|\^/| 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.
| Type ? for help.
#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(0.0));
> end;
exact_soln_y := proc(x) return c(0.) end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]);
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if (rad_given < glob_least_given_sing) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])*
(array_x[1] - array_given_rad_poles[1, 1])
+ array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if rad_given < glob_least_given_sing then
glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if array_rad_test_poles[1, 1] < glob_least_ratio_sing then
glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_float(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if array_rad_test_poles[1, 2] < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if array_rad_test_poles[1, 3] < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_c1,
> array_tmp2_a1,
> array_tmp2_a2,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y[1]) < min_size) then # if number 3
> min_size := float_abs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < glob__1) then # if number 3
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2_c1, array_tmp2_a1, array_tmp2_a2, array_tmp2, array_tmp3,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y[1]) < min_size then
min_size := float_abs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_c1,
> array_tmp2_a1,
> array_tmp2_a2,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2_c1, array_tmp2_a1, array_tmp2_a2, array_tmp2, array_tmp3,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := float_abs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_c1,
> array_tmp2_a1,
> array_tmp2_a2,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
> est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
> fi;# end if 3;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 3
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2_c1, array_tmp2_a1, array_tmp2_a2, array_tmp2, array_tmp3,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y[no_terms - 3]))
+ c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_c1,
> array_tmp2_a1,
> array_tmp2_a2,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2_c1, array_tmp2_a1, array_tmp2_a2, array_tmp2, array_tmp3,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_c1,
> array_tmp2_a1,
> array_tmp2_a2,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 3
> if (iter >= 0) then # if number 4
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> closed_form_val_y := evalf(exact_soln_y(ind_var));
> omniout_float(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := float_abs(numeric_val - closed_form_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 5
> relerr := abserr*glob__100/float_abs(closed_form_val_y);
> if (c(relerr) > c(glob_prec)) then # if number 6
> glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 6;
> else
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 5;
> if (glob_good_digits < glob_min_good_digits) then # if number 5
> glob_min_good_digits := glob_good_digits;
> fi;# end if 5;
> if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 5
> glob_min_apfp_est_good_digits := glob_apfp_est_good_digits;
> fi;# end if 5;
> if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 5
> est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*22*ATS_MAX_TERMS/float_abs(numeric_val));
> if (evalf(est_rel_err) > glob_prec) then # if number 6
> glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
> else
> glob_est_digits := Digits;
> fi;# end if 6;
> else
> relerr := glob__m1 ;
> glob_est_digits := -16;
> fi;# end if 5;
> array_est_digits[1] := glob_est_digits;
> if (glob_iter = 1) then # if number 5
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 5;
> array_est_rel_error[1] := est_rel_err;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," ");
> omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," ");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 4;
> #BOTTOM DISPLAY ALOT
> fi;# end if 3;
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2_c1, array_tmp2_a1, array_tmp2_a2, array_tmp2, array_tmp3,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
closed_form_val_y := evalf(exact_soln_y(ind_var));
omniout_float(ALWAYS, "y[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := float_abs(numeric_val - closed_form_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if c(glob_prec) < c(float_abs(closed_form_val_y)) then
relerr := abserr*glob__100/float_abs(closed_form_val_y);
if c(glob_prec) < c(relerr) then
glob_good_digits := -int_trunc(log10(c(relerr))) + 3
else glob_good_digits := Digits
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits
then glob_min_apfp_est_good_digits := glob_apfp_est_good_digits
end if;
if glob_prec < evalf(float_abs(numeric_val)) then
est_rel_err := evalf(array_max_est_error[1]*100.0*
sqrt(glob_iter)*22*ATS_MAX_TERMS/float_abs(numeric_val))
;
if glob_prec < evalf(est_rel_err) then
glob_est_digits := -int_trunc(log10(est_rel_err)) + 3
else glob_est_digits := Digits
end if
else relerr := glob__m1; glob_est_digits := -16
end if;
array_est_digits[1] := glob_est_digits;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
array_est_rel_error[1] := est_rel_err;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Desired digits ", 32,
glob_desired_digits_correct, 4, " ");
omniout_int(INFO, "Estimated correct digits ", 32,
glob_est_digits, 4, " ");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_c1,
> array_tmp2_a1,
> array_tmp2_a2,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr((glob_clock_sec));
> if (c(percent_done) < glob__100) then # if number 3
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 3;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr((left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2_c1, array_tmp2_a1, array_tmp2_a2, array_tmp2, array_tmp3,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(glob_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(left_sec);
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_c1,
> array_tmp2_a1,
> array_tmp2_a2,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 3;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 4
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_rad_test_poles[1,1]) then # if number 6
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,2]) then # if number 8
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 9
> glob_min_pole_est := rad_c;
> fi;# end if 9;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[1,3]) then # if number 10
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 11
> glob_min_pole_est := rad_c;
> fi;# end if 11;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test1
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 10;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 9;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 9
> display_poles();
> fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2_c1, array_tmp2_a1, array_tmp2_a2, array_tmp2, array_tmp3,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4],
array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
if
float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_poles() end if
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_c1,
> array_tmp2_a1,
> array_tmp2_a2,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre sin 1 $eq_no = 1
> array_tmp1[1] := sin(array_x[1]);
> array_tmp1_g[1] := cos(array_x[1]);
> #emit pre expt CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := expt(array_const_2D0[1] ,c( array_tmp1[1]));
> array_tmp2_c1[1] := ln(array_const_2D0[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre 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 expt CONST FULL $eq_no = 1 iii = 2
> array_tmp2[2] := att(1,array_tmp2,array_tmp1,1) * array_tmp2_c1[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp3[2] := array_tmp2[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre 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 expt CONST FULL $eq_no = 1 iii = 3
> array_tmp2[3] := att(2,array_tmp2,array_tmp1,1) * array_tmp2_c1[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp3[3] := array_tmp2[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre 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 expt CONST FULL $eq_no = 1 iii = 4
> array_tmp2[4] := att(3,array_tmp2,array_tmp1,1) * array_tmp2_c1[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp3[4] := array_tmp2[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre 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 expt CONST FULL $eq_no = 1 iii = 5
> array_tmp2[5] := att(4,array_tmp2,array_tmp1,1) * array_tmp2_c1[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp3[5] := array_tmp2[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit 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 expt CONST FULL $eq_no = 1 i = 1
> array_tmp2[kkk] := att(kkk-1,array_tmp2,array_tmp1,1) * array_tmp2_c1[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp3[kkk] := array_tmp2[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp3[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2_c1, array_tmp2_a1, array_tmp2_a2, array_tmp2, array_tmp3,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
array_tmp1[1] := sin(array_x[1]);
array_tmp1_g[1] := cos(array_x[1]);
array_tmp2[1] := expt(array_const_2D0[1], c(array_tmp1[1]));
array_tmp2_c1[1] := ln(array_const_2D0[1]);
array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_tmp1_g[1]*array_x[2]/c(1);
array_tmp1_g[2] := neg(array_tmp1[1])*array_x[2]/c(1);
array_tmp2[2] := att(1, array_tmp2, array_tmp1, 1)*array_tmp2_c1[1];
array_tmp3[2] := array_tmp2[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp1[3] := array_tmp1_g[2]*array_x[2]/c(2);
array_tmp1_g[3] := neg(array_tmp1[2])*array_x[2]/c(2);
array_tmp2[3] := att(2, array_tmp2, array_tmp1, 1)*array_tmp2_c1[1];
array_tmp3[3] := array_tmp2[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp1[4] := array_tmp1_g[3]*array_x[2]/c(3);
array_tmp1_g[4] := neg(array_tmp1[3])*array_x[2]/c(3);
array_tmp2[4] := att(3, array_tmp2, array_tmp1, 1)*array_tmp2_c1[1];
array_tmp3[4] := array_tmp2[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp1[5] := array_tmp1_g[4]*array_x[2]/c(4);
array_tmp1_g[5] := neg(array_tmp1[4])*array_x[2]/c(4);
array_tmp2[5] := att(4, array_tmp2, array_tmp1, 1)*array_tmp2_c1[1];
array_tmp3[5] := array_tmp2[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp1[kkk] := array_tmp1_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] :=
att(kkk - 1, array_tmp2, array_tmp1, 1)*array_tmp2_c1[1];
array_tmp3[kkk] := array_tmp2[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y_set_initial[1, kkk + order_d] then
temporary := c(array_tmp3[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2_c1,
> array_tmp2_a1,
> array_tmp2_a2,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 30;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(30),[]);
> array_norms:= Array(0..(30),[]);
> array_fact_1:= Array(0..(30),[]);
> array_1st_rel_error:= Array(0..(2),[]);
> array_last_rel_error:= Array(0..(2),[]);
> array_est_rel_error:= Array(0..(2),[]);
> array_max_est_error:= Array(0..(2),[]);
> array_type_pole:= Array(0..(2),[]);
> array_type_real_pole:= Array(0..(2),[]);
> array_type_complex_pole:= Array(0..(2),[]);
> array_est_digits:= Array(0..(2),[]);
> array_y:= Array(0..(30),[]);
> array_x:= Array(0..(30),[]);
> array_tmp0:= Array(0..(30),[]);
> array_tmp1_g:= Array(0..(30),[]);
> array_tmp1:= Array(0..(30),[]);
> array_tmp2_c1:= Array(0..(30),[]);
> array_tmp2_a1:= Array(0..(30),[]);
> array_tmp2_a2:= Array(0..(30),[]);
> array_tmp2:= Array(0..(30),[]);
> array_tmp3:= Array(0..(30),[]);
> array_m1:= Array(0..(30),[]);
> array_y_higher := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..30+ 1),[]);
> array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(30) ,(0..30+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 30) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp1_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp2_c1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp2_a1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp2_a2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=30) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1_g);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2_c1);
> zero_ats_ar(array_tmp2_a1);
> zero_ats_ar(array_tmp2_a2);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_2D0);
> array_const_2D0[1] := c(2.0);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_h := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 1000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 30;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/expt_c_sinpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = expt ( 2.0 , sin ( x ) ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := c(0.1);");
> omniout_str(ALWAYS,"x_end := c(5.0) ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 0;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=100000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=false;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(c(0.0));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := c(0.1);
> x_end := c(5.0) ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_type_given_pole := 0;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=100000;
> glob_upper_ratio_limit:=c(1.000001);
> glob_lower_ratio_limit:=c(0.999999);
> glob_look_poles:=false;
> glob_h:=c(0.001);
> glob_display_interval:=c(0.01);
> #END OVERRIDE BLOCK
> #END BLOCK 2
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
> # after second input block
> glob_check_sign := c(my_check_sign(x_start,x_end));
> glob__pi := arccos(glob__m1);
> glob_prec = expt(10.0,c(-Digits));
> if (glob_optimize) then # if number 9
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> found_h := false;
> glob_min_pole_est := glob_larger_float;
> last_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> glob_min_h := float_abs(glob_min_h) * glob_check_sign;
> glob_max_h := float_abs(glob_max_h) * glob_check_sign;
> glob_h := float_abs(glob_min_h) * glob_check_sign;
> glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign));
> display_max := c(x_end) - c(x_start)/glob__10;
> if ((glob_display_interval) > (display_max)) then # if number 10
