relative error = 9.094605654167862e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=132.4MB, alloc=44.3MB, time=1.61
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (closed_form) = 1.103947502474475
y[1] (numeric) = 1.103947502474465
absolute error = 1.0e-14
relative error = 9.058401760577574e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (closed_form) = 1.108431711804671
y[1] (numeric) = 1.108431711804662
absolute error = 9e-15
relative error = 8.119580037408736e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (closed_form) = 1.113005077220716
y[1] (numeric) = 1.113005077220707
absolute error = 9e-15
relative error = 8.086216482025304e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (closed_form) = 1.117667141389878
y[1] (numeric) = 1.11766714138987
absolute error = 8e-15
relative error = 7.157766121719905e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (closed_form) = 1.122417438109627
y[1] (numeric) = 1.122417438109619
absolute error = 8e-15
relative error = 7.127473013492718e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (closed_form) = 1.127255492354249
y[1] (numeric) = 1.127255492354241
absolute error = 8e-15
relative error = 7.096882698075989e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (closed_form) = 1.13218082032235
y[1] (numeric) = 1.132180820322343
absolute error = 7e-15
relative error = 6.182757978541792e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (closed_form) = 1.137192929485239
y[1] (numeric) = 1.137192929485234
absolute error = 5e-15
relative error = 4.396791318658037e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (closed_form) = 1.142291318636176
y[1] (numeric) = 1.142291318636172
absolute error = 4e-15
relative error = 3.501733695022517e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (closed_form) = 1.147475477940494
y[1] (numeric) = 1.147475477940491
absolute error = 3e-15
relative error = 2.614434955407016e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (closed_form) = 1.152744888986584
y[1] (numeric) = 1.152744888986581
absolute error = 3e-15
relative error = 2.602483887512526e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (closed_form) = 1.158099024837731
y[1] (numeric) = 1.158099024837728
absolute error = 3e-15
relative error = 2.590452056049654e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (closed_form) = 1.163537350084813
y[1] (numeric) = 1.16353735008481
absolute error = 3e-15
relative error = 2.578344390733416e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (closed_form) = 1.169059320899836
y[1] (numeric) = 1.169059320899835
absolute error = 1e-15
relative error = 8.553885864665024e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
memory used=175.1MB, alloc=44.3MB, time=2.09
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (closed_form) = 1.174664385090322
y[1] (numeric) = 1.174664385090321
absolute error = 1e-15
relative error = 8.513069883557492e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (closed_form) = 1.18035198215452
y[1] (numeric) = 1.180351982154521
absolute error = 1e-15
relative error = 8.472049143973818e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (closed_form) = 1.186121543337466
y[1] (numeric) = 1.186121543337466
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (closed_form) = 1.191972491687848
y[1] (numeric) = 1.191972491687848
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (closed_form) = 1.197904242115707
y[1] (numeric) = 1.197904242115707
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (closed_form) = 1.203916201450944
y[1] (numeric) = 1.203916201450943
absolute error = 1e-15
relative error = 8.306225954886338e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (closed_form) = 1.210007768502635
y[1] (numeric) = 1.210007768502634
absolute error = 1e-15
relative error = 8.264409750339734e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (closed_form) = 1.216178334119151
y[1] (numeric) = 1.21617833411915
absolute error = 1e-15
relative error = 8.222478331882768e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (closed_form) = 1.222427281249072
y[1] (numeric) = 1.222427281249072
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (closed_form) = 1.228753985002893
y[1] (numeric) = 1.228753985002894
absolute error = 1e-15
relative error = 8.138325590029688e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (closed_form) = 1.235157812715512
y[1] (numeric) = 1.235157812715512
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (closed_form) = 1.241638124009492
y[1] (numeric) = 1.241638124009492
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (closed_form) = 1.248194270859105
y[1] (numeric) = 1.248194270859104
absolute error = 1e-15
relative error = 8.011573385220890e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (closed_form) = 1.25482559765513
y[1] (numeric) = 1.254825597655129
absolute error = 1e-15
relative error = 7.969234942837331e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (closed_form) = 1.261531441270412
y[1] (numeric) = 1.261531441270412
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
memory used=217.9MB, alloc=44.3MB, time=2.59
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (closed_form) = 1.268311131126179
y[1] (numeric) = 1.268311131126179
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (closed_form) = 1.275163989259095
y[1] (numeric) = 1.275163989259094
absolute error = 1e-15
relative error = 7.842128607952827e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (closed_form) = 1.282089330389057
y[1] (numeric) = 1.282089330389055
absolute error = 2e-15
relative error = 1.559953704156550e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (closed_form) = 1.289086461987723
y[1] (numeric) = 1.289086461987722
absolute error = 1e-15
relative error = 7.757431557058147e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (closed_form) = 1.296154684347764
y[1] (numeric) = 1.296154684347765
absolute error = 1e-15
relative error = 7.715128541954917e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (closed_form) = 1.303293290652835
y[1] (numeric) = 1.303293290652838
absolute error = 3e-15
relative error = 2.301861002059839e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (closed_form) = 1.310501567048253
y[1] (numeric) = 1.310501567048257
absolute error = 4e-15
relative error = 3.052266476116864e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (closed_form) = 1.317778792712386
y[1] (numeric) = 1.31777879271239
absolute error = 4e-15
relative error = 3.035410815624673e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (closed_form) = 1.325124239928733
y[1] (numeric) = 1.325124239928735
absolute error = 2e-15
relative error = 1.509292441973262e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (closed_form) = 1.332537174158692
y[1] (numeric) = 1.332537174158694
absolute error = 2e-15
relative error = 1.500896214218351e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (closed_form) = 1.340016854115018
y[1] (numeric) = 1.34001685411502
absolute error = 2e-15
relative error = 1.492518540985704e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (closed_form) = 1.347562531835948
y[1] (numeric) = 1.347562531835949
absolute error = 1e-15
relative error = 7.420805909745640e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (closed_form) = 1.355173452759999
y[1] (numeric) = 1.355173452759999
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (closed_form) = 1.36284885580142
y[1] (numeric) = 1.362848855801419
absolute error = 1e-15
relative error = 7.337570822642342e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (closed_form) = 1.370587973426303
y[1] (numeric) = 1.370587973426303
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
memory used=260.7MB, alloc=44.3MB, time=3.09
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (closed_form) = 1.378390031729336
y[1] (numeric) = 1.378390031729335
absolute error = 1e-15
relative error = 7.254840625518702e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (closed_form) = 1.386254250511188
y[1] (numeric) = 1.386254250511189
absolute error = 1e-15
relative error = 7.213683922925720e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (closed_form) = 1.394179843356537
y[1] (numeric) = 1.394179843356538
absolute error = 1e-15
relative error = 7.172675783293960e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (closed_form) = 1.402166017712702
y[1] (numeric) = 1.4021660177127
absolute error = 2e-15
relative error = 1.426364620690581e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (closed_form) = 1.410211974968902
y[1] (numeric) = 1.410211974968902
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (closed_form) = 1.418316910536116
y[1] (numeric) = 1.418316910536117
absolute error = 1e-15
relative error = 7.050610428257571e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (closed_form) = 1.426480013927543
y[1] (numeric) = 1.426480013927544
absolute error = 1e-15
relative error = 7.010262956623480e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (closed_form) = 1.434700468839646
y[1] (numeric) = 1.434700468839645
absolute error = 1e-15
relative error = 6.970096000657042e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (closed_form) = 1.442977453233783
y[1] (numeric) = 1.442977453233784
absolute error = 1e-15
relative error = 6.930115212534687e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (closed_form) = 1.451310139418412
y[1] (numeric) = 1.451310139418413
absolute error = 1e-15
relative error = 6.890326008476266e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (closed_form) = 1.45969769413186
y[1] (numeric) = 1.45969769413186
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (closed_form) = 1.468139278625644
y[1] (numeric) = 1.468139278625644
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (closed_form) = 1.47663404874835
y[1] (numeric) = 1.47663404874835
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (closed_form) = 1.485181155030045
y[1] (numeric) = 1.485181155030044
absolute error = 1e-15
relative error = 6.733185353269380e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
memory used=303.5MB, alloc=44.3MB, time=3.59
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (closed_form) = 1.493779742767222
y[1] (numeric) = 1.493779742767221
absolute error = 1e-15
relative error = 6.694427373526323e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (closed_form) = 1.502428952108273