> glob_display_interval := c(display_max);
> fi;# end if 10;
> chk_data();
> min_value := glob_larger_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := glob_small_float;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> atomall();
> if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> glob_h := glob_check_sign * float_abs(glob_min_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
> glob_h_reason := 2;
> glob_h := glob_display_interval;
> found_h := true;
> fi;# end if 10;
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if ( not found_h) then # if number 10
> est_answer := est_size_answer();
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := test_suggested_h();
> omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
> if (estimated_step_error < est_needed_step_err) then # if number 11
> omniout_str(ALWAYS,"Double H and LOOP");
> glob_h := glob_h*glob__2;
> else
> omniout_str(ALWAYS,"Found H for OPTIMAL");
> found_h := true;
> glob_h_reason := 3;
> glob_h := glob_h/glob__2;
> fi;# end if 11;
> fi;# end if 10;
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 10
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 10;
> if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MAX H");
> glob_h := glob_check_sign * float_abs(glob_max_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> else
> found_h := true;
> glob_h := glob_h * glob_check_sign;
> fi;# end if 9;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 9
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 9;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 9
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> glob_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and (glob_check_sign * array_x[1] < glob_check_sign * x_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1
> #left paren 0001C
> if (reached_interval()) then # if number 10
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 10;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> track_estimated_error();
> atomall();
> track_estimated_error();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if (reached_interval()) then # if number 10
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 10;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 10
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 10;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 10;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = expt ( 2.0 , 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,"2015-04-24T20:13:06-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"expt_c_sin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = expt ( 2.0 , 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,"expt_c_sin diffeq.mxt")
> ;
> logitem_str(html_log_file,"expt_c_sin maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> fi;# end if 14
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2_c1, array_tmp2_a1, array_tmp2_a2, array_tmp2, array_tmp3,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
ATS_MAX_TERMS := 30;
Digits := 32;
max_terms := 30;
glob_html_log := true;
array_y_init := Array(0 .. 30, []);
array_norms := Array(0 .. 30, []);
array_fact_1 := Array(0 .. 30, []);
array_1st_rel_error := Array(0 .. 2, []);
array_last_rel_error := Array(0 .. 2, []);
array_est_rel_error := Array(0 .. 2, []);
array_max_est_error := Array(0 .. 2, []);
array_type_pole := Array(0 .. 2, []);
array_type_real_pole := Array(0 .. 2, []);
array_type_complex_pole := Array(0 .. 2, []);
array_est_digits := Array(0 .. 2, []);
array_y := Array(0 .. 30, []);
array_x := Array(0 .. 30, []);
array_tmp0 := Array(0 .. 30, []);
array_tmp1_g := Array(0 .. 30, []);
array_tmp1 := Array(0 .. 30, []);
array_tmp2_c1 := Array(0 .. 30, []);
array_tmp2_a1 := Array(0 .. 30, []);
array_tmp2_a2 := Array(0 .. 30, []);
array_tmp2 := Array(0 .. 30, []);
array_tmp3 := Array(0 .. 30, []);
array_m1 := Array(0 .. 30, []);
array_y_higher := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []);
array_y_set_initial := Array(0 .. 2, 0 .. 31, []);
array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
array_fact_2 := Array(0 .. 30, 0 .. 31, []);
term := 1;
while term <= 30 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 30 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 30 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp1_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp2_c1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp2_a1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp2_a2[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 30 do
term := 1;
while term <= 30 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1_g);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2_c1);
zero_ats_ar(array_tmp2_a1);
zero_ats_ar(array_tmp2_a2);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_2D0);
array_const_2D0[1] := c(2.0);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_h := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 1000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 30;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/expt_c_sinpostode.ode#################");
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = expt ( 2.0 , sin ( x ) ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := c(0.1);");
omniout_str(ALWAYS, "x_end := c(5.0) ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 0;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=100000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=false;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(c(0.0));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := c(0.1);
x_end := c(5.0);
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 0;
glob_desired_digits_correct := 8;
glob_max_minutes := 3.0;
glob_subiter_method := 3;
glob_max_iter := 100000;
glob_upper_ratio_limit := c(1.000001);
glob_lower_ratio_limit := c(0.999999);
glob_look_poles := false;
glob_h := c(0.001);
glob_display_interval := c(0.01);
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
glob_check_sign := c(my_check_sign(x_start, x_end));
glob__pi := arccos(glob__m1);
glob_prec = expt(10.0, c(-Digits));
if glob_optimize then
omniout_str(ALWAYS, "START of Optimize");
found_h := false;
glob_min_pole_est := glob_larger_float;
last_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
glob_min_h := float_abs(glob_min_h)*glob_check_sign;
glob_max_h := float_abs(glob_max_h)*glob_check_sign;
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_display_interval :=
c(float_abs(c(glob_display_interval))*glob_check_sign);
display_max := c(x_end) - c(x_start)/glob__10;
if display_max < glob_display_interval then
glob_display_interval := c(display_max)
end if;
chk_data();
min_value := glob_larger_float;
est_answer := est_size_answer();
opt_iter := 1;
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
;
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := glob_small_float;
while opt_iter <= 100 and not found_h do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] :=
array_y_init[it]*expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
atomall();
if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if;
if
glob_check_sign*glob_display_interval <= glob_check_sign*glob_h
then
omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL");
glob_h_reason := 2;
glob_h := glob_display_interval;
found_h := true
end if;
if glob_look_poles then check_for_pole() end if;
if not found_h then
est_answer := est_size_answer();
est_needed_step_err := estimated_needed_step_error(x_start,
x_end, glob_h, est_answer);
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := test_suggested_h();
omniout_float(ALWAYS, "estimated_step_error", 32,
estimated_step_error, 32, "");
if estimated_step_error < est_needed_step_err then
omniout_str(ALWAYS, "Double H and LOOP");
glob_h := glob_h*glob__2
else
omniout_str(ALWAYS, "Found H for OPTIMAL");
found_h := true;
glob_h_reason := 3;
glob_h := glob_h/glob__2
end if
end if;
opt_iter := opt_iter + 1
end do;
if not found_h and opt_iter = 1 then
omniout_str(ALWAYS, "Beginning glob_h too large.");
found_h := false
end if;
if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then
omniout_str(ALWAYS, "SETTING H FOR MAX H");
glob_h := float_abs(glob_max_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if
else found_h := true; glob_h := glob_check_sign*glob_h
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
glob_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
glob_clock_sec - glob_orig_start_sec < glob_max_sec do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
track_estimated_error();
atomall();
track_estimated_error();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = expt ( 2.0 , \
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, "2015-04-24T20:13:06-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"expt_c_sin");
logitem_str(html_log_file, "diff ( y , x , 1 ) = e\
xpt ( 2.0 , 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, "expt_c_sin diffeq.mxt");
logitem_str(html_log_file, "expt_c_sin 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/expt_c_sinpostode.ode#################
diff ( y , x , 1 ) = expt ( 2.0 , sin ( x ) ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(0.1);
x_end := c(5.0) ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 0;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=100000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=false;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(0.0));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 0
absolute error = 0
relative error = -1 %
Desired digits = 8
Estimated correct digits = -16
Correct digits = -16
h = 0.001
memory used=4.2MB, alloc=40.3MB, time=0.08
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (closed_form) = 0
y[1] (numeric) = 0.010749818412970448346740393558939
absolute error = 0.010749818412970448346740393558939
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (closed_form) = 0
y[1] (numeric) = 0.021573957690963883581500533074767
absolute error = 0.021573957690963883581500533074767
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (closed_form) = 0
y[1] (numeric) = 0.032472845351092423927526010467324
absolute error = 0.032472845351092423927526010467324
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (closed_form) = 0
y[1] (numeric) = 0.043446903122511798494782057568721
absolute error = 0.043446903122511798494782057568721
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (closed_form) = 0
y[1] (numeric) = 0.05449654674977484185883922428678
absolute error = 0.05449654674977484185883922428678
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (closed_form) = 0
y[1] (numeric) = 0.065622185794335564336892582171863
absolute error = 0.065622185794335564336892582171863
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
memory used=39.6MB, alloc=44.3MB, time=0.52
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (closed_form) = 0
y[1] (numeric) = 0.076824223434271066890573689831222
absolute error = 0.076824223434271066890573689831222
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (closed_form) = 0
y[1] (numeric) = 0.088103056262291382816185834630782
absolute error = 0.088103056262291382816185834630782
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (closed_form) = 0
y[1] (numeric) = 0.099459074082110154747188988070178
absolute error = 0.099459074082110154747188988070178
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (closed_form) = 0
y[1] (numeric) = 0.11089265970325189237605886607136
absolute error = 0.11089265970325189237605886607136
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (closed_form) = 0
y[1] (numeric) = 0.12240418873437440099804494816034
absolute error = 0.12240418873437440099804494816034
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (closed_form) = 0
y[1] (numeric) = 0.1339940293751878206941653249665
absolute error = 0.1339940293751878206941653249665
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (closed_form) = 0
y[1] (numeric) = 0.14566254220705456782399609197267
absolute error = 0.14566254220705456782399609197267
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=82.7MB, alloc=52.3MB, time=1.02
x[1] = 0.24
y[1] (closed_form) = 0
y[1] (numeric) = 0.15741007998235732152368480841546
absolute error = 0.15741007998235732152368480841546
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (closed_form) = 0
y[1] (numeric) = 0.16923698741272504505039923562137
absolute error = 0.16923698741272504505039923562137
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (closed_form) = 0
y[1] (numeric) = 0.18114360095620987194834543252355
absolute error = 0.18114360095620987194834543252355
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (closed_form) = 0
y[1] (numeric) = 0.19313024860351051692091977895293
absolute error = 0.19313024860351051692091977895293
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (closed_form) = 0
y[1] (numeric) = 0.20519724966334068768836495051897
absolute error = 0.20519724966334068768836495051897
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (closed_form) = 0
y[1] (numeric) = 0.21734491454704377362542011008363
absolute error = 0.21734491454704377362542011008363
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (closed_form) = 0
y[1] (numeric) = 0.22957354455255786617168224652312
absolute error = 0.22957354455255786617168224652312
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (closed_form) = 0
y[1] (numeric) = 0.24188343164783792138236046914367
absolute error = 0.24188343164783792138236046914367
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
memory used=126.0MB, alloc=52.3MB, time=1.50
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (closed_form) = 0
y[1] (numeric) = 0.25427485825384460296647839676416
absolute error = 0.25427485825384460296647839676416
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (closed_form) = 0
y[1] (numeric) = 0.26674809702721204110847902233352
absolute error = 0.26674809702721204110847902233352
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (closed_form) = 0
y[1] (numeric) = 0.27930341064270940459379554156448
absolute error = 0.27930341064270940459379554156448
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (closed_form) = 0
y[1] (numeric) = 0.29194105157561380751035044475365
absolute error = 0.29194105157561380751035044475365
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (closed_form) = 0