y[1] (numeric) = 1.502428952108273
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (closed_form) = 1.511127918139472
y[1] (numeric) = 1.511127918139472
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (closed_form) = 1.519875770971466
y[1] (numeric) = 1.519875770971465
absolute error = 1e-15
relative error = 6.579485107265217e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (closed_form) = 1.52867163582626
y[1] (numeric) = 1.52867163582626
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (closed_form) = 1.537514633124699
y[1] (numeric) = 1.537514633124698
absolute error = 1e-15
relative error = 6.504003138934000e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (closed_form) = 1.546403878574423
y[1] (numeric) = 1.546403878574421
absolute error = 2e-15
relative error = 1.293323191767814e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (closed_form) = 1.555338483258293
y[1] (numeric) = 1.55533848325829
absolute error = 3e-15
relative error = 1.928840591480301e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (closed_form) = 1.564317553723288
y[1] (numeric) = 1.564317553723284
absolute error = 4e-15
relative error = 2.557025579927463e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (closed_form) = 1.573340192069843
y[1] (numeric) = 1.57334019206984
absolute error = 3e-15
relative error = 1.906771348701950e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (closed_form) = 1.582405496041642
y[1] (numeric) = 1.58240549604164
absolute error = 2e-15
relative error = 1.263898542442479e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (closed_form) = 1.591512559115843
y[1] (numeric) = 1.591512559115841
absolute error = 2e-15
relative error = 1.256666174919217e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (closed_form) = 1.600660470593727
y[1] (numeric) = 1.600660470593726
absolute error = 1e-15
relative error = 6.247421101297477e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (closed_form) = 1.60984831569177
y[1] (numeric) = 1.60984831569177
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (closed_form) = 1.619075175633118
y[1] (numeric) = 1.619075175633119
absolute error = 1e-15
relative error = 6.176365464988142e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
memory used=346.5MB, alloc=44.3MB, time=4.09
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (closed_form) = 1.628340127739467
y[1] (numeric) = 1.628340127739468
absolute error = 1e-15
relative error = 6.141223095620961e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (closed_form) = 1.637642245523326
y[1] (numeric) = 1.637642245523326
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (closed_form) = 1.64698059878067
y[1] (numeric) = 1.646980598780669
absolute error = 1e-15
relative error = 6.071716939108710e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (closed_form) = 1.656354253683953
y[1] (numeric) = 1.656354253683954
absolute error = 1e-15
relative error = 6.037355823948087e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (closed_form) = 1.665762272875497
y[1] (numeric) = 1.665762272875499
absolute error = 2e-15
relative error = 1.200651517066436e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (closed_form) = 1.675203715561224
y[1] (numeric) = 1.675203715561224
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (closed_form) = 1.684677637604731
y[1] (numeric) = 1.684677637604732
absolute error = 1e-15
relative error = 5.935853706836144e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (closed_form) = 1.694183091621711
y[1] (numeric) = 1.694183091621712
absolute error = 1e-15
relative error = 5.902549759499589e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (closed_form) = 1.703719127074681
y[1] (numeric) = 1.703719127074681
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (closed_form) = 1.713284790368044
y[1] (numeric) = 1.713284790368043
absolute error = 1e-15
relative error = 5.836741244782674e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (closed_form) = 1.722879124943442
y[1] (numeric) = 1.722879124943442
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (closed_form) = 1.732501171375413
y[1] (numeric) = 1.732501171375411
absolute error = 2e-15
relative error = 1.154400373889631e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (closed_form) = 1.74214996746733
y[1] (numeric) = 1.742149967467328
absolute error = 2e-15
relative error = 1.148006794677683e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (closed_form) = 1.751824548347627
y[1] (numeric) = 1.751824548347624
absolute error = 3e-15
relative error = 1.712500263128342e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=389.2MB, alloc=44.3MB, time=4.64
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (closed_form) = 1.761523946566277
y[1] (numeric) = 1.761523946566273
absolute error = 4e-15
relative error = 2.270761069014795e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (closed_form) = 1.77124719219154
y[1] (numeric) = 1.771247192191537
absolute error = 3e-15
relative error = 1.693721809821553e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (closed_form) = 1.780993312906958
y[1] (numeric) = 1.780993312906954
absolute error = 4e-15
relative error = 2.245937686015875e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (closed_form) = 1.790761334108581
y[1] (numeric) = 1.790761334108577
absolute error = 4e-15
relative error = 2.233686825716030e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (closed_form) = 1.800550279002427
y[1] (numeric) = 1.800550279002423
absolute error = 4e-15
relative error = 2.221543073052173e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (closed_form) = 1.810359168702166
y[1] (numeric) = 1.810359168702162
absolute error = 4e-15
relative error = 2.209506306346697e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (closed_form) = 1.820187022327
y[1] (numeric) = 1.820187022326996
absolute error = 4e-15
relative error = 2.197576375907922e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (closed_form) = 1.830032857099759
y[1] (numeric) = 1.830032857099753
absolute error = 6e-15
relative error = 3.278629657780471e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (closed_form) = 1.839895688445169
y[1] (numeric) = 1.839895688445162
absolute error = 7e-15
relative error = 3.804563510834385e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (closed_form) = 1.849774530088314
y[1] (numeric) = 1.849774530088308
absolute error = 6e-15
relative error = 3.243638563730003e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (closed_form) = 1.859668394153263
y[1] (numeric) = 1.859668394153258
absolute error = 5e-15
relative error = 2.688651383074444e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (closed_form) = 1.869576291261854
y[1] (numeric) = 1.869576291261849
absolute error = 5e-15
relative error = 2.674402763540232e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (closed_form) = 1.879497230632633
y[1] (numeric) = 1.879497230632629
absolute error = 4e-15
relative error = 2.128228727771848e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (closed_form) = 1.88943022017993
y[1] (numeric) = 1.889430220179925
absolute error = 5e-15
relative error = 2.646300427820960e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (closed_form) = 1.899374266613068
y[1] (numeric) = 1.899374266613063
absolute error = 5e-15
relative error = 2.632445899625625e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=432.1MB, alloc=44.3MB, time=5.20
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (closed_form) = 1.90932837553569
y[1] (numeric) = 1.909328375535683
absolute error = 7e-15
relative error = 3.666210637044583e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (closed_form) = 1.919291551545199
y[1] (numeric) = 1.919291551545191
absolute error = 8e-15
relative error = 4.168204665705580e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (closed_form) = 1.929262798332297
y[1] (numeric) = 1.929262798332288
absolute error = 9e-15
relative error = 4.664994322069458e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (closed_form) = 1.939241118780614
y[1] (numeric) = 1.939241118780605
absolute error = 9e-15
relative error = 4.640990701382796e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (closed_form) = 1.949225515066421
y[1] (numeric) = 1.949225515066411
absolute error = 1.0e-14
relative error = 5.130242715737919e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (closed_form) = 1.959214988758409
y[1] (numeric) = 1.959214988758399
absolute error = 1.0e-14
relative error = 5.104085083759586e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (closed_form) = 1.969208540917534
y[1] (numeric) = 1.969208540917524
absolute error = 1.0e-14
relative error = 5.078182321584181e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (closed_form) = 1.979205172196908
y[1] (numeric) = 1.979205172196898
absolute error = 1.0e-14
relative error = 5.052533279761011e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (closed_form) = 1.989203882941733
y[1] (numeric) = 1.989203882941723
absolute error = 1.0e-14
relative error = 5.027136778564652e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (closed_form) = 1.999203673289267
y[1] (numeric) = 1.999203673289256
absolute error = 1.1e-14
relative error = 5.502190770739144e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (closed_form) = 2.009203543268808
y[1] (numeric) = 2.009203543268797
absolute error = 1.1e-14
relative error = 5.474806192161054e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (closed_form) = 2.019202492901693
y[1] (numeric) = 2.019202492901682
absolute error = 1.1e-14
relative error = 5.447695334504298e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (closed_form) = 2.029199522301289
y[1] (numeric) = 2.02919952230128
absolute error = 9e-15
relative error = 4.435246461024797e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (closed_form) = 2.039193631772988
y[1] (numeric) = 2.039193631772979
absolute error = 9e-15
relative error = 4.413509271395135e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=475.0MB, alloc=44.3MB, time=5.80
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (closed_form) = 2.04918382191417
y[1] (numeric) = 2.049183821914162
absolute error = 8e-15
relative error = 3.903993343323925e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (closed_form) = 2.059169093714148
y[1] (numeric) = 2.059169093714141
absolute error = 7e-15