y[1] (numeric) = 0.30466126188411465327614801376894
absolute error = 0.30466126188411465327614801376894
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (closed_form) = 0
y[1] (numeric) = 0.31746427299187205410132751732935
absolute error = 0.31746427299187205410132751732935
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (closed_form) = 0
y[1] (numeric) = 0.33035030547085444934207450208427
absolute error = 0.33035030547085444934207450208427
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (closed_form) = 0
y[1] (numeric) = 0.34331956882458297761676363870532
absolute error = 0.34331956882458297761676363870532
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=169.1MB, alloc=52.3MB, time=1.97
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (closed_form) = 0
y[1] (numeric) = 0.35637226127191253107189259867231
absolute error = 0.35637226127191253107189259867231
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (closed_form) = 0
y[1] (numeric) = 0.36950856953148173181922621365418
absolute error = 0.36950856953148173181922621365418
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (closed_form) = 0
y[1] (numeric) = 0.38272866860696631630601430075828
absolute error = 0.38272866860696631630601430075828
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (closed_form) = 0
y[1] (numeric) = 0.39603272157327258919996799389294
absolute error = 0.39603272157327258919996799389294
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (closed_form) = 0
y[1] (numeric) = 0.40942087936380971023117260662823
absolute error = 0.40942087936380971023117260662823
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (closed_form) = 0
y[1] (numeric) = 0.42289328055898160128987263244395
absolute error = 0.42289328055898160128987263244395
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (closed_form) = 0
y[1] (numeric) = 0.43645005117604120288794573503066
absolute error = 0.43645005117604120288794573503066
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=212.2MB, alloc=52.3MB, time=2.44
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (closed_form) = 0
y[1] (numeric) = 0.45009130446045166481514637149163
absolute error = 0.45009130446045166481514637149163
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (closed_form) = 0
y[1] (numeric) = 0.46381714067890082143379475561388
absolute error = 0.46381714067890082143379475561388
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (closed_form) = 0
y[1] (numeric) = 0.47762764691411697355159128991517
absolute error = 0.47762764691411697355159128991517
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (closed_form) = 0
y[1] (numeric) = 0.49152289686163557221143799323823
absolute error = 0.49152289686163557221143799323823
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (closed_form) = 0
y[1] (numeric) = 0.5055029506286678710917557145078
absolute error = 0.5055029506286678710917557145078
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (closed_form) = 0
y[1] (numeric) = 0.51956785453522397961226279684577
absolute error = 0.51956785453522397961226279684577
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (closed_form) = 0
y[1] (numeric) = 0.53371764091764400442619111885796
absolute error = 0.53371764091764400442619111885796
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (closed_form) = 0
y[1] (numeric) = 0.54795232793469210894136888032162
absolute error = 0.54795232793469210894136888032162
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=255.4MB, alloc=52.3MB, time=2.91
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (closed_form) = 0
y[1] (numeric) = 0.56227191937636934510078734451451
absolute error = 0.56227191937636934510078734451451
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (closed_form) = 0
y[1] (numeric) = 0.57667640447560201518707668413284
absolute error = 0.57667640447560201518707668413284
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (closed_form) = 0
y[1] (numeric) = 0.59116575772296310028850248525472
absolute error = 0.59116575772296310028850248525472
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (closed_form) = 0
y[1] (numeric) = 0.60573993868458494275262101919291
absolute error = 0.60573993868458494275262101919291
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (closed_form) = 0
y[1] (numeric) = 0.62039889182342188902313267058933
absolute error = 0.62039889182342188902313267058933
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (closed_form) = 0
y[1] (numeric) = 0.63514254632402198336825121492937
absolute error = 0.63514254632402198336825121492937
relative error = -1 %
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) = 0
y[1] (numeric) = 0.64997081592096704893193782097907
absolute error = 0.64997081592096704893193782097907
relative error = -1 %
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) = 0
y[1] (numeric) = 0.66488359873114059715128428873793
absolute error = 0.66488359873114059715128428873793
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=298.5MB, alloc=52.3MB, time=3.39
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (closed_form) = 0
y[1] (numeric) = 0.6798807770899829668819809335725
absolute error = 0.6798807770899829668819809335725
relative error = -1 %
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) = 0
y[1] (numeric) = 0.69496221739189290768349021610269
absolute error = 0.69496221739189290768349021610269
relative error = -1 %
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) = 0
y[1] (numeric) = 0.71012776993493448489439566590486
absolute error = 0.71012776993493448489439566590486
relative error = -1 %
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) = 0
y[1] (numeric) = 0.72537726877000769477557727211177
absolute error = 0.72537726877000769477557727211177
relative error = -1 %
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) = 0
y[1] (numeric) = 0.7407105315546405336617441829781
absolute error = 0.7407105315546405336617441829781
relative error = -1 %
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) = 0
y[1] (numeric) = 0.7561273594115594634430461095779
absolute error = 0.7561273594115594634430461095779
relative error = -1 %
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) = 0
y[1] (numeric) = 0.77162753679219425466278543971134
absolute error = 0.77162753679219425466278543971134
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=341.6MB, alloc=52.3MB, time=3.86
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (closed_form) = 0
y[1] (numeric) = 0.78721083134527206609845460985432
absolute error = 0.78721083134527206609845460985432
relative error = -1 %
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) = 0
y[1] (numeric) = 0.80287699379065433410086974930826
absolute error = 0.80287699379065433410086974930826
relative error = -1 %
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) = 0
y[1] (numeric) = 0.8186257577985685945916455684123
absolute error = 0.8186257577985685945916455684123
relative error = -1 %
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) = 0
y[1] (numeric) = 0.83445683987438574404269147702607
absolute error = 0.83445683987438574404269147702607
relative error = -1 %
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) = 0
y[1] (numeric) = 0.85036993924909146175739690368687
absolute error = 0.85036993924909146175739690368687
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (closed_form) = 0
y[1] (numeric) = 0.86636473777559856331675627901799
absolute error = 0.86636473777559856331675627901799
relative error = -1 %
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) = 0
y[1] (numeric) = 0.88244089983104493332600962310225
absolute error = 0.88244089983104493332600962310225
relative error = -1 %
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) = 0
y[1] (numeric) = 0.89859807222521939399110513061838
absolute error = 0.89859807222521939399110513061838
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=384.9MB, alloc=52.3MB, time=4.33
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (closed_form) = 0
y[1] (numeric) = 0.91483588411525540417874039556662
absolute error = 0.91483588411525540417874039556662
relative error = -1 %
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) = 0
y[1] (numeric) = 0.93115394692672985129973228433784
absolute error = 0.93115394692672985129973228433784
relative error = -1 %
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) = 0
y[1] (numeric) = 0.94755185428130139565988982068618
absolute error = 0.94755185428130139565988982068618
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (closed_form) = 0
y[1] (numeric) = 0.96402918193101985413261287615267
absolute error = 0.96402918193101985413261287615267
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (closed_form) = 0
y[1] (numeric) = 0.98058548769943496764452025719721
absolute error = 0.98058548769943496764452025719721
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (closed_form) = 0
y[1] (numeric) = 0.99722031142962958578871184568137
absolute error = 0.99722031142962958578871184568137
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (closed_form) = 0
y[1] (numeric) = 1.0139331749392988228899626874116
absolute error = 1.0139331749392988228899626874116
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (closed_form) = 0
y[1] (numeric) = 1.0307235819829930942862187429072
absolute error = 1.0307235819829930942862187429072
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=428.1MB, alloc=52.3MB, time=4.81
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (closed_form) = 0
y[1] (numeric) = 1.0475910182216391309514586058208
absolute error = 1.0475910182216391309514586058208
relative error = -1 %
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) = 0
y[1] (numeric) = 1.0645349511994490966048481851244
absolute error = 1.0645349511994490966048481851244
relative error = -1 %
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) = 0
y[1] (numeric) = 1.0815548303283237961186239990481
absolute error = 1.0815548303283237961186239990481
relative error = -1 %
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) = 0
y[1] (numeric) = 1.0986500868798516695919138513939
absolute error = 1.0986500868798516695919138513939
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (closed_form) = 0
y[1] (numeric) = 1.1158201339850008153912746726365
absolute error = 1.1158201339850008153912746726365
relative error = -1 %
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) = 0
y[1] (numeric) = 1.1330643666415966805148751738915
absolute error = 1.1330643666415966805148751738915
relative error = -1 %
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) = 0
y[1] (numeric) = 1.150382161729673300811878275779
absolute error = 1.150382161729673300811878275779
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=471.2MB, alloc=52.3MB, time=5.28
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (closed_form) = 0
y[1] (numeric) = 1.1677728780347810701291287391466
absolute error = 1.1677728780347810701291287391466
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (closed_form) = 0
y[1] (numeric) = 1.1852358562793289698616595937889
absolute error = 1.1852358562793289698616595937889
relative error = -1 %
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) = 0
y[1] (numeric) = 1.2027704191620340023986980676665
absolute error = 1.2027704191620340023986980676665
relative error = -1 %
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) = 0
y[1] (numeric) = 1.220375871405545247576642404774
absolute error = 1.220375871405545247576642404774
relative error = -1 %
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) = 0
y[1] (numeric) = 1.2380514998123045047132367409097
absolute error = 1.2380514998123045047132367409097
relative error = -1 %
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) = 0
y[1] (numeric) = 1.2557965733286998985827375615671
absolute error = 1.2557965733286998985827375615671
relative error = -1 %
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) = 0
y[1] (numeric) = 1.2736103431175631205181303144631
absolute error = 1.2736103431175631205181303144631
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (closed_form) = 0
y[1] (numeric) = 1.2914920426390551506453985930805
absolute error = 1.2914920426390551506453985930805
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=514.3MB, alloc=52.3MB, time=5.75
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (closed_form) = 0
y[1] (numeric) = 1.3094408877399793692481032363505
absolute error = 1.3094408877399793692481032363505
relative error = -1 %
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) = 0
y[1] (numeric) = 1.3274560767515549198344515924594
absolute error = 1.3274560767515549198344515924594
relative error = -1 %
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) = 0
y[1] (numeric) = 1.3455367905956770392592966918397
absolute error = 1.3455367905956770392592966918397
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (closed_form) = 0
y[1] (numeric) = 1.3636821928996848270791880513609
absolute error = 1.3636821928996848270791880513609
relative error = -1 %
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) = 0
y[1] (numeric) = 1.3818914301196505932358322512835
absolute error = 1.3818914301196505932358322512835
relative error = -1 %
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) = 0
y[1] (numeric) = 1.4001636316721985064184484830709
absolute error = 1.4001636316721985064184484830709
relative error = -1 %
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) = 0
y[1] (numeric) = 1.4184979100748537714877571479203
absolute error = 1.4184979100748537714877571479203
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=557.4MB, alloc=52.3MB, time=6.23
x[1] = 1.08
y[1] (closed_form) = 0
y[1] (numeric) = 1.4368933610949169997780923064946
absolute error = 1.4368933610949169997780923064946
relative error = -1 %
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) = 0
y[1] (numeric) = 1.4553490639068518077306887363128
absolute error = 1.4553490639068518077306887363128
relative error = -1 %
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) = 0
y[1] (numeric) = 1.4738640812581669941201624518281
absolute error = 1.4738640812581669941201624518281
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (closed_form) = 0
y[1] (numeric) = 1.4924374596437679112464119216188
absolute error = 1.4924374596437679112464119216188
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (closed_form) = 0
y[1] (numeric) = 1.5110682294887448681542077449288
absolute error = 1.5110682294887448681542077449288
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (closed_form) = 0
y[1] (numeric) = 1.529755405339559591631096431463
absolute error = 1.529755405339559591631096431463
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (closed_form) = 0
y[1] (numeric) = 1.5484979860635839309690518830115
absolute error = 1.5484979860635839309690518830115
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (closed_form) = 0
y[1] (numeric) = 1.5672949550569381329237377370782
absolute error = 1.5672949550569381329237377370782
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=600.6MB, alloc=52.3MB, time=6.70
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (closed_form) = 0
y[1] (numeric) = 1.586145280460569141742551306525
absolute error = 1.586145280460569141742551306525
relative error = -1 %
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) = 0
y[1] (numeric) = 1.6050479153845025034308661948941
absolute error = 1.6050479153845025034308661948941
relative error = -1 %
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) = 0
y[1] (numeric) = 1.6240017981401945815423534844651
absolute error = 1.6240017981401945815423534844651
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (closed_form) = 0
y[1] (numeric) = 1.6430058524809049317445616557202
absolute error = 1.6430058524809049317445616557202
relative error = -1 %
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) = 0
y[1] (numeric) = 1.6620589878500018423168989950031
absolute error = 1.6620589878500018423168989950031
relative error = -1 %
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) = 0
y[1] (numeric) = 1.681160099637107235725439404222
absolute error = 1.681160099637107235725439404222
relative error = -1 %
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) = 0
y[1] (numeric) = 1.70030806944198035066443824847
absolute error = 1.70030806944198035066443824847
relative error = -1 %
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) = 0
y[1] (numeric) = 1.7195017653460328926584045107795
memory used=643.7MB, alloc=52.3MB, time=7.17
absolute error = 1.7195017653460328926584045107795
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (closed_form) = 0
y[1] (numeric) = 1.7387400421913616626918002005688
absolute error = 1.7387400421913616626918002005688
relative error = -1 %
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) = 0
y[1] (numeric) = 1.7580217418671780555840553932545
absolute error = 1.7580217418671780555840553932545
relative error = -1 %
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) = 0
y[1] (numeric) = 1.7773456936035072711478539491468
absolute error = 1.7773456936035072711478539491468
relative error = -1 %
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) = 0
y[1] (numeric) = 1.7967107142720236097216263532995
absolute error = 1.7967107142720236097216263532995
relative error = -1 %
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) = 0
y[1] (numeric) = 1.8161156086938818375733720511794
absolute error = 1.8161156086938818375733720511794
relative error = -1 %
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) = 0
y[1] (numeric) = 1.8355591699543983149968162415919
absolute error = 1.8355591699543983149968162415919
relative error = -1 %
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) = 0
y[1] (numeric) = 1.855040179724429388657548189487
absolute error = 1.855040179724429388657548189487
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=686.9MB, alloc=52.3MB, time=7.64
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (closed_form) = 0
y[1] (numeric) = 1.8745574085882884678084104206503
absolute error = 1.8745574085882884678084104206503
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (closed_form) = 0
y[1] (numeric) = 1.8941096163780372391960232073444
absolute error = 1.8941096163780372391960232073444
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (closed_form) = 0
y[1] (numeric) = 1.9136955525139806355304504542521
absolute error = 1.9136955525139806355304504542521
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (closed_form) = 0
y[1] (numeric) = 1.9333139563511894648714701833779
absolute error = 1.9333139563511894648714701833779
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (closed_form) = 0
y[1] (numeric) = 1.9529635575318690406457948418142
absolute error = 1.9529635575318690406457948418142
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (closed_form) = 0
y[1] (numeric) = 1.9726430763433867315493508950168
absolute error = 1.9726430763433867315493508950168
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (closed_form) = 0
y[1] (numeric) = 1.9923512240817660844454947526531
absolute error = 1.9923512240817660844454947526531
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (closed_form) = 0
y[1] (numeric) = 2.012086703420450068508111343224
absolute error = 2.012086703420450068508111343224
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=729.8MB, alloc=52.3MB, time=8.13
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (closed_form) = 0
y[1] (numeric) = 2.0318482087841310520561464397966
absolute error = 2.0318482087841310520561464397966
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (closed_form) = 0
y[1] (numeric) = 2.0516344267274403613634640007442
absolute error = 2.0516344267274403613634640007442
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (closed_form) = 0
y[1] (numeric) = 2.0714440363182856895754908351296
absolute error = 2.0714440363182856895754908351296
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (closed_form) = 0
y[1] (numeric) = 2.0912757095256202298713590088928
absolute error = 2.0912757095256202298713590088928
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (closed_form) = 0
y[1] (numeric) = 2.1111281116114232060945845184109
absolute error = 2.1111281116114232060945845184109
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (closed_form) = 0
y[1] (numeric) = 2.1309999015266674719114707622197
absolute error = 2.1309999015266674719114707622197
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (closed_form) = 0
y[1] (numeric) = 2.1508897323110460515662605834824
absolute error = 2.1508897323110460515662605834824
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=772.8MB, alloc=52.3MB, time=8.59
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (closed_form) = 0
y[1] (numeric) = 2.1707962514962259066447721858224
absolute error = 2.1707962514962259066447721858224
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (closed_form) = 0
y[1] (numeric) = 2.1907181015123938388210133298139
absolute error = 2.1907181015123938388210133298139
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (closed_form) = 0
y[1] (numeric) = 2.2106539200978562829503467976754
absolute error = 2.2106539200978562829503467976754
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (closed_form) = 0
y[1] (numeric) = 2.2306023407114518124051594727344
absolute error = 2.2306023407114518124051594727344
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (closed_form) = 0
y[1] (numeric) = 2.2505619929475324732444749040619
absolute error = 2.2505619929475324732444749040619
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (closed_form) = 0
y[1] (numeric) = 2.2705315029532675893828213112031
absolute error = 2.2705315029532675893828213112031
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (closed_form) = 0
y[1] (numeric) = 2.2905094938480214407798553790559
absolute error = 2.2905094938480214407798553790559
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=815.9MB, alloc=52.3MB, time=9.05
x[1] = 1.53
y[1] (closed_form) = 0
y[1] (numeric) = 2.3104945861445542138970797015389
absolute error = 2.3104945861445542138970797015389
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (closed_form) = 0
y[1] (numeric) = 2.3304853981717938610245319239376
absolute error = 2.3304853981717938610245319239376
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (closed_form) = 0
y[1] (numeric) = 2.3504805464989249850032479092993
absolute error = 2.3504805464989249850032479092993
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (closed_form) = 0
y[1] (numeric) = 2.3704786463605395904604252453183
absolute error = 2.3704786463605395904604252453183
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (closed_form) = 0
y[1] (numeric) = 2.3904783120825935136986032892681
absolute error = 2.3904783120825935136986032892681
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (closed_form) = 0
y[1] (numeric) = 2.4104781575089115622628838252712
absolute error = 2.4104781575089115622628838252712
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (closed_form) = 0
y[1] (numeric) = 2.4304767964279838630336424875366
absolute error = 2.4304767964279838630336424875366
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (closed_form) = 0
y[1] (numeric) = 2.4504728429997956351940688786626
absolute error = 2.4504728429997956351940688786626
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=858.9MB, alloc=52.3MB, time=9.51
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (closed_form) = 0
y[1] (numeric) = 2.4704649121824325719939425044231
absolute error = 2.4704649121824325719939425044231
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (closed_form) = 0
y[1] (numeric) = 2.4904516201582042329182721333021
absolute error = 2.4904516201582042329182721333021
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (closed_form) = 0
y[1] (numeric) = 2.5104315847590283153699346425086
absolute error = 2.5104315847590283153699346425086
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (closed_form) = 0
y[1] (numeric) = 2.53040342589081939164110884075
absolute error = 2.53040342589081939164110884075
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (closed_form) = 0
y[1] (numeric) = 2.5503657659566266617859006292509
absolute error = 2.5503657659566266617859006292509
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (closed_form) = 0
y[1] (numeric) = 2.5703172302782664846796559646818
absolute error = 2.5703172302782664846796559646818
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (closed_form) = 0
y[1] (numeric) = 2.5902564475161969063818567792972
absolute error = 2.5902564475161969063818567792972
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=902.0MB, alloc=52.3MB, time=9.98
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (closed_form) = 0
y[1] (numeric) = 2.6101820500873831048943360134899
absolute error = 2.6101820500873831048943360134899
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (closed_form) = 0
y[1] (numeric) = 2.6300926745809046111760433066533
absolute error = 2.6300926745809046111760433066533
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (closed_form) = 0
y[1] (numeric) = 2.649986962171057345161359551928
absolute error = 2.649986962171057345161359551928
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (closed_form) = 0
y[1] (numeric) = 2.6698635590277059195279567656122
absolute error = 2.6698635590277059195279567656122
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (closed_form) = 0
y[1] (numeric) = 2.689721116723644309750262540778
absolute error = 2.689721116723644309750262540778
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (closed_form) = 0
y[1] (numeric) = 2.7095582926387258629205282404503
absolute error = 2.7095582926387258629205282404503
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (closed_form) = 0
y[1] (numeric) = 2.7293737503605267159797791518382
absolute error = 2.7293737503605267159797791518382
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (closed_form) = 0
y[1] (numeric) = 2.7491661600813100121348725861905
absolute error = 2.7491661600813100121348725861905
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=944.9MB, alloc=52.3MB, time=10.45
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (closed_form) = 0
y[1] (numeric) = 2.7689341989910618378134518864184
absolute error = 2.7689341989910618378134518864184
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (closed_form) = 0
y[1] (numeric) = 2.7886765516663735467105833747396
absolute error = 2.7886765516663735467105833747396
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (closed_form) = 0
y[1] (numeric) = 2.8083919104549490872197545992423
absolute error = 2.8083919104549490872197545992423
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (closed_form) = 0
y[1] (numeric) = 2.8280789758555200994620114770855
absolute error = 2.8280789758555200994620114770855
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (closed_form) = 0
y[1] (numeric) = 2.8477364568929558926201753993357
absolute error = 2.8477364568929558926201753993357
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (closed_form) = 0
y[1] (numeric) = 2.8673630714883599464948158795536
absolute error = 2.8673630714883599464948158795536
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (closed_form) = 0
y[1] (numeric) = 2.8869575468239492970346335464409
absolute error = 2.8869575468239492970346335464409
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=987.7MB, alloc=52.3MB, time=10.92
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (closed_form) = 0
y[1] (numeric) = 2.9065186197025180577418714490869
absolute error = 2.9065186197025180577418714490869
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (closed_form) = 0
y[1] (numeric) = 2.9260450369012913907863810076979
absolute error = 2.9260450369012913907863810076979
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (closed_form) = 0
y[1] (numeric) = 2.9455355555199814666519942611473
absolute error = 2.9455355555199814666519942611473
relative error = -1 %
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) = 0
y[1] (numeric) = 2.9649889433228623322686730853108
absolute error = 2.9649889433228623322686730853108
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (closed_form) = 0
y[1] (numeric) = 2.9844039790746861377592742597435
absolute error = 2.9844039790746861377592742597435
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (closed_form) = 0
y[1] (numeric) = 3.0037794528702688438918466390083
absolute error = 3.0037794528702688438918466390083
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (closed_form) = 0
y[1] (numeric) = 3.0231141664575793386663779861987
absolute error = 3.0231141664575793386663779861987
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (closed_form) = 0
y[1] (numeric) = 3.0424069335541718246289504823918