relative error = 3.399429421006905e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (closed_form) = 2.069148448654062
y[1] (numeric) = 2.069148448654056
absolute error = 6e-15
relative error = 2.899743613805416e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (closed_form) = 2.079120888806734
y[1] (numeric) = 2.079120888806729
absolute error = 5e-15
relative error = 2.404862568077819e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (closed_form) = 2.089085416936459
y[1] (numeric) = 2.089085416936455
absolute error = 4e-15
relative error = 1.914713475845235e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (closed_form) = 2.099041036598728
y[1] (numeric) = 2.099041036598724
absolute error = 4e-15
relative error = 1.905632110214278e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (closed_form) = 2.108986752239871
y[1] (numeric) = 2.108986752239868
absolute error = 3e-15
relative error = 1.422484042070828e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (closed_form) = 2.118921569296612
y[1] (numeric) = 2.118921569296608
absolute error = 4e-15
relative error = 1.887752740809478e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (closed_form) = 2.128844494295525
y[1] (numeric) = 2.12884449429552
absolute error = 5e-15
relative error = 2.348691984500538e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (closed_form) = 2.138754534952378
y[1] (numeric) = 2.138754534952374
absolute error = 4e-15
relative error = 1.870247349394429e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (closed_form) = 2.148650700271364
y[1] (numeric) = 2.14865070027136
absolute error = 4e-15
relative error = 1.861633442557611e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (closed_form) = 2.158532000644198
y[1] (numeric) = 2.158532000644194
absolute error = 4e-15
relative error = 1.853111280632499e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (closed_form) = 2.168397447949077
y[1] (numeric) = 2.168397447949073
absolute error = 4e-15
relative error = 1.844680274726987e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (closed_form) = 2.178246055649492
y[1] (numeric) = 2.178246055649488
absolute error = 4e-15
relative error = 1.836339833888652e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (closed_form) = 2.18807683889288
y[1] (numeric) = 2.188076838892877
absolute error = 3e-15
relative error = 1.371067024098631e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=517.9MB, alloc=44.3MB, time=6.33
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (closed_form) = 2.197888814609109
y[1] (numeric) = 2.197888814609105
absolute error = 4e-15
relative error = 1.819928275448908e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (closed_form) = 2.207681001608784
y[1] (numeric) = 2.20768100160878
absolute error = 4e-15
relative error = 1.811855968813028e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (closed_form) = 2.217452420681365
y[1] (numeric) = 2.217452420681361
absolute error = 4e-15
relative error = 1.803871849827968e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (closed_form) = 2.227202094693087
y[1] (numeric) = 2.227202094693083
absolute error = 4e-15
relative error = 1.795975322370199e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (closed_form) = 2.236929048684675
y[1] (numeric) = 2.236929048684671
absolute error = 4e-15
relative error = 1.788165790216734e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (closed_form) = 2.246632309968834
y[1] (numeric) = 2.246632309968831
absolute error = 3e-15
relative error = 1.335331992996049e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (closed_form) = 2.256310908227523
y[1] (numeric) = 2.25631090822752
absolute error = 3e-15
relative error = 1.329603996089658e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (closed_form) = 2.26596387560898
y[1] (numeric) = 2.265963875608977
absolute error = 3e-15
relative error = 1.323939905791193e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (closed_form) = 2.275590246824513
y[1] (numeric) = 2.275590246824511
absolute error = 2e-15
relative error = 8.788928511145242e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (closed_form) = 2.285189059245021
y[1] (numeric) = 2.285189059245017
absolute error = 4e-15
relative error = 1.750402218940046e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (closed_form) = 2.294759352997261
y[1] (numeric) = 2.294759352997256
absolute error = 5e-15
relative error = 2.178877708230859e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (closed_form) = 2.304300171059833
y[1] (numeric) = 2.304300171059828
absolute error = 5e-15
relative error = 2.169856194429875e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (closed_form) = 2.313810559358882
y[1] (numeric) = 2.313810559358877
absolute error = 5e-15
relative error = 2.160937497573447e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (closed_form) = 2.323289566863503
y[1] (numeric) = 2.323289566863498
absolute error = 5e-15
relative error = 2.152120885538224e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=560.7MB, alloc=44.3MB, time=6.83
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (closed_form) = 2.332736245680845
y[1] (numeric) = 2.332736245680841
absolute error = 4e-15
relative error = 1.714724503212123e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (closed_form) = 2.342149651150898
y[1] (numeric) = 2.342149651150893
absolute error = 5e-15
relative error = 2.134791001737687e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.93
y[1] (closed_form) = 2.35152884194096
y[1] (numeric) = 2.351528841940955
absolute error = 5e-15
relative error = 2.126276280699574e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (closed_form) = 2.360872880139767
y[1] (numeric) = 2.360872880139761
absolute error = 6e-15
relative error = 2.541432895635106e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (closed_form) = 2.370180831351287
y[1] (numeric) = 2.370180831351281
absolute error = 6e-15
relative error = 2.531452419425433e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (closed_form) = 2.379451764788154
y[1] (numeric) = 2.37945176478815
absolute error = 4e-15
relative error = 1.681059502526258e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (closed_form) = 2.388684753364752
y[1] (numeric) = 2.388684753364748
absolute error = 4e-15
relative error = 1.674561699431252e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (closed_form) = 2.397878873789916
y[1] (numeric) = 2.397878873789913
absolute error = 3e-15
relative error = 1.251105730481880e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (closed_form) = 2.407033206659266
y[1] (numeric) = 2.407033206659262
absolute error = 4e-15
relative error = 1.661796766631077e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (closed_form) = 2.416146836547142
y[1] (numeric) = 2.416146836547139
absolute error = 3e-15
relative error = 1.241646391113890e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (closed_form) = 2.425218852098152
y[1] (numeric) = 2.425218852098149
absolute error = 3e-15
relative error = 1.237001764770459e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (closed_form) = 2.4342483461183
y[1] (numeric) = 2.434248346118295
absolute error = 5e-15
relative error = 2.054022141156262e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (closed_form) = 2.443234415665709
y[1] (numeric) = 2.443234415665704
absolute error = 5e-15
relative error = 2.046467570995495e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (closed_form) = 2.452176162140912
y[1] (numeric) = 2.452176162140907
absolute error = 5e-15
relative error = 2.039005222053325e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (closed_form) = 2.461072691376713
y[1] (numeric) = 2.461072691376708
absolute error = 5e-15
relative error = 2.031634424094569e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=603.4MB, alloc=44.3MB, time=7.33
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (closed_form) = 2.469923113727602
y[1] (numeric) = 2.469923113727596
absolute error = 6e-15
relative error = 2.429225414610099e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (closed_form) = 2.47872654415872
y[1] (numeric) = 2.478726544158714
absolute error = 6e-15
relative error = 2.420597792095860e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (closed_form) = 2.487482102334359
y[1] (numeric) = 2.487482102334353
absolute error = 6e-15
relative error = 2.412077656506290e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (closed_form) = 2.496188912705999
y[1] (numeric) = 2.496188912705994
absolute error = 5e-15
relative error = 2.003053524734928e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (closed_form) = 2.504846104599858
y[1] (numeric) = 2.504846104599853
absolute error = 5e-15
relative error = 1.996130616894221e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (closed_form) = 2.51345281230396
y[1] (numeric) = 2.513452812303954
absolute error = 6e-15
relative error = 2.387154423838215e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (closed_form) = 2.522008175154707
y[1] (numeric) = 2.522008175154702
absolute error = 5e-15
relative error = 1.982547102446758e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (closed_form) = 2.530511337622945
y[1] (numeric) = 2.530511337622939
absolute error = 6e-15
relative error = 2.371062287211938e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (closed_form) = 2.538961449399511
y[1] (numeric) = 2.538961449399504
absolute error = 7e-15
relative error = 2.757032802390744e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (closed_form) = 2.547357665480271
y[1] (numeric) = 2.547357665480264
absolute error = 7e-15
relative error = 2.747945486752149e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (closed_form) = 2.555699146250613
y[1] (numeric) = 2.555699146250605
absolute error = 8e-15
relative error = 3.130258900675595e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (closed_form) = 2.56398505756941
y[1] (numeric) = 2.563985057569402
absolute error = 8e-15
relative error = 3.120142988502354e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (closed_form) = 2.572214570852437
y[1] (numeric) = 2.572214570852428
absolute error = 9e-15
relative error = 3.498930494362833e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (closed_form) = 2.580386863155222
y[1] (numeric) = 2.580386863155213
absolute error = 9e-15
relative error = 3.487849100655807e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=646.2MB, alloc=44.3MB, time=7.83
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (closed_form) = 2.588501117255346
y[1] (numeric) = 2.588501117255337
absolute error = 9e-15
relative error = 3.476915632759290e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (closed_form) = 2.59655652173416
y[1] (numeric) = 2.596556521734152
absolute error = 8e-15
relative error = 3.081003603440547e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (closed_form) = 2.60455227105793
y[1] (numeric) = 2.604552271057922
absolute error = 8e-15
relative error = 3.071545189895736e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (closed_form) = 2.612487565658385
y[1] (numeric) = 2.612487565658378
absolute error = 7e-15
relative error = 2.679438590260198e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (closed_form) = 2.62036161201268
y[1] (numeric) = 2.620361612012673
absolute error = 7e-15
relative error = 2.671387020749153e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (closed_form) = 2.628173622722739
y[1] (numeric) = 2.628173622722733
absolute error = 6e-15
relative error = 2.282954196071762e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (closed_form) = 2.635922816594002
y[1] (numeric) = 2.635922816593997
absolute error = 5e-15
relative error = 1.896868894841440e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (closed_form) = 2.64360841871354
y[1] (numeric) = 2.643608418713536
absolute error = 4e-15
relative error = 1.513083394531828e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (closed_form) = 2.651229660527546
y[1] (numeric) = 2.651229660527543
absolute error = 3e-15
relative error = 1.131550406464242e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (closed_form) = 2.658785779918188
y[1] (numeric) = 2.658785779918184
absolute error = 4e-15
relative error = 1.504446138614101e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (closed_form) = 2.666276021279824
y[1] (numeric) = 2.666276021279819
absolute error = 5e-15
relative error = 1.875274712780854e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (closed_form) = 2.673699635594561
y[1] (numeric) = 2.673699635594556
absolute error = 5e-15
relative error = 1.870067951326975e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (closed_form) = 2.681055880507153
y[1] (numeric) = 2.681055880507149
absolute error = 4e-15
relative error = 1.491949507312527e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (closed_form) = 2.688344020399238
y[1] (numeric) = 2.688344020399235
absolute error = 3e-15
relative error = 1.115928607810573e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=689.1MB, alloc=44.3MB, time=8.33
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (closed_form) = 2.695563326462902
y[1] (numeric) = 2.695563326462899
absolute error = 3e-15
relative error = 1.112939907791585e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (closed_form) = 2.702713076773554
y[1] (numeric) = 2.702713076773551
absolute error = 3e-15
relative error = 1.109995739385455e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (closed_form) = 2.70979255636212
y[1] (numeric) = 2.709792556362119
absolute error = 1e-15
relative error = 3.690319384973490e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (closed_form) = 2.716801057286543
y[1] (numeric) = 2.716801057286542
absolute error = 1e-15
relative error = 3.680799509842539e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (closed_form) = 2.723737878702569
y[1] (numeric) = 2.723737878702566
absolute error = 3e-15
relative error = 1.101427572549318e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (closed_form) = 2.730602326933837
y[1] (numeric) = 2.730602326933834
absolute error = 3e-15
relative error = 1.098658699001647e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (closed_form) = 2.737393715541246
y[1] (numeric) = 2.737393715541241
absolute error = 5e-15
relative error = 1.826554934941605e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (closed_form) = 2.744111365391592
y[1] (numeric) = 2.744111365391588
absolute error = 4e-15
relative error = 1.457666788034745e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (closed_form) = 2.750754604725491
y[1] (numeric) = 2.750754604725485
absolute error = 6e-15
relative error = 2.181219651397717e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (closed_form) = 2.757322769224544
y[1] (numeric) = 2.757322769224536
absolute error = 8e-15
relative error = 2.901365081118117e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (closed_form) = 2.763815202077774
y[1] (numeric) = 2.763815202077767
absolute error = 7e-15
relative error = 2.532730840592221e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (closed_form) = 2.770231254047307
y[1] (numeric) = 2.770231254047298
absolute error = 9e-15
relative error = 3.248826243964652e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (closed_form) = 2.776570283533293
y[1] (numeric) = 2.776570283533283
absolute error = 1.0e-14
relative error = 3.601565593100929e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (closed_form) = 2.782831656638065
y[1] (numeric) = 2.782831656638054
absolute error = 1.1e-14
relative error = 3.952808274895465e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (closed_form) = 2.789014747229531
y[1] (numeric) = 2.789014747229521
absolute error = 1.0e-14
relative error = 3.585495562522036e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=731.9MB, alloc=44.3MB, time=8.83
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (closed_form) = 2.795118937003784
y[1] (numeric) = 2.795118937003773
absolute error = 1.1e-14
relative error = 3.935431818079056e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (closed_form) = 2.801143615546934
y[1] (numeric) = 2.801143615546922
absolute error = 1.2e-14
relative error = 4.283964568398952e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (closed_form) = 2.807088180396146
y[1] (numeric) = 2.807088180396133
absolute error = 1.3e-14
relative error = 4.631133460925120e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (closed_form) = 2.81295203709989
y[1] (numeric) = 2.812952037099877
absolute error = 1.3e-14
relative error = 4.621479438164470e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (closed_form) = 2.818734599277382
y[1] (numeric) = 2.81873459927737
absolute error = 1.2e-14
relative error = 4.257229468526888e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (closed_form) = 2.824435288677222
y[1] (numeric) = 2.824435288677212
absolute error = 1.0e-14
relative error = 3.540530753205302e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (closed_form) = 2.830053535235222
y[1] (numeric) = 2.830053535235212
absolute error = 1.0e-14
relative error = 3.533502061178798e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (closed_form) = 2.835588777131408
y[1] (numeric) = 2.835588777131397
absolute error = 1.1e-14
relative error = 3.879264895076933e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (closed_form) = 2.841040460846202
y[1] (numeric) = 2.841040460846191
absolute error = 1.1e-14
relative error = 3.871820958411714e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (closed_form) = 2.846408041215776
y[1] (numeric) = 2.846408041215765
absolute error = 1.1e-14
relative error = 3.864519717735764e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (closed_form) = 2.851690981486566
y[1] (numeric) = 2.851690981486554
absolute error = 1.2e-14
relative error = 4.208029578907770e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (closed_form) = 2.856888753368947
y[1] (numeric) = 2.856888753368934
absolute error = 1.3e-14
relative error = 4.550404696252148e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (closed_form) = 2.862000837090064
y[1] (numeric) = 2.862000837090051
absolute error = 1.3e-14
relative error = 4.542276798639142e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (closed_form) = 2.867026721445802
y[1] (numeric) = 2.867026721445791
absolute error = 1.1e-14
relative error = 3.836727407428157e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=774.6MB, alloc=44.3MB, time=9.33
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (closed_form) = 2.871965903851917
y[1] (numeric) = 2.871965903851906
absolute error = 1.1e-14
relative error = 3.830129036436909e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (closed_form) = 2.876817890394281
y[1] (numeric) = 2.876817890394272
absolute error = 9e-15
relative error = 3.128456629128689e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (closed_form) = 2.881582195878286
y[1] (numeric) = 2.881582195878275
absolute error = 1.1e-14
relative error = 3.817347294737597e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (closed_form) = 2.886258343877352
y[1] (numeric) = 2.886258343877343
absolute error = 9e-15
relative error = 3.118223986806929e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (closed_form) = 2.890845866780576
y[1] (numeric) = 2.890845866780569
absolute error = 7e-15
relative error = 2.421436604572637e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (closed_form) = 2.895344305839492
y[1] (numeric) = 2.895344305839483
absolute error = 9e-15
relative error = 3.108438599806005e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (closed_form) = 2.899753211213941
y[1] (numeric) = 2.899753211213933
absolute error = 8e-15
relative error = 2.758855467100565e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (closed_form) = 2.904072142017061
y[1] (numeric) = 2.904072142017053
absolute error = 8e-15
relative error = 2.754752502272032e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (closed_form) = 2.90830066635937
y[1] (numeric) = 2.908300666359361
absolute error = 9e-15
relative error = 3.094590632978212e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (closed_form) = 2.912438361391958
y[1] (numeric) = 2.912438361391948
absolute error = 1.0e-14
relative error = 3.433549060664290e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (closed_form) = 2.916484813348769
y[1] (numeric) = 2.916484813348762
absolute error = 7e-15
relative error = 2.400149648632133e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (closed_form) = 2.920439617587981
y[1] (numeric) = 2.920439617587972
absolute error = 9e-15
relative error = 3.081727814469654e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (closed_form) = 2.924302378632464
y[1] (numeric) = 2.924302378632456
absolute error = 8e-15
relative error = 2.735695206643152e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (closed_form) = 2.928072710209333