absolute error = 3.0424069335541718246289504823918
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1030.5MB, alloc=52.3MB, time=11.39
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (closed_form) = 0
y[1] (numeric) = 3.0616565801568073908203782727122
absolute error = 3.0616565801568073908203782727122
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (closed_form) = 0
y[1] (numeric) = 3.0808619448441168469416917943232
absolute error = 3.0808619448441168469416917943232
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.93
y[1] (closed_form) = 0
y[1] (numeric) = 3.1000218790721631644667439035334
absolute error = 3.1000218790721631644667439035334
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (closed_form) = 0
y[1] (numeric) = 3.1191352474627682320778706644132
absolute error = 3.1191352474627682320778706644132
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (closed_form) = 0
y[1] (numeric) = 3.1382009280844750828961640786718
absolute error = 3.1382009280844750828961640786718
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (closed_form) = 0
y[1] (numeric) = 3.1572178127260232804162437700114
absolute error = 3.1572178127260232804162437700114
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (closed_form) = 0
y[1] (numeric) = 3.1761848071622217506831353652182
absolute error = 3.1761848071622217506831353652182
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1073.2MB, alloc=52.3MB, time=11.86
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (closed_form) = 0
y[1] (numeric) = 3.1951008314121100118800046640779
absolute error = 3.1951008314121100118800046640779
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (closed_form) = 0
y[1] (numeric) = 3.2139648199893054709247714529652
absolute error = 3.2139648199893054709247714529652
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (closed_form) = 0
y[1] (numeric) = 3.2327757221444412216896851752431
absolute error = 3.2327757221444412216896851752431
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (closed_form) = 0
y[1] (numeric) = 3.2515325020996055828565166802395
absolute error = 3.2515325020996055828565166802395
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (closed_form) = 0
y[1] (numeric) = 3.2702341392747014470169203867596
absolute error = 3.2702341392747014470169203867596
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (closed_form) = 0
y[1] (numeric) = 3.2888796285056503682714892274653
absolute error = 3.2888796285056503682714892274653
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (closed_form) = 0
y[1] (numeric) = 3.3074679802543731851663782702636
absolute error = 3.3074679802543731851663782702636
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (closed_form) = 0
y[1] (numeric) = 3.3259982208104858512854469232333
absolute error = 3.3259982208104858512854469232333
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1116.1MB, alloc=52.3MB, time=12.33
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (closed_form) = 0
y[1] (numeric) = 3.344469392484656019211219846082
absolute error = 3.344469392484656019211219846082
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (closed_form) = 0
y[1] (numeric) = 3.3628805537935727869843139821826
absolute error = 3.3628805537935727869843139821826
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (closed_form) = 0
y[1] (numeric) = 3.3812307796364888618268731525058
absolute error = 3.3812307796364888618268731525058
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (closed_form) = 0
y[1] (numeric) = 3.3995191614633012160547328847355
absolute error = 3.3995191614633012160547328847355
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (closed_form) = 0
y[1] (numeric) = 3.4177448074341430972054783096743
absolute error = 3.4177448074341430972054783096743
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (closed_form) = 0
y[1] (numeric) = 3.4359068425704670010021599627483
absolute error = 3.4359068425704670010021599627483
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (closed_form) = 0
y[1] (numeric) = 3.4540044088976049145393718376826
absolute error = 3.4540044088976049145393718376826
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1158.8MB, alloc=52.3MB, time=12.80
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (closed_form) = 0
y[1] (numeric) = 3.4720366655787987808510877398551
absolute error = 3.4720366655787987808510877398551
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (closed_form) = 0
y[1] (numeric) = 3.4900027890407007177863249018549
absolute error = 3.4900027890407007177863249018549
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (closed_form) = 0
y[1] (numeric) = 3.507901973090349037033571002102
absolute error = 3.507901973090349037033571002102
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (closed_form) = 0
y[1] (numeric) = 3.5257334290236325465269198324039
absolute error = 3.5257334290236325465269198324039
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (closed_form) = 0
y[1] (numeric) = 3.5434963857252619748480133341272
absolute error = 3.5434963857252619748480133341272
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (closed_form) = 0
y[1] (numeric) = 3.5611900897602736233111153739641
absolute error = 3.5611900897602736233111153739641
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (closed_form) = 0
y[1] (numeric) = 3.5788138054570965240852316807495
absolute error = 3.5788138054570965240852316807495
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (closed_form) = 0
y[1] (numeric) = 3.5963668149822204550737441819126
absolute error = 3.5963668149822204550737441819126
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1201.7MB, alloc=52.3MB, time=13.27
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (closed_form) = 0
y[1] (numeric) = 3.6138484184065081286569609195034
absolute error = 3.6138484184065081286569609195034
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (closed_form) = 0
y[1] (numeric) = 3.6312579337632007263425387180303
absolute error = 3.6312579337632007263425387180303
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (closed_form) = 0
y[1] (numeric) = 3.648594697097671689622526447331
absolute error = 3.648594697097671689622526447331
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (closed_form) = 0
y[1] (numeric) = 3.6658580625089892938918350943072
absolute error = 3.6658580625089892938918350943072
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (closed_form) = 0
y[1] (numeric) = 3.6830474021833540223622877806186
absolute error = 3.6830474021833540223622877806186
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (closed_form) = 0
y[1] (numeric) = 3.700162106419482115967124564359
absolute error = 3.700162106419482115967124564359
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (closed_form) = 0
y[1] (numeric) = 3.7172015836460118989916730844806
absolute error = 3.7172015836460118989916730844806
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1244.6MB, alloc=52.3MB, time=13.73
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (closed_form) = 0
y[1] (numeric) = 3.7341652604310145645293394951453
absolute error = 3.7341652604310145645293394951453
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (closed_form) = 0
y[1] (numeric) = 3.7510525814836960450369826266302
absolute error = 3.7510525814836960450369826266302
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (closed_form) = 0
y[1] (numeric) = 3.7678630096483813876874593251312
absolute error = 3.7678630096483813876874593251312
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (closed_form) = 0
y[1] (numeric) = 3.7845960258908776985771633103084
absolute error = 3.7845960258908776985771633103084
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (closed_form) = 0
y[1] (numeric) = 3.8012511292773162110815304836738
absolute error = 3.8012511292773162110815304836738
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (closed_form) = 0
y[1] (numeric) = 3.8178278369455783689525743946991
absolute error = 3.8178278369455783689525743946991
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (closed_form) = 0
y[1] (numeric) = 3.8343256840694149915626282301493
absolute error = 3.8343256840694149915626282301493
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (closed_form) = 0
y[1] (numeric) = 3.8507442238153716047127295459446
absolute error = 3.8507442238153716047127295459446
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1287.4MB, alloc=52.3MB, time=14.20
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (closed_form) = 0
y[1] (numeric) = 3.867083027292636873588999775155
absolute error = 3.867083027292636873588999775155
relative error = -1 %
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) = 0
y[1] (numeric) = 3.8833416834959347629627379267841
absolute error = 3.8833416834959347629627379267841
relative error = -1 %
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) = 0
y[1] (numeric) = 3.8995197992415845720353265729466
absolute error = 3.8995197992415845720353265729466
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (closed_form) = 0
y[1] (numeric) = 3.9156169990968563461198243941325
absolute error = 3.9156169990968563461198243941325
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (closed_form) = 0
y[1] (numeric) = 3.9316329253027523535641650672532
absolute error = 3.9316329253027523535641650672532
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (closed_form) = 0
y[1] (numeric) = 3.9475672376903483331348232986203
absolute error = 3.9475672376903483331348232986203
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (closed_form) = 0
y[1] (numeric) = 3.9634196135908310639119170186868
absolute error = 3.9634196135908310639119170186868
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1330.1MB, alloc=52.3MB, time=14.67
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (closed_form) = 0
y[1] (numeric) = 3.9791897477393714862494349675075
absolute error = 3.9791897477393714862494349675075
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (closed_form) = 0
y[1] (numeric) = 3.9948773521729751084114072143246
absolute error = 3.9948773521729751084114072143246
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (closed_form) = 0
y[1] (numeric) = 4.0104821561224537692173635871597
absolute error = 4.0104821561224537692173635871597
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (closed_form) = 0
y[1] (numeric) = 4.0260039058986649927520616986065
absolute error = 4.0260039058986649927520616986065
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (closed_form) = 0
y[1] (numeric) = 4.0414423647731671674668620200553
absolute error = 4.0414423647731671674668620200553
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (closed_form) = 0
y[1] (numeric) = 4.0567973128534406095878043480079
absolute error = 4.0567973128534406095878043480079
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (closed_form) = 0
y[1] (numeric) = 4.0720685469528262306204535146421
absolute error = 4.0720685469528262306204535146421
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (closed_form) = 0
y[1] (numeric) = 4.0872558804553350220779273268757
absolute error = 4.0872558804553350220779273268757
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1373.0MB, alloc=52.3MB, time=15.14
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (closed_form) = 0
y[1] (numeric) = 4.1023591431754828987262987598214
absolute error = 4.1023591431754828987262987598214
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (closed_form) = 0
y[1] (numeric) = 4.1173781812133066062009332478522
absolute error = 4.1173781812133066062009332478522
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (closed_form) = 0
y[1] (numeric) = 4.1323128568047174015422317675428
absolute error = 4.1323128568047174015422317675428
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (closed_form) = 0
y[1] (numeric) = 4.1471630481673500579510023032225
absolute error = 4.1471630481673500579510023032225
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (closed_form) = 0
y[1] (numeric) = 4.1619286493420654299643109649552
absolute error = 4.1619286493420654299643109649552
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (closed_form) = 0
y[1] (numeric) = 4.1766095700302653445581685721813
absolute error = 4.1766095700302653445581685721813
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (closed_form) = 0
y[1] (numeric) = 4.1912057354271789598068465894396
absolute error = 4.1912057354271789598068465894396
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1415.9MB, alloc=52.3MB, time=15.61
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (closed_form) = 0
y[1] (numeric) = 4.2057170860512799582330788792263
absolute error = 4.2057170860512799582330788792263
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (closed_form) = 0
y[1] (numeric) = 4.2201435775699940195748890443386
absolute error = 4.2201435775699940195748890443386
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (closed_form) = 0
y[1] (numeric) = 4.2344851806218559502149743267534
absolute error = 4.2344851806218559502149743267534
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (closed_form) = 0
y[1] (numeric) = 4.2487418806352756369375699671426
absolute error = 4.2487418806352756369375699671426
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (closed_form) = 0
y[1] (numeric) = 4.2629136776440716440866750604658
absolute error = 4.2629136776440716440866750604658
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (closed_form) = 0
y[1] (numeric) = 4.277000586099930788803297139791
absolute error = 4.277000586099930788803297139791
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (closed_form) = 0
y[1] (numeric) = 4.291002634681951412129116478207
absolute error = 4.291002634681951412129116478207
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (closed_form) = 0
y[1] (numeric) = 4.3049198661034273177897182411951
absolute error = 4.3049198661034273177897182411951
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1458.7MB, alloc=52.3MB, time=16.08
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (closed_form) = 0
y[1] (numeric) = 4.3187523369160284789138152401041
absolute error = 4.3187523369160284789138152401041
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (closed_form) = 0
y[1] (numeric) = 4.3325001173115336193913210005385
absolute error = 4.3325001173115336193913210005385
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (closed_form) = 0