y[1] (numeric) = 2.928072710209325
absolute error = 8e-15
relative error = 2.732172589876727e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (closed_form) = 2.931750235288572
y[1] (numeric) = 2.931750235288563
absolute error = 9e-15
relative error = 3.069838587090326e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=817.4MB, alloc=44.3MB, time=9.81
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (closed_form) = 2.935334586120739
y[1] (numeric) = 2.93533458612073
absolute error = 9e-15
relative error = 3.066089992791644e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (closed_form) = 2.938825404273736
y[1] (numeric) = 2.938825404273728
absolute error = 8e-15
relative error = 2.722176005544984e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (closed_form) = 2.942222340668658
y[1] (numeric) = 2.942222340668651
absolute error = 7e-15
relative error = 2.379153982771118e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (closed_form) = 2.945525055614696
y[1] (numeric) = 2.94552505561469
absolute error = 6e-15
relative error = 2.036988274319015e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (closed_form) = 2.948733218843107
y[1] (numeric) = 2.948733218843102
absolute error = 5e-15
relative error = 1.695643392914900e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (closed_form) = 2.951846509540242
y[1] (numeric) = 2.951846509540238
absolute error = 4e-15
relative error = 1.355084008288429e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (closed_form) = 2.954864616379626
y[1] (numeric) = 2.954864616379621
absolute error = 5e-15
relative error = 1.692124902198100e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (closed_form) = 2.95778723755309
y[1] (numeric) = 2.957787237553085
absolute error = 5e-15
relative error = 1.690452895501837e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (closed_form) = 2.960614080800952
y[1] (numeric) = 2.960614080800947
absolute error = 5e-15
relative error = 1.688838823142840e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (closed_form) = 2.963344863441243
y[1] (numeric) = 2.963344863441239
absolute error = 4e-15
relative error = 1.349826019019238e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (closed_form) = 2.965979312397975
y[1] (numeric) = 2.96597931239797
absolute error = 5e-15
relative error = 1.685783841815651e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (closed_form) = 2.968517164228447
y[1] (numeric) = 2.968517164228443
absolute error = 4e-15
relative error = 1.347474101952733e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (closed_form) = 2.97095816514959
y[1] (numeric) = 2.970958165149587
absolute error = 3e-15
relative error = 1.009775241937460e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (closed_form) = 2.973302071063349
y[1] (numeric) = 2.973302071063345
absolute error = 4e-15
relative error = 1.345305624655039e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=860.1MB, alloc=44.3MB, time=10.33
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (closed_form) = 2.975548647581083
y[1] (numeric) = 2.97554864758108
absolute error = 3e-15
relative error = 1.008217426537050e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (closed_form) = 2.977697670047013
y[1] (numeric) = 2.97769767004701
absolute error = 3e-15
relative error = 1.007489789906252e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (closed_form) = 2.979748923560684
y[1] (numeric) = 2.979748923560681
absolute error = 3e-15
relative error = 1.006796235843628e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (closed_form) = 2.981702202998454
y[1] (numeric) = 2.981702202998451
absolute error = 3e-15
relative error = 1.006136695000307e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (closed_form) = 2.983557313034006
y[1] (numeric) = 2.983557313034002
absolute error = 4e-15
relative error = 1.340681468569600e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (closed_form) = 2.985314068157884
y[1] (numeric) = 2.985314068157881
absolute error = 3e-15
relative error = 1.004919392568695e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (closed_form) = 2.986972292696038
y[1] (numeric) = 2.986972292696034
absolute error = 4e-15
relative error = 1.339148679008872e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (closed_form) = 2.988531820827396
y[1] (numeric) = 2.988531820827392
absolute error = 4e-15
relative error = 1.338449860939601e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (closed_form) = 2.989992496600446
y[1] (numeric) = 2.98999249660044
absolute error = 6e-15
relative error = 2.006693999005638e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (closed_form) = 2.991354173948826
y[1] (numeric) = 2.99135417394882
absolute error = 6e-15
relative error = 2.005780543224516e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (closed_form) = 2.992616716705937
y[1] (numeric) = 2.992616716705932
absolute error = 5e-15
relative error = 1.670778610601243e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (closed_form) = 2.993779998618556
y[1] (numeric) = 2.99377999861855
absolute error = 6e-15
relative error = 2.004155282876039e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (closed_form) = 2.99484390335946
y[1] (numeric) = 2.994843903359454
absolute error = 6e-15
relative error = 2.003443315783341e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (closed_form) = 2.995808324539061
y[1] (numeric) = 2.995808324539055
absolute error = 6e-15
relative error = 2.002798360246618e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (closed_form) = 2.996673165716047
y[1] (numeric) = 2.99667316571604
absolute error = 7e-15
relative error = 2.335923743731782e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=902.9MB, alloc=44.3MB, time=10.83
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (closed_form) = 2.997438340407018
y[1] (numeric) = 2.997438340407013
absolute error = 5e-15
relative error = 1.668091027127203e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (closed_form) = 2.998103772095146
y[1] (numeric) = 2.99810377209514
absolute error = 6e-15
relative error = 2.001264951482002e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (closed_form) = 2.998669394237814
y[1] (numeric) = 2.998669394237808
absolute error = 6e-15
relative error = 2.000887464129752e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (closed_form) = 2.99913515027328
y[1] (numeric) = 2.999135150273273
absolute error = 7e-15
relative error = 2.334006188204677e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (closed_form) = 2.999500993626328
y[1] (numeric) = 2.999500993626322
absolute error = 6e-15
relative error = 2.000332726259956e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (closed_form) = 2.999766887712928
y[1] (numeric) = 2.999766887712923
absolute error = 5e-15
relative error = 1.666796183556811e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (closed_form) = 2.999932805943894
y[1] (numeric) = 2.999932805943888
absolute error = 6e-15
relative error = 2.000044797040769e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (closed_form) = 2.99999873172754
y[1] (numeric) = 2.999998731727534
absolute error = 6e-15
relative error = 2.000000845515331e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (closed_form) = 2.999964658471342
y[1] (numeric) = 2.999964658471338
absolute error = 4e-15
relative error = 1.333349040864446e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (closed_form) = 2.999830589582598
y[1] (numeric) = 2.999830589582594
absolute error = 4e-15
relative error = 1.333408631104254e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (closed_form) = 2.999596538468086
y[1] (numeric) = 2.999596538468081
absolute error = 5e-15
relative error = 1.666890842110897e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (closed_form) = 2.999262528532721
y[1] (numeric) = 2.999262528532717
absolute error = 4e-15
relative error = 1.333661179022182e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (closed_form) = 2.998828593177219
y[1] (numeric) = 2.998828593177214
absolute error = 5e-15
relative error = 1.667317702444129e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (closed_form) = 2.998294775794753
y[1] (numeric) = 2.998294775794749
absolute error = 4e-15
relative error = 1.334091641786531e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
memory used=945.5MB, alloc=44.3MB, time=11.33
x[1] = 3.21
y[1] (closed_form) = 2.997661129766618
y[1] (numeric) = 2.997661129766614
absolute error = 4e-15
relative error = 1.334373642264034e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (closed_form) = 2.996927718456887
y[1] (numeric) = 2.996927718456883
absolute error = 4e-15
relative error = 1.334700191588068e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (closed_form) = 2.996094615206081
y[1] (numeric) = 2.996094615206077
absolute error = 4e-15
relative error = 1.335071322413784e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (closed_form) = 2.99516190332383
y[1] (numeric) = 2.995161903323827
absolute error = 3e-15
relative error = 1.001615303890852e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (closed_form) = 2.994129676080546
y[1] (numeric) = 2.994129676080541
absolute error = 5e-15
relative error = 1.669934351856540e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (closed_form) = 2.992998036698093
y[1] (numeric) = 2.992998036698088
absolute error = 5e-15
relative error = 1.670565746683901e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (closed_form) = 2.991767098339465
y[1] (numeric) = 2.99176709833946
absolute error = 5e-15
relative error = 1.671253087439585e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (closed_form) = 2.990436984097473
y[1] (numeric) = 2.990436984097467
absolute error = 6e-15
relative error = 2.006395731428805e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (closed_form) = 2.989007826982433
y[1] (numeric) = 2.989007826982428
absolute error = 5e-15
relative error = 1.672795887271989e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (closed_form) = 2.987479769908865
y[1] (numeric) = 2.98747976990886
absolute error = 5e-15
relative error = 1.673651500626740e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (closed_form) = 2.985852965681203
y[1] (numeric) = 2.985852965681199
absolute error = 4e-15
relative error = 1.339650694784773e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (closed_form) = 2.984127576978514
y[1] (numeric) = 2.98412757697851
absolute error = 4e-15
relative error = 1.340425265614842e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (closed_form) = 2.982303776338232
y[1] (numeric) = 2.982303776338227
absolute error = 5e-15
relative error = 1.676556238056728e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (closed_form) = 2.980381746138899
y[1] (numeric) = 2.980381746138894
absolute error = 5e-15
relative error = 1.677637439055426e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (closed_form) = 2.978361678581934
y[1] (numeric) = 2.978361678581931
absolute error = 3e-15
relative error = 1.007265175876279e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=988.3MB, alloc=44.3MB, time=11.84
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (closed_form) = 2.97624377567241
y[1] (numeric) = 2.976243775672408
absolute error = 2e-15
relative error = 6.719879656188944e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (closed_form) = 2.974028249198852
y[1] (numeric) = 2.97402824919885
absolute error = 2e-15
relative error = 6.724885685059524e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (closed_form) = 2.971715320712062
y[1] (numeric) = 2.971715320712059
absolute error = 3e-15
relative error = 1.009517963948566e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (closed_form) = 2.969305221502961
y[1] (numeric) = 2.969305221502958
absolute error = 3e-15
relative error = 1.010337360495902e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (closed_form) = 2.966798192579461
y[1] (numeric) = 2.966798192579458
absolute error = 3e-15
relative error = 1.011191124325066e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (closed_form) = 2.964194484642366
y[1] (numeric) = 2.964194484642363
absolute error = 3e-15
relative error = 1.012079340793306e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (closed_form) = 2.961494358060299
y[1] (numeric) = 2.961494358060296
absolute error = 3e-15
relative error = 1.013002098698888e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (closed_form) = 2.958698082843669
y[1] (numeric) = 2.958698082843666
absolute error = 3e-15
relative error = 1.013959490289268e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (closed_form) = 2.955805938617666
y[1] (numeric) = 2.955805938617663
absolute error = 3e-15
relative error = 1.014951611269515e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (closed_form) = 2.952818214594305
y[1] (numeric) = 2.952818214594302
absolute error = 3e-15
relative error = 1.015978560810990e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (closed_form) = 2.949735209543496
y[1] (numeric) = 2.949735209543494
absolute error = 2e-15
relative error = 6.780269610401816e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (closed_form) = 2.946557231763177
y[1] (numeric) = 2.946557231763174
absolute error = 3e-15
relative error = 1.018137359648312e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (closed_form) = 2.943284599048476
y[1] (numeric) = 2.943284599048473
absolute error = 3e-15
relative error = 1.019269424699827e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (closed_form) = 2.939917638659938
y[1] (numeric) = 2.939917638659936
absolute error = 2e-15
relative error = 6.802911665619423e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (closed_form) = 2.936456687290796
y[1] (numeric) = 2.936456687290794
absolute error = 2e-15
relative error = 6.810929678125850e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
memory used=1031.1MB, alloc=44.3MB, time=12.34
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (closed_form) = 2.932902091033304
y[1] (numeric) = 2.932902091033301
absolute error = 3e-15
relative error = 1.022877650492266e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (closed_form) = 2.929254205344123
y[1] (numeric) = 2.92925420534412
absolute error = 3e-15
relative error = 1.024151469861103e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (closed_form) = 2.925513395008784
y[1] (numeric) = 2.925513395008781
absolute error = 3e-15
relative error = 1.025461037067305e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (closed_form) = 2.921680034105203
y[1] (numeric) = 2.9216800341052
absolute error = 3e-15
relative error = 1.026806482907285e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (closed_form) = 2.917754505966276
y[1] (numeric) = 2.917754505966273
absolute error = 3e-15
relative error = 1.028187941742716e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (closed_form) = 2.913737203141545
y[1] (numeric) = 2.913737203141543
absolute error = 2e-15
relative error = 6.864037010076378e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (closed_form) = 2.909628527357944
y[1] (numeric) = 2.909628527357943
absolute error = 1e-15
relative error = 3.436864845795415e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (closed_form) = 2.90542888947963
y[1] (numeric) = 2.905428889479628
absolute error = 2e-15
relative error = 6.883665290318653e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (closed_form) = 2.901138709466888
y[1] (numeric) = 2.901138709466887
absolute error = 1e-15
relative error = 3.446922398907840e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (closed_form) = 2.896758416334147
y[1] (numeric) = 2.896758416334145
absolute error = 2e-15
relative error = 6.904269229779277e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (closed_form) = 2.892288448107068
y[1] (numeric) = 2.892288448107067
absolute error = 1e-15
relative error = 3.457469813062648e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (closed_form) = 2.88772925177875
y[1] (numeric) = 2.887729251778749
absolute error = 1e-15
relative error = 3.462928525532758e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (closed_form) = 2.883081283265026
y[1] (numeric) = 2.883081283265025
absolute error = 1e-15
relative error = 3.468511296592797e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (closed_form) = 2.878345007358874
y[1] (numeric) = 2.878345007358873
absolute error = 1e-15
relative error = 3.474218682761678e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
memory used=1073.9MB, alloc=44.3MB, time=12.84
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (closed_form) = 2.873520897683938
y[1] (numeric) = 2.873520897683938
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (closed_form) = 2.868609436647165
y[1] (numeric) = 2.868609436647164
absolute error = 1e-15
relative error = 3.486009587867777e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (closed_form) = 2.863611115390566
y[1] (numeric) = 2.863611115390566
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (closed_form) = 2.858526433742102
y[1] (numeric) = 2.858526433742101
absolute error = 1e-15
relative error = 3.498305939018021e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (closed_form) = 2.8533559001657
y[1] (numeric) = 2.853355900165698
absolute error = 2e-15
relative error = 7.009290358359629e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (closed_form) = 2.848100031710408
y[1] (numeric) = 2.848100031710406
absolute error = 2e-15
relative error = 7.022225265026639e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (closed_form) = 2.842759353958694
y[1] (numeric) = 2.842759353958691
absolute error = 3e-15
relative error = 1.055312682665995e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (closed_form) = 2.83733440097388
y[1] (numeric) = 2.837334400973876
absolute error = 4e-15
relative error = 1.409773905616148e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (closed_form) = 2.831825715246746
y[1] (numeric) = 2.831825715246741
absolute error = 5e-15
relative error = 1.765645383146164e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (closed_form) = 2.826233847641272
y[1] (numeric) = 2.82623384764127
absolute error = 2e-15
relative error = 7.076555259817467e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (closed_form) = 2.820559357339561
y[1] (numeric) = 2.820559357339558
absolute error = 3e-15
relative error = 1.063618814542408e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (closed_form) = 2.814802811785912
y[1] (numeric) = 2.814802811785911
absolute error = 1e-15
relative error = 3.552646728264168e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (closed_form) = 2.808964786630086
y[1] (numeric) = 2.808964786630084
absolute error = 2e-15
relative error = 7.120060776551775e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (closed_form) = 2.803045865669731
y[1] (numeric) = 2.803045865669728
absolute error = 3e-15
relative error = 1.070264328080558e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (closed_form) = 2.797046640792012
y[1] (numeric) = 2.797046640792008
absolute error = 4e-15
relative error = 1.430079835517995e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=1116.7MB, alloc=44.3MB, time=13.34
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (closed_form) = 2.790967711914417
y[1] (numeric) = 2.790967711914414
absolute error = 3e-15
relative error = 1.074895989370726e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (closed_form) = 2.784809686924768
y[1] (numeric) = 2.784809686924766
absolute error = 2e-15
relative error = 7.181819315662379e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (closed_form) = 2.778573181620432
y[1] (numeric) = 2.778573181620429
absolute error = 3e-15
relative error = 1.079690835513799e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (closed_form) = 2.772258819646744
y[1] (numeric) = 2.772258819646741
absolute error = 3e-15
relative error = 1.082150042679737e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (closed_form) = 2.765867232434637
y[1] (numeric) = 2.765867232434635
absolute error = 2e-15
relative error = 7.231005076984526e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (closed_form) = 2.759399059137508
y[1] (numeric) = 2.759399059137506
absolute error = 2e-15
relative error = 7.247954924740499e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (closed_form) = 2.752854946567295
y[1] (numeric) = 2.752854946567292
absolute error = 3e-15
relative error = 1.089777724663948e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (closed_form) = 2.746235549129803
y[1] (numeric) = 2.7462355491298
absolute error = 3e-15
relative error = 1.092404473808012e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (closed_form) = 2.739541528759258
y[1] (numeric) = 2.739541528759254
absolute error = 4e-15