y[1] (numeric) = 4.3461632909212686646851358060165
absolute error = 4.3461632909212686646851358060165
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (closed_form) = 0
y[1] (numeric) = 4.3597419546134038304209566469381
absolute error = 4.3597419546134038304209566469381
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (closed_form) = 0
y[1] (numeric) = 4.3732362182882607797804395010994
absolute error = 4.3732362182882607797804395010994
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (closed_form) = 0
y[1] (numeric) = 4.3866462046717798364648408563991
absolute error = 4.3866462046717798364648408563991
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (closed_form) = 0
y[1] (numeric) = 4.3999720491072956926760742022782
absolute error = 4.3999720491072956926760742022782
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1501.4MB, alloc=52.3MB, time=16.55
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (closed_form) = 0
y[1] (numeric) = 4.4132138993457684051182109166965
absolute error = 4.4132138993457684051182109166965
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (closed_form) = 0
y[1] (numeric) = 4.4263719153346147304272897978427
absolute error = 4.4263719153346147304272897978427
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (closed_form) = 0
y[1] (numeric) = 4.4394462690052830186907690776319
absolute error = 4.4394462690052830186907690776319
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (closed_form) = 0
y[1] (numeric) = 4.4524371440597129638407749660517
absolute error = 4.4524371440597129638407749660517
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (closed_form) = 0
y[1] (numeric) = 4.4653447357558195067325328664537
absolute error = 4.4653447357558195067325328664537
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (closed_form) = 0
y[1] (numeric) = 4.4781692506921381046940882893183
absolute error = 4.4781692506921381046940882893183
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (closed_form) = 0
y[1] (numeric) = 4.4909109065917664243005522494278
absolute error = 4.4909109065917664243005522494278
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (closed_form) = 0
y[1] (numeric) = 4.5035699320857352861263880776876
absolute error = 4.5035699320857352861263880776876
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1544.3MB, alloc=52.3MB, time=17.02
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (closed_form) = 0
y[1] (numeric) = 4.5161465664959393952934281550013
absolute error = 4.5161465664959393952934281550013
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (closed_form) = 0
y[1] (numeric) = 4.5286410596177560337754269265364
absolute error = 4.5286410596177560337754269265364
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (closed_form) = 0
y[1] (numeric) = 4.541053671502477473635915661199
absolute error = 4.541053671502477473635915661199
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (closed_form) = 0
y[1] (numeric) = 4.5533846722396803986323615580022
absolute error = 4.5533846722396803986323615580022
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (closed_form) = 0
y[1] (numeric) = 4.5656343417396530988520232335772
absolute error = 4.5656343417396530988520232335772
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (closed_form) = 0
y[1] (numeric) = 4.5778029695159986331528399984284
absolute error = 4.5778029695159986331528399984284
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (closed_form) = 0
y[1] (numeric) = 4.5898908544685295410244183557594
absolute error = 4.5898908544685295410244183557594
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1587.0MB, alloc=52.3MB, time=17.48
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (closed_form) = 0
y[1] (numeric) = 4.6018983046665670328722261635981
absolute error = 4.6018983046665670328722261635981
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (closed_form) = 0
y[1] (numeric) = 4.6138256371327548994250287756227
absolute error = 4.6138256371327548994250287756227
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (closed_form) = 0
y[1] (numeric) = 4.6256731776274956606798810163311
absolute error = 4.6256731776274956606798810163311
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (closed_form) = 0
y[1] (numeric) = 4.637441260434113726181142025306
absolute error = 4.637441260434113726181142025306
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (closed_form) = 0
y[1] (numeric) = 4.6491302281448475650688901614418
absolute error = 4.6491302281448475650688901614418
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (closed_form) = 0
y[1] (numeric) = 4.6607404314477700897515676377601
absolute error = 4.6607404314477700897515676377601
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (closed_form) = 0
y[1] (numeric) = 4.6722722289147336447131138785628
absolute error = 4.6722722289147336447131138785628
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1629.8MB, alloc=52.3MB, time=17.97
x[1] = 2.95
y[1] (closed_form) = 0
y[1] (numeric) = 4.6837259867904331652402937367386
absolute error = 4.6837259867904331652402937367386
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (closed_form) = 0
y[1] (numeric) = 4.6951020787826782330612057357455
absolute error = 4.6951020787826782330612057357455
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (closed_form) = 0
y[1] (numeric) = 4.706400885853961910254028214836
absolute error = 4.706400885853961910254028214836
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (closed_form) = 0
y[1] (numeric) = 4.7176227960144113824696183273189
absolute error = 4.7176227960144113824696183273189
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (closed_form) = 0
y[1] (numeric) = 4.7287682041162025905848253258591
absolute error = 4.7287682041162025905848253258591
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (closed_form) = 0
y[1] (numeric) = 4.7398375116495181793540224539042
absolute error = 4.7398375116495181793540224539042
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (closed_form) = 0
y[1] (numeric) = 4.7508311265401252453577968030811
absolute error = 4.7508311265401252453577968030811
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (closed_form) = 0
y[1] (numeric) = 4.7617494629486465273764312758473
absolute error = 4.7617494629486465273764312758473
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1672.6MB, alloc=52.3MB, time=18.44
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (closed_form) = 0
y[1] (numeric) = 4.7725929410715958529698826374515
absolute error = 4.7725929410715958529698826374515
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (closed_form) = 0
y[1] (numeric) = 4.7833619869442458381639327287755
absolute error = 4.7833619869442458381639327287755
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (closed_form) = 0
y[1] (numeric) = 4.7940570322453930352719576343353
absolute error = 4.7940570322453930352719576343353
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (closed_form) = 0
y[1] (numeric) = 4.804678514104082939479707999276
absolute error = 4.804678514104082939479707999276
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (closed_form) = 0
y[1] (numeric) = 4.8152268749083545002508115395883
absolute error = 4.8152268749083545002508115395883
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (closed_form) = 0
y[1] (numeric) = 4.8257025621160610411448676928321
absolute error = 4.8257025621160610411448676928321
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (closed_form) = 0
y[1] (numeric) = 4.8361060280678217734564060172815
absolute error = 4.8361060280678217734564060172815
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1715.3MB, alloc=52.3MB, time=18.91
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (closed_form) = 0
y[1] (numeric) = 4.8464377298021553972667656175893
absolute error = 4.8464377298021553972667656175893
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (closed_form) = 0
y[1] (numeric) = 4.8566981288728446200439697957014
absolute error = 4.8566981288728446200439697957014
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (closed_form) = 0
y[1] (numeric) = 4.866887691168577789726589653457
absolute error = 4.866887691168577789726589653457
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (closed_form) = 0
y[1] (numeric) = 4.8770068867349112380921723550799
absolute error = 4.8770068867349112380921723550799
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (closed_form) = 0
y[1] (numeric) = 4.8870561895985933628523076086132
absolute error = 4.8870561895985933628523076086132
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (closed_form) = 0
y[1] (numeric) = 4.8970360775942889449561067744087
absolute error = 4.8970360775942889449561067744087
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (closed_form) = 0
y[1] (numeric) = 4.9069470321937397025517632047181
absolute error = 4.9069470321937397025517632047181
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (closed_form) = 0
y[1] (numeric) = 4.9167895383373946263914366273428
absolute error = 4.9167895383373946263914366273428
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1758.1MB, alloc=52.3MB, time=19.38
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (closed_form) = 0
y[1] (numeric) = 4.9265640842685412245178524726571
absolute error = 4.9265640842685412245178524726571
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (closed_form) = 0
y[1] (numeric) = 4.9362711613699664281030528966904
absolute error = 4.9362711613699664281030528966904
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (closed_form) = 0
y[1] (numeric) = 4.9459112640031735764945627104227
absolute error = 4.9459112640031735764945627104227
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (closed_form) = 0
y[1] (numeric) = 4.9554848893501796089495114399411
absolute error = 4.9554848893501796089495114399411
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (closed_form) = 0
y[1] (numeric) = 4.9649925372579143442057649612864
absolute error = 4.9649925372579143442057649612864
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (closed_form) = 0
y[1] (numeric) = 4.9744347100852415278701731006405
absolute error = 4.9744347100852415278701731006405
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (closed_form) = 0
y[1] (numeric) = 4.9838119125526191724349586758106
absolute error = 4.9838119125526191724349586758106
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1800.9MB, alloc=52.3MB, time=19.84
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (closed_form) = 0
y[1] (numeric) = 4.9931246515944146063209751026497
absolute error = 4.9931246515944146063209751026497
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (closed_form) = 0
y[1] (numeric) = 5.0023734362138875873691949174125
absolute error = 5.0023734362138875873691949174125
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (closed_form) = 0
y[1] (numeric) = 5.0115587773408528232604554329903
absolute error = 5.0115587773408528232604554329903
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (closed_form) = 0
y[1] (numeric) = 5.0206811876920312769639891702919
absolute error = 5.0206811876920312769639891702919
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (closed_form) = 0
y[1] (numeric) = 5.0297411816340977199499532249625
absolute error = 5.0297411816340977199499532249625
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (closed_form) = 0
y[1] (numeric) = 5.0387392750494301299308039085798
absolute error = 5.0387392750494301299308039085798
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (closed_form) = 0
y[1] (numeric) = 5.0476759852045647136320332651075
absolute error = 5.0476759852045647136320332651075
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (closed_form) = 0
y[1] (numeric) = 5.0565518306213585687778748596035
absolute error = 5.0565518306213585687778748596035
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1843.6MB, alloc=52.3MB, time=20.31
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (closed_form) = 0
y[1] (numeric) = 5.065367330950860283289762585713
absolute error = 5.065367330950860283289762585713
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (closed_form) = 0
y[1] (numeric) = 5.074123006849887103748557787863
absolute error = 5.074123006849887103748557787863
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (closed_form) = 0
y[1] (numeric) = 5.0828193798603056895181678908498
absolute error = 5.0828193798603056895181678908498
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (closed_form) = 0
y[1] (numeric) = 5.091456972291011903560903735424
absolute error = 5.091456972291011903560903735424
relative error = -1 %
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) = 0
y[1] (numeric) = 5.1000363071026035758290042320525
absolute error = 5.1000363071026035758290042320525
relative error = -1 %
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) = 0
y[1] (numeric) = 5.1085579077947387100720330500083
absolute error = 5.1085579077947387100720330500083
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (closed_form) = 0
y[1] (numeric) = 5.1170222982961701897828579639746
absolute error = 5.1170222982961701897828579639746
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1886.4MB, alloc=52.3MB, time=20.78
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (closed_form) = 0
y[1] (numeric) = 5.1254300028574466735909973687252
absolute error = 5.1254300028574466735909973687252
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (closed_form) = 0
y[1] (numeric) = 5.133781545946268054427506434729
absolute error = 5.133781545946268054427506434729
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (closed_form) = 0
y[1] (numeric) = 5.1420774521454825899095321574278
absolute error = 5.1420774521454825899095321574278
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (closed_form) = 0
y[1] (numeric) = 5.1503182460537115932595486944137
absolute error = 5.1503182460537115932595486944137
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (closed_form) = 0
y[1] (numeric) = 5.1585044521885864042756324279159
absolute error = 5.1585044521885864042756324279159
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (closed_form) = 0
y[1] (numeric) = 5.1666365948925812379557427226267
absolute error = 5.1666365948925812379557427226267
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (closed_form) = 0
y[1] (numeric) = 5.1747151982414244338629348804386