relative error = 1.460098325945658e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (closed_form) = 2.732773554852121
y[1] (numeric) = 2.732773554852115
absolute error = 6e-15
relative error = 2.195571597707692e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (closed_form) = 2.72593230420014
y[1] (numeric) = 2.725932304200135
absolute error = 5e-15
relative error = 1.834234838589336e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (closed_form) = 2.719018460922681
y[1] (numeric) = 2.719018460922677
absolute error = 4e-15
relative error = 1.471119103267370e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (closed_form) = 2.71203271639831
y[1] (numeric) = 2.712032716398305
absolute error = 5e-15
relative error = 1.843635576284715e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (closed_form) = 2.704975769195658
y[1] (numeric) = 2.704975769195652
absolute error = 6e-15
relative error = 2.218134472156155e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=1159.5MB, alloc=44.3MB, time=13.84
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (closed_form) = 2.697848325003564
y[1] (numeric) = 2.697848325003559
absolute error = 5e-15
relative error = 1.853328800459305e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (closed_form) = 2.690651096560508
y[1] (numeric) = 2.690651096560502
absolute error = 6e-15
relative error = 2.229943528415807e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (closed_form) = 2.683384803583336
y[1] (numeric) = 2.683384803583331
absolute error = 5e-15
relative error = 1.863318296102409e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (closed_form) = 2.676050172695292
y[1] (numeric) = 2.676050172695288
absolute error = 4e-15
relative error = 1.494740285818796e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (closed_form) = 2.668647937353351
y[1] (numeric) = 2.668647937353349
absolute error = 2e-15
relative error = 7.494431813225663e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (closed_form) = 2.66117883777488
y[1] (numeric) = 2.661178837774877
absolute error = 3e-15
relative error = 1.127319952126337e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (closed_form) = 2.653643620863612
y[1] (numeric) = 2.65364362086361
absolute error = 2e-15
relative error = 7.536807068875030e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (closed_form) = 2.646043040134959
y[1] (numeric) = 2.646043040134956
absolute error = 3e-15
relative error = 1.133768406067570e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (closed_form) = 2.638377855640659
y[1] (numeric) = 2.638377855640657
absolute error = 2e-15
relative error = 7.580415351516638e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (closed_form) = 2.630648833892776
y[1] (numeric) = 2.630648833892773
absolute error = 3e-15
relative error = 1.140403067619127e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (closed_form) = 2.622856747787042
y[1] (numeric) = 2.622856747787041
absolute error = 1e-15
relative error = 3.812636739859012e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (closed_form) = 2.615002376525574
y[1] (numeric) = 2.615002376525573
absolute error = 1e-15
relative error = 3.824088302851377e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (closed_form) = 2.607086505538955
y[1] (numeric) = 2.607086505538952
absolute error = 3e-15
relative error = 1.150709803309660e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (closed_form) = 2.599109926407685
y[1] (numeric) = 2.599109926407682
absolute error = 3e-15
relative error = 1.154241292189745e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (closed_form) = 2.591073436783031
y[1] (numeric) = 2.591073436783027
absolute error = 4e-15
relative error = 1.543761725629141e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=1202.5MB, alloc=44.3MB, time=14.34
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (closed_form) = 2.582977840307259
y[1] (numeric) = 2.582977840307255
absolute error = 4e-15
relative error = 1.548600199963070e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (closed_form) = 2.574823946533269
y[1] (numeric) = 2.574823946533266
absolute error = 3e-15
relative error = 1.165128203828920e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (closed_form) = 2.566612570843644
y[1] (numeric) = 2.566612570843639
absolute error = 5e-15
relative error = 1.948093006634228e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (closed_form) = 2.55834453436911
y[1] (numeric) = 2.558344534369104
absolute error = 6e-15
relative error = 2.345266604788868e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (closed_form) = 2.550020663906425
y[1] (numeric) = 2.55002066390642
absolute error = 5e-15
relative error = 1.960768424652844e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (closed_form) = 2.541641791835698
y[1] (numeric) = 2.541641791835693
absolute error = 5e-15
relative error = 1.967232367700704e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (closed_form) = 2.533208756037155
y[1] (numeric) = 2.533208756037148
absolute error = 7e-15
relative error = 2.763293780395148e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (closed_form) = 2.524722399807346
y[1] (numeric) = 2.524722399807338
absolute error = 8e-15
relative error = 3.168665196859051e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (closed_form) = 2.516183571774825
y[1] (numeric) = 2.516183571774817
absolute error = 8e-15
relative error = 3.179418262538408e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (closed_form) = 2.507593125815277
y[1] (numeric) = 2.507593125815269
absolute error = 8e-15
relative error = 3.190310229215919e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (closed_form) = 2.498951920966141
y[1] (numeric) = 2.498951920966132
absolute error = 9e-15
relative error = 3.601509866792649e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (closed_form) = 2.4902608213407
y[1] (numeric) = 2.49026082134069
absolute error = 1.0e-14
relative error = 4.015643628291203e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (closed_form) = 2.481520696041674
y[1] (numeric) = 2.481520696041663
absolute error = 1.1e-14
relative error = 4.432765770419055e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (closed_form) = 2.47273241907431
y[1] (numeric) = 2.472732419074299
absolute error = 1.1e-14
relative error = 4.448520153311999e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=1245.2MB, alloc=44.3MB, time=14.84
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (closed_form) = 2.46389686925898
y[1] (numeric) = 2.46389686925897
absolute error = 1.0e-14
relative error = 4.058611431657654e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (closed_form) = 2.455014930143305
y[1] (numeric) = 2.455014930143294
absolute error = 1.1e-14
relative error = 4.480624482132133e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (closed_form) = 2.446087489913793
y[1] (numeric) = 2.446087489913783
absolute error = 1.0e-14
relative error = 4.088161213053106e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (closed_form) = 2.437115441307028
y[1] (numeric) = 2.437115441307018
absolute error = 1.0e-14
relative error = 4.103211456670673e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (closed_form) = 2.428099681520394
y[1] (numeric) = 2.428099681520385
absolute error = 9e-15
relative error = 3.706602355947967e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (closed_form) = 2.419041112122356
y[1] (numeric) = 2.419041112122347
absolute error = 9e-15
relative error = 3.720482448561534e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (closed_form) = 2.409940638962306
y[1] (numeric) = 2.409940638962296
absolute error = 1.0e-14
relative error = 4.149479799762159e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (closed_form) = 2.400799172079975
y[1] (numeric) = 2.400799172079964
absolute error = 1.1e-14
relative error = 4.581807644689395e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (closed_form) = 2.391617625614435
y[1] (numeric) = 2.391617625614425
absolute error = 1.0e-14
relative error = 4.181270405812000e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (closed_form) = 2.38239691771268
y[1] (numeric) = 2.382396917712669
absolute error = 1.1e-14
relative error = 4.617198720421873e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (closed_form) = 2.373137970437818
y[1] (numeric) = 2.373137970437808
absolute error = 1.0e-14
relative error = 4.213830010968603e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (closed_form) = 2.363841709676858
y[1] (numeric) = 2.36384170967685
absolute error = 8e-15
relative error = 3.384321364349568e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (closed_form) = 2.354509065048132
y[1] (numeric) = 2.354509065048123
absolute error = 9e-15
relative error = 3.822452898399020e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (closed_form) = 2.345140969808323
y[1] (numeric) = 2.345140969808316
absolute error = 7e-15
relative error = 2.984895189721638e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=1288.0MB, alloc=44.3MB, time=15.34
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (closed_form) = 2.335738360759151
y[1] (numeric) = 2.335738360759144
absolute error = 7e-15
relative error = 2.996911005787862e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (closed_form) = 2.326302178153683
y[1] (numeric) = 2.326302178153677
absolute error = 6e-15
relative error = 2.579200611316120e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (closed_form) = 2.316833365602318
y[1] (numeric) = 2.316833365602311
absolute error = 7e-15
relative error = 3.021365327316139e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (closed_form) = 2.30733286997842
y[1] (numeric) = 2.307332869978413
absolute error = 7e-15
relative error = 3.033805867839723e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (closed_form) = 2.297801641323633
y[1] (numeric) = 2.297801641323628
absolute error = 5e-15
relative error = 2.175992875137727e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (closed_form) = 2.288240632752882
y[1] (numeric) = 2.288240632752875
absolute error = 7e-15
relative error = 3.059118826842353e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (closed_form) = 2.278650800359054
y[1] (numeric) = 2.278650800359047
absolute error = 7e-15
relative error = 3.071993303623788e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (closed_form) = 2.269033103117399
y[1] (numeric) = 2.269033103117393
absolute error = 6e-15
relative error = 2.644298133754271e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (closed_form) = 2.259388502789626
y[1] (numeric) = 2.259388502789619
absolute error = 7e-15
relative error = 3.098183420583590e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (closed_form) = 2.249717963827731
y[1] (numeric) = 2.249717963827724
absolute error = 7e-15
relative error = 3.111501135942396e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (closed_form) = 2.24002245327755
y[1] (numeric) = 2.240022453277543
absolute error = 7e-15
relative error = 3.124968675987046e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (closed_form) = 2.230302940682059
y[1] (numeric) = 2.230302940682052
absolute error = 7e-15
relative error = 3.138587082640575e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (closed_form) = 2.220560397984419
y[1] (numeric) = 2.220560397984412
absolute error = 7e-15
relative error = 3.152357398769172e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (closed_form) = 2.21079579943078
y[1] (numeric) = 2.210795799430773
absolute error = 7e-15
relative error = 3.166280667713549e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (closed_form) = 2.20101012147286
y[1] (numeric) = 2.201010121472855
absolute error = 5e-15
relative error = 2.271684237714512e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=1330.8MB, alloc=44.3MB, time=15.84
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (closed_form) = 2.191204342670301
y[1] (numeric) = 2.191204342670297
absolute error = 4e-15
relative error = 1.825480135332982e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (closed_form) = 2.181379443592812
y[1] (numeric) = 2.181379443592807
absolute error = 5e-15
relative error = 2.292127586828643e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (closed_form) = 2.171536406722112
y[1] (numeric) = 2.171536406722108
absolute error = 4e-15
relative error = 1.842013786928820e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (closed_form) = 2.161676216353686
y[1] (numeric) = 2.161676216353683
absolute error = 3e-15
relative error = 1.387811910638679e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (closed_form) = 2.151799858498355
y[1] (numeric) = 2.151799858498352
absolute error = 3e-15
relative error = 1.394181707072686e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (closed_form) = 2.141908320783674
y[1] (numeric) = 2.14190832078367
absolute error = 4e-15
relative error = 1.867493562253166e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (closed_form) = 2.13200259235517
y[1] (numeric) = 2.132002592355167
absolute error = 3e-15
relative error = 1.407127744946114e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (closed_form) = 2.122083663777433
y[1] (numeric) = 2.122083663777429
absolute error = 4e-15
relative error = 1.884939820364936e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (closed_form) = 2.112152526935054
y[1] (numeric) = 2.11215252693505
absolute error = 4e-15
relative error = 1.893802625042616e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (closed_form) = 2.102210174933442
y[1] (numeric) = 2.102210174933437
absolute error = 5e-15
relative error = 2.378449148243850e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (closed_form) = 2.092257601999512
y[1] (numeric) = 2.092257601999506
absolute error = 6e-15
relative error = 2.867715712570942e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (closed_form) = 2.082295803382262
y[1] (numeric) = 2.082295803382255
absolute error = 7e-15
relative error = 3.361674162061863e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (closed_form) = 2.072325775253254
y[1] (numeric) = 2.072325775253248
absolute error = 6e-15
relative error = 2.895297675514727e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (closed_form) = 2.062348514606992
y[1] (numeric) = 2.062348514606986
absolute error = 6e-15
relative error = 2.909304590132953e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=1373.7MB, alloc=44.3MB, time=16.34
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (closed_form) = 2.052365019161226
y[1] (numeric) = 2.052365019161219
absolute error = 7e-15
relative error = 3.410699332061704e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (closed_form) = 2.042376287257181
y[1] (numeric) = 2.042376287257176
absolute error = 5e-15
relative error = 2.448128697535347e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (closed_form) = 2.032383317759724
y[1] (numeric) = 2.032383317759719
absolute error = 5e-15
relative error = 2.460165834027535e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (closed_form) = 2.022387109957478
y[1] (numeric) = 2.022387109957473
absolute error = 5e-15
relative error = 2.472325884288853e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (closed_form) = 2.012388663462891
y[1] (numeric) = 2.012388663462887
absolute error = 4e-15
relative error = 1.987687603604790e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (closed_form) = 2.002388978112282
y[1] (numeric) = 2.002388978112278
absolute error = 4e-15
relative error = 1.997613872091391e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (closed_form) = 1.992389053865852
y[1] (numeric) = 1.992389053865849
absolute error = 3e-15
relative error = 1.505730015018438e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (closed_form) = 1.982389890707693
y[1] (numeric) = 1.982389890707691
absolute error = 2e-15
relative error = 1.008883272344584e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (closed_form) = 1.972392488545789
y[1] (numeric) = 1.972392488545787
absolute error = 2e-15
relative error = 1.013996966432662e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (closed_form) = 1.962397847112023
y[1] (numeric) = 1.962397847112023
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (closed_form) = 1.952406965862212
y[1] (numeric) = 1.952406965862211
absolute error = 1e-15
relative error = 5.121882975655053e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (closed_form) = 1.942420843876154
y[1] (numeric) = 1.942420843876153
absolute error = 1e-15
relative error = 5.148214935772995e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (closed_form) = 1.932440479757725
y[1] (numeric) = 1.932440479757726
absolute error = 1e-15
relative error = 5.174803625130915e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (closed_form) = 1.922466871535021
y[1] (numeric) = 1.922466871535021
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (closed_form) = 1.912501016560553
y[1] (numeric) = 1.912501016560554
absolute error = 1e-15
relative error = 5.228755390668512e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
memory used=1416.4MB, alloc=44.3MB, time=16.84
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (closed_form) = 1.902543911411514
y[1] (numeric) = 1.902543911411514
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (closed_form) = 1.89259655179012
y[1] (numeric) = 1.892596551790118
absolute error = 2e-15
relative error = 1.056749257050211e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (closed_form) = 1.882659932424045
y[1] (numeric) = 1.882659932424044
absolute error = 1e-15
relative error = 5.311633730433919e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (closed_form) = 1.872735046966944
y[1] (numeric) = 1.872735046966943
absolute error = 1e-15
relative error = 5.339783658236045e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (closed_form) = 1.862822887899092
y[1] (numeric) = 1.862822887899092
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (closed_form) = 1.852924446428137
y[1] (numeric) = 1.852924446428136
absolute error = 1e-15
relative error = 5.396874124725860e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (closed_form) = 1.843040712389977
y[1] (numeric) = 1.843040712389974
absolute error = 3e-15
relative error = 1.627744834844005e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (closed_form) = 1.833172674149778
y[1] (numeric) = 1.833172674149776
absolute error = 2e-15
relative error = 1.091004698140395e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (closed_form) = 1.823321318503142
y[1] (numeric) = 1.823321318503141
absolute error = 1e-15
relative error = 5.484496834715624e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (closed_form) = 1.813487630577425
y[1] (numeric) = 1.813487630577424
absolute error = 1e-15
relative error = 5.514236673792995e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (closed_form) = 1.803672593733223
y[1] (numeric) = 1.803672593733222
absolute error = 1e-15
relative error = 5.544243470097920e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (closed_form) = 1.793877189466042
y[1] (numeric) = 1.793877189466039
absolute error = 3e-15
relative error = 1.672355285867126e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (closed_form) = 1.784102397308146
y[1] (numeric) = 1.784102397308143
absolute error = 3e-15
relative error = 1.681517834697381e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (closed_form) = 1.774349194730605
y[1] (numeric) = 1.774349194730601
absolute error = 4e-15
relative error = 2.254347685269083e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
memory used=1459.2MB, alloc=44.3MB, time=17.33
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (closed_form) = 1.764618557045549
y[1] (numeric) = 1.764618557045544
absolute error = 5e-15
relative error = 2.833473545904084e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (closed_form) = 1.754911457308638
y[1] (numeric) = 1.754911457308632
absolute error = 6e-15
relative error = 3.418975911868341e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (closed_form) = 1.745228866221757
y[1] (numeric) = 1.745228866221752
absolute error = 5e-15
relative error = 2.864953758657735e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (closed_form) = 1.735571752035945
y[1] (numeric) = 1.73557175203594
absolute error = 5e-15
relative error = 2.880895010036120e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (closed_form) = 1.725941080454573
y[1] (numeric) = 1.725941080454568
absolute error = 5e-15
relative error = 2.896970271246522e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.001
Finished!
diff ( y , x , 1 ) = sin ( x ) ;
Iterations = 5000
Total Elapsed Time = 17 Seconds
Elapsed Time(since restart) = 17 Seconds
Time to Timeout = 2 Minutes 42 Seconds
Percent Done = 100 %
> quit
memory used=1475.3MB, alloc=44.3MB, time=17.52