absolute error = 5.1747151982414244338629348804386
relative error = -1 %
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) = 0
y[1] (numeric) = 5.1827407859550696016751755780154
absolute error = 5.1827407859550696016751755780154
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1929.1MB, alloc=52.3MB, time=21.25
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (closed_form) = 0
y[1] (numeric) = 5.1907138813112071770337291653728
absolute error = 5.1907138813112071770337291653728
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (closed_form) = 0
y[1] (numeric) = 5.1986350070612959661960311935231
absolute error = 5.1986350070612959661960311935231
relative error = -1 %
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) = 0
y[1] (numeric) = 5.2065046853490933674899385610359
absolute error = 5.2065046853490933674899385610359
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (closed_form) = 0
y[1] (numeric) = 5.2143234376316621115048234422566
absolute error = 5.2143234376316621115048234422566
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (closed_form) = 0
y[1] (numeric) = 5.2220917846028305596628379662664
absolute error = 5.2220917846028305596628379662664
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (closed_form) = 0
y[1] (numeric) = 5.2298102461190828415874522746515
absolute error = 5.2298102461190828415874522746515
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (closed_form) = 0
y[1] (numeric) = 5.2374793411278543947994736291451
absolute error = 5.2374793411278543947994736291451
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1971.9MB, alloc=52.3MB, time=21.72
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (closed_form) = 0
y[1] (numeric) = 5.2450995875982077949751676389479
absolute error = 5.2450995875982077949751676389479
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (closed_form) = 0
y[1] (numeric) = 5.2526715024538631305291156190983
absolute error = 5.2526715024538631305291156190983
relative error = -1 %
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) = 0
y[1] (numeric) = 5.2601956015085565808503644331183
absolute error = 5.2601956015085565808503644331183
relative error = -1 %
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) = 0
y[1] (numeric) = 5.2676723994037003023222503472063
absolute error = 5.2676723994037003023222503472063
relative error = -1 %
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) = 0
y[1] (numeric) = 5.275102409548316209477305690921
absolute error = 5.275102409548316209477305690921
relative error = -1 %
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) = 0
y[1] (numeric) = 5.2824861440612157594490702077586
absolute error = 5.2824861440612157594490702077586
relative error = -1 %
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) = 0
y[1] (numeric) = 5.2898241137153974054410302544311
absolute error = 5.2898241137153974054410302544311
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=2014.6MB, alloc=52.3MB, time=22.19
x[1] = 3.62
y[1] (closed_form) = 0
y[1] (numeric) = 5.2971168278846329783878084618835
absolute error = 5.2971168278846329783878084618835
relative error = -1 %
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) = 0
y[1] (numeric) = 5.3043647944922138844749849159901
absolute error = 5.3043647944922138844749849159901
relative error = -1 %
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) = 0
y[1] (numeric) = 5.3115685199618276688441568918438
absolute error = 5.3115685199618276688441568918438
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (closed_form) = 0
y[1] (numeric) = 5.3187285091705351917657441903457
absolute error = 5.3187285091705351917657441903457
relative error = -1 %
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) = 0
y[1] (numeric) = 5.3258452654038183919357289441654
absolute error = 5.3258452654038183919357289441654
relative error = -1 %
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) = 0
y[1] (numeric) = 5.3329192903126683714627475651249
absolute error = 5.3329192903126683714627475651249
relative error = -1 %
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) = 0
y[1] (numeric) = 5.339951083872683327675359848493
absolute error = 5.339951083872683327675359848493
relative error = -1 %
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) = 0
y[1] (numeric) = 5.3469411443451456772115658005591
absolute error = 5.3469411443451456772115658005591
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2057.5MB, alloc=52.3MB, time=22.66
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (closed_form) = 0
y[1] (numeric) = 5.3538899682400475670695269435875
absolute error = 5.3538899682400475670695269435875
relative error = -1 %
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) = 0
y[1] (numeric) = 5.3607980502810338445169885845633
absolute error = 5.3607980502810338445169885845633
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (closed_form) = 0
y[1] (numeric) = 5.3676658833722314620963372486399
absolute error = 5.3676658833722314620963372486399
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (closed_form) = 0
y[1] (numeric) = 5.374493958566934224545013861522
absolute error = 5.374493958566934224545013861522
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (closed_form) = 0
y[1] (numeric) = 5.3812827650381117404037240435357
absolute error = 5.3812827650381117404037240435357
relative error = -1 %
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) = 0
y[1] (numeric) = 5.3880327900507114215391461514057
absolute error = 5.3880327900507114215391461514057
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (closed_form) = 0
y[1] (numeric) = 5.394744518935722377901096353168
absolute error = 5.394744518935722377901096353168
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=2100.4MB, alloc=52.3MB, time=23.13
x[1] = 3.77
y[1] (closed_form) = 0
y[1] (numeric) = 5.401418435065970081710479786154
absolute error = 5.401418435065970081710479786154
relative error = -1 %
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) = 0
y[1] (numeric) = 5.4080550198336107240853507117679
absolute error = 5.4080550198336107240853507117679
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (closed_form) = 0
y[1] (numeric) = 5.4146547526292942570176441693717
absolute error = 5.4146547526292942570176441693717
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (closed_form) = 0
y[1] (numeric) = 5.4212181108229652037810223582745
absolute error = 5.4212181108229652037810223582745
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (closed_form) = 0
y[1] (numeric) = 5.427745569746270430458593725063
absolute error = 5.427745569746270430458593725063
relative error = -1 %
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) = 0
y[1] (numeric) = 5.4342376026765431995157848994098
absolute error = 5.4342376026765431995157848994098
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (closed_form) = 0
y[1] (numeric) = 5.440694680822332972406672376526
absolute error = 5.440694680822332972406672376526
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (closed_form) = 0
y[1] (numeric) = 5.4471172733104505913009375105328
absolute error = 5.4471172733104505913009375105328
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2143.2MB, alloc=52.3MB, time=23.59
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (closed_form) = 0
y[1] (numeric) = 5.4535058471744986493741148410616
absolute error = 5.4535058471744986493741148410616
relative error = -1 %
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) = 0
y[1] (numeric) = 5.4598608673448570539487038536842
absolute error = 5.4598608673448570539487038536842
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (closed_form) = 0
y[1] (numeric) = 5.4661827966400939963530690866149
absolute error = 5.4661827966400939963530690866149
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (closed_form) = 0
y[1] (numeric) = 5.4724720957597727659365997150411
absolute error = 5.4724720957597727659365997150411
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (closed_form) = 0
y[1] (numeric) = 5.4787292232786250825140738220205
absolute error = 5.4787292232786250825140738220205
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (closed_form) = 0
y[1] (numeric) = 5.4849546356420618708936019102633
absolute error = 5.4849546356420618708936019102633
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (closed_form) = 0
y[1] (numeric) = 5.4911487871629926623684863598637
absolute error = 5.4911487871629926623684863598637
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=2186.1MB, alloc=52.3MB, time=24.06
x[1] = 3.92
y[1] (closed_form) = 0
y[1] (numeric) = 5.497312130019925080435184359947
absolute error = 5.497312130019925080435184359947
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (closed_form) = 0
y[1] (numeric) = 5.5034451142563161508626338086498
absolute error = 5.5034451142563161508626338086498
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (closed_form) = 0
y[1] (numeric) = 5.5095481877811474689219732597914
absolute error = 5.5095481877811474689219732597914
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (closed_form) = 0
y[1] (numeric) = 5.5156217963706965584439242432262
absolute error = 5.5156217963706965584439242432262
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (closed_form) = 0
y[1] (numeric) = 5.5216663836714770677719756120904
absolute error = 5.5216663836714770677719756120904
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (closed_form) = 0
y[1] (numeric) = 5.5276823912043207660056748137058
absolute error = 5.5276823912043207660056748137058
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (closed_form) = 0
y[1] (numeric) = 5.5336702583695746285770057802492
absolute error = 5.5336702583695746285770057802492
relative error = -1 %
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) = 0
y[1] (numeric) = 5.5396304224533866335858296466723
absolute error = 5.5396304224533866335858296466723
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2229.0MB, alloc=52.3MB, time=24.53
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (closed_form) = 0
y[1] (numeric) = 5.5455633186350542288641094950387
absolute error = 5.5455633186350542288641094950387
relative error = -1 %
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) = 0
y[1] (numeric) = 5.5514693799954097738841716651135
absolute error = 5.5514693799954097738841716651135
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (closed_form) = 0
y[1] (numeric) = 5.5573490375262176098291987205504
absolute error = 5.5573490375262176098291987205504
relative error = -1 %
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) = 0
y[1] (numeric) = 5.5632027201405577648746710580819
absolute error = 5.5632027201405577648746710580819
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (closed_form) = 0
y[1] (numeric) = 5.569030854684171659472224482647
absolute error = 5.569030854684171659472224482647
relative error = -1 %
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) = 0
y[1] (numeric) = 5.5748338659477455376814199002983
absolute error = 5.5748338659477455376814199002983
relative error = -1 %
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) = 0
y[1] (numeric) = 5.5806121766801077148735829443548
absolute error = 5.5806121766801077148735829443548
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (closed_form) = 0
y[1] (numeric) = 5.5863662076023160989627120303714
absolute error = 5.5863662076023160989627120303714
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2271.9MB, alloc=52.3MB, time=25.02
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (closed_form) = 0
y[1] (numeric) = 5.5920963774226128112430837638702
absolute error = 5.5920963774226128112430837638702
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (closed_form) = 0
y[1] (numeric) = 5.5978031028522231034871388476858
absolute error = 5.5978031028522231034871388476858
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (closed_form) = 0
y[1] (numeric) = 5.6034867986219761397498127142818
absolute error = 5.6034867986219761397498127142818
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (closed_form) = 0
y[1] (numeric) = 5.609147877499725583919588616295
absolute error = 5.609147877499725583919588616295
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (closed_form) = 0
y[1] (numeric) = 5.6147867503085483070485270693135
absolute error = 5.6147867503085483070485270693135
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (closed_form) = 0
y[1] (numeric) = 5.620403825945699901492930824798
absolute error = 5.620403825945699901492930824798
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (closed_form) = 0
y[1] (numeric) = 5.6259995114023060615257435325322
absolute error = 5.6259995114023060615257435325322
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2314.8MB, alloc=52.3MB, time=25.48
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (closed_form) = 0
y[1] (numeric) = 5.6315742117837692619766885060268
absolute error = 5.6315742117837692619766885060268
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (closed_form) = 0
y[1] (numeric) = 5.6371283303308705372645827993289
absolute error = 5.6371283303308705372645827993289
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (closed_form) = 0
y[1] (numeric) = 5.6426622684415465325686553264876
absolute error = 5.6426622684415465325686553264876
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (closed_form) = 0
y[1] (numeric) = 5.6481764256933223665146635815666
absolute error = 5.6481764256933223665146635815666
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (closed_form) = 0
y[1] (numeric) = 5.6536711998663812103116770216224
absolute error = 5.6536711998663812103116770216224
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (closed_form) = 0
y[1] (numeric) = 5.6591469869672518514627985460576
absolute error = 5.6591469869672518514627985460576
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (closed_form) = 0
y[1] (numeric) = 5.6646041812530958706954920187514
absolute error = 5.6646041812530958706954920187514
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=2357.6MB, alloc=52.3MB, time=25.95
x[1] = 4.22
y[1] (closed_form) = 0
y[1] (numeric) = 5.6700431752565764183334279513546
absolute error = 5.6700431752565764183334279513546
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (closed_form) = 0
y[1] (numeric) = 5.6754643598112909306916436966862
absolute error = 5.6754643598112909306916436966862
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (closed_form) = 0
y[1] (numeric) = 5.6808681240777504779608127830544
absolute error = 5.6808681240777504779608127830544
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (closed_form) = 0
y[1] (numeric) = 5.6862548555698887822054272812226
absolute error = 5.6862548555698887822054272812226
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (closed_form) = 0
y[1] (numeric) = 5.6916249401820842872957767113658
absolute error = 5.6916249401820842872957767113658
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (closed_form) = 0
y[1] (numeric) = 5.6969787622166790015957169957688
absolute error = 5.6969787622166790015957169957688
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (closed_form) = 0
y[1] (numeric) = 5.7023167044119781688179614186912
absolute error = 5.7023167044119781688179614186912
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (closed_form) = 0
y[1] (numeric) = 5.7076391479707151524259656517344
absolute error = 5.7076391479707151524259656517344
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2400.5MB, alloc=52.3MB, time=26.42
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (closed_form) = 0
y[1] (numeric) = 5.7129464725889662441055061250308
absolute error = 5.7129464725889662441055061250308
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (closed_form) = 0
y[1] (numeric) = 5.7182390564855004269577009127918
absolute error = 5.7182390564855004269577009127918
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (closed_form) = 0
y[1] (numeric) = 5.7235172764315494389950191989836
absolute error = 5.7235172764315494389950191989836
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (closed_form) = 0
y[1] (numeric) = 5.7287815077809837920776225725644
absolute error = 5.7287815077809837920776225725644
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (closed_form) = 0
y[1] (numeric) = 5.73403212450088070544210298855
absolute error = 5.73403212450088070544210298855
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (closed_form) = 0
y[1] (numeric) = 5.7392694992024702112890672189868
absolute error = 5.7392694992024702112890672189868
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (closed_form) = 0
y[1] (numeric) = 5.7444940031724459823583664126728
absolute error = 5.7444940031724459823583664126728
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (closed_form) = 0
y[1] (numeric) = 5.7497060064046277178866931415118
absolute error = 5.7497060064046277178866931415118
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2443.4MB, alloc=52.3MB, time=26.89
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (closed_form) = 0
y[1] (numeric) = 5.754905877631962204674441417761
absolute error = 5.754905877631962204674441417761
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (closed_form) = 0
y[1] (numeric) = 5.7600939843588504440566411330796
absolute error = 5.7600939843588504440566411330796
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (closed_form) = 0
y[1] (numeric) = 5.7652706928937885032525094573208
absolute error = 5.7652706928937885032525094573208
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (closed_form) = 0
y[1] (numeric) = 5.77043636838231001074212254892
absolute error = 5.77043636838231001074212254892
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (closed_form) = 0
y[1] (numeric) = 5.7755913748402184698754262569408
absolute error = 5.7755913748402184698754262569408
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (closed_form) = 0
y[1] (numeric) = 5.7807360751870978127526816164875
absolute error = 5.7807360751870978127526816164875
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (closed_form) = 0
y[1] (numeric) = 5.7858708312800898574265466379663
absolute error = 5.7858708312800898574265466379663
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2486.3MB, alloc=52.3MB, time=27.36
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (closed_form) = 0
y[1] (numeric) = 5.7909960039479275655698383843102
absolute error = 5.7909960039479275655698383843102
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (closed_form) = 0
y[1] (numeric) = 5.7961119530252132248403353172603
absolute error = 5.7961119530252132248403353172603
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (closed_form) = 0
y[1] (numeric) = 5.801219037386930900170526907316
absolute error = 5.801219037386930900170526907316
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (closed_form) = 0
y[1] (numeric) = 5.8063176149831827110365717485652
absolute error = 5.8063176149831827110365717485652
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (closed_form) = 0
y[1] (numeric) = 5.8114080428741386973420852698635
absolute error = 5.8114080428741386973420852698635
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (closed_form) = 0
y[1] (numeric) = 5.816490677265190234818373421222
absolute error = 5.816490677265190234818373421222
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (closed_form) = 0
y[1] (numeric) = 5.8215658735422971517272359890031
absolute error = 5.8215658735422971517272359890031
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (closed_form) = 0
y[1] (numeric) = 5.826633986307518882093427067809
absolute error = 5.826633986307518882093427067809
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2529.1MB, alloc=52.3MB, time=27.84
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (closed_form) = 0
y[1] (numeric) = 5.8316953694147201666331209298299
absolute error = 5.8316953694147201666331209298299
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (closed_form) = 0
y[1] (numeric) = 5.8367503760054419809278588527922
absolute error = 5.8367503760054419809278588527922
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (closed_form) = 0
y[1] (numeric) = 5.8417993585449285311695860465411
absolute error = 5.8417993585449285311695860465411
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (closed_form) = 0
y[1] (numeric) = 5.8468426688583013109240840930554
absolute error = 5.8468426688583013109240840930554
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (closed_form) = 0
y[1] (numeric) = 5.8518806581668713577831900605035
absolute error = 5.8518806581668713577831900605035
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (closed_form) = 0
y[1] (numeric) = 5.8569136771245809864596260690028
absolute error = 5.8569136771245809864596260690028
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (closed_form) = 0
y[1] (numeric) = 5.8619420758545664047839977036278
absolute error = 5.8619420758545664047839977036278
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2571.9MB, alloc=52.3MB, time=28.31
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (closed_form) = 0
y[1] (numeric) = 5.8669662039858327411563831445054
absolute error = 5.8669662039858327411563831445054
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (closed_form) = 0
y[1] (numeric) = 5.8719864106900331262525067543453
absolute error = 5.8719864106900331262525067543453
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (closed_form) = 0
y[1] (numeric) = 5.8770030447183435781569913374226
absolute error = 5.8770030447183435781569913374226
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (closed_form) = 0
y[1] (numeric) = 5.8820164544384255385663683007914
absolute error = 5.8820164544384255385663683007914
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (closed_form) = 0
y[1] (numeric) = 5.8870269878714679982475883826887
absolute error = 5.8870269878714679982475883826887
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (closed_form) = 0
y[1] (numeric) = 5.8920349927293012325312586585296
absolute error = 5.8920349927293012325312586585296
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (closed_form) = 0
y[1] (numeric) = 5.8970408164515742422425393169024
absolute error = 5.8970408164515742422425393169024
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2614.7MB, alloc=52.3MB, time=28.78
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (closed_form) = 0
y[1] (numeric) = 5.9020448062429880621085591513211
absolute error = 5.9020448062429880621085591513211
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (closed_form) = 0
y[1] (numeric) = 5.9070473091105771573134637610737
absolute error = 5.9070473091105771573134637610737
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (closed_form) = 0
y[1] (numeric) = 5.9120486719010311794869645175281
absolute error = 5.9120486719010311794869645175281
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (closed_form) = 0
y[1] (numeric) = 5.9170492413380493959976822191288
absolute error = 5.9170492413380493959976822191288
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (closed_form) = 0
y[1] (numeric) = 5.9220493640597201409688064354157
absolute error = 5.9220493640597201409688064354157
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (closed_form) = 0
y[1] (numeric) = 5.9270493866559176629326665048495
absolute error = 5.9270493866559176629326665048495
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (closed_form) = 0
y[1] (numeric) = 5.9320496557057087624866650221736
absolute error = 5.9320496557057087624866650221736
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (closed_form) = 0
y[1] (numeric) = 5.937050517814761623701452292621
absolute error = 5.937050517814761623701452292621
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2657.6MB, alloc=52.3MB, time=29.25
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (closed_form) = 0
y[1] (numeric) = 5.9420523196527492453608572965552
absolute error = 5.9420523196527492453608572965552
relative error = -1 %
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) = 0
y[1] (numeric) = 5.9470554079907398723814080368959
absolute error = 5.9470554079907398723814080368959
relative error = -1 %
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) = 0
y[1] (numeric) = 5.9520601297385668139685746010273
absolute error = 5.9520601297385668139685746010273
relative error = -1 %
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) = 0
y[1] (numeric) = 5.9570668319821700132202920575194
absolute error = 5.9570668319821700132202920575194
relative error = -1 %
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) = 0
y[1] (numeric) = 5.9620758620209017029908577070296
absolute error = 5.9620758620209017029908577070296
relative error = -1 %
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) = 0
y[1] (numeric) = 5.9670875674047884448868087778402
absolute error = 5.9670875674047884448868087778402
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (closed_form) = 0
y[1] (numeric) = 5.9721022959717418022896308779321
absolute error = 5.9721022959717418022896308779321
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2700.3MB, alloc=52.3MB, time=29.72
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (closed_form) = 0
y[1] (numeric) = 5.9771203958847098442988158449338
absolute error = 5.9771203958847098442988158449338
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (closed_form) = 0
y[1] (numeric) = 5.9821422156687616154755469842508
absolute error = 5.9821422156687616154755469842508
relative error = -1 %
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) = 0
y[1] (numeric) = 5.9871681042480966362568322881462
absolute error = 5.9871681042480966362568322881462
relative error = -1 %
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) = 0
y[1] (numeric) = 5.9921984109829714209190068819501
absolute error = 5.9921984109829714209190068819501
relative error = -1 %
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) = 0
y[1] (numeric) = 5.9972334857065349140171065975656
absolute error = 5.9972334857065349140171065975656
relative error = -1 %
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) = 0
y[1] (numeric) = 6.0022736787615646523338162385433
absolute error = 6.0022736787615646523338162385433
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (closed_form) = 0
y[1] (numeric) = 6.0073193410370953575619580388858
absolute error = 6.0073193410370953575619580388858
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (closed_form) = 0
y[1] (numeric) = 6.0123708240049315552436319914524
absolute error = 6.0123708240049315552436319914524
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2743.2MB, alloc=52.3MB, time=30.19
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (closed_form) = 0
y[1] (numeric) = 6.017428479756035697925452445195
absolute error = 6.017428479756035697925452445195
relative error = -1 %
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) = 0
y[1] (numeric) = 6.0224926610367831450937261264892
absolute error = 6.0224926610367831450937261264892
relative error = -1 %
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) = 0
y[1] (numeric) = 6.0275637212850752192594541120367
absolute error = 6.0275637212850752192594541120367
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (closed_form) = 0
y[1] (numeric) = 6.0326420146663014166070849435394
absolute error = 6.0326420146663014166070849435394
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (closed_form) = 0
y[1] (numeric) = 6.0377278961091417019422927817819
absolute error = 6.0377278961091417019422927817819
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (closed_form) = 0
y[1] (numeric) = 6.042821721341199661315051006077
absolute error = 6.042821721341199661315051006077
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (closed_form) = 0
y[1] (numeric) = 6.0479238469244571217004545157422
absolute error = 6.0479238469244571217004545157422
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2786.0MB, alloc=52.3MB, time=30.66
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (closed_form) = 0
y[1] (numeric) = 6.0530346302905406755399810772526
absolute error = 6.0530346302905406755399810772526
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (closed_form) = 0
y[1] (numeric) = 6.0581544297757903688325218963361
absolute error = 6.0581544297757903688325218963361
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (closed_form) = 0
y[1] (numeric) = 6.0632836046561206248735391835186
absolute error = 6.0632836046561206248735391835186
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Finished!
diff ( y , x , 1 ) = expt ( 2.0 , sin ( x ) ) ;
Iterations = 4900
Total Elapsed Time = 30 Seconds
Elapsed Time(since restart) = 30 Seconds
Time to Timeout = 2 Minutes 29 Seconds
Percent Done = 100 %
> quit
memory used=2804.7MB, alloc=52.3MB, time=30.84