|\^/| Maple 2016 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number 0
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
> if (years_int > 0) then # if number 1
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 2
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 7
# Begin Function number 8
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 8
# Begin Function number 9
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 9
# Begin Function number 10
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 7
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 7;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 10
# Begin Function number 11
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 7
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 11
# Begin Function number 12
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 12
# Begin Function number 13
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 16
# Begin Function number 17
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 17
# Begin Function number 18
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 6
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 7
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 8
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 9
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 10
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 11
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 12
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 12
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 19
# Begin Function number 20
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 20
# Begin Function number 21
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 12
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 12;
> if (errflag) then # if number 12
> quit;
> fi;# end if 12
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 21
# Begin Function number 22
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 12
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 13
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 13
> fi;# end if 12;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 22
# Begin Function number 23
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 12
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 12;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 23
# Begin Function number 24
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 24
# Begin Function number 25
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 25
# Begin Function number 26
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalf(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalf(in_val); ret end proc
# End Function number 26
# Begin Function number 27
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 12
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 27
# Begin Function number 28
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 28
# Begin Function number 29
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 12
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 13
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 15
> if (rcs > glob__0) then # if number 16
> rad_c := sqrt(rcs) * float_abs(glob_h);
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 16
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> fi;# end if 13
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 12;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := sqrt(rcs)*float_abs(glob_h)
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 29
# Begin Function number 30
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 30
# Begin Function number 31
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 31
# Begin Function number 32
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 12
> if (array_fact_1[nnn] = 0) then # if number 13
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 13;
> else
> ret := factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 32
# Begin Function number 33
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 12
> if (array_fact_2[mmm,nnn] = 0) then # if number 13
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 13;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 33
# Begin Function number 34
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 34
# Begin Function number 35
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 35
# Begin Function number 36
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 36
# Begin Function number 37
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 37
# Begin Function number 38
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 38
# Begin Function number 39
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 39
# Begin Function number 40
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 40
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(0.0));
> 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,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> 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_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, 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,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> 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_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, 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,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> 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_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, 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,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> 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_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, 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,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> 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)*24*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_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, 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)*24*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,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> 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_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, 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,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> 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_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, 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,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_2D0[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_3D0[1];
> #emit pre sqrt 1 $eq_no = 1
> array_tmp3[1] := sqrt(array_tmp2[1]);
> array_tmp4_a1[1] := sin(array_tmp3[1]);
> array_tmp4_a2[1] := cos(array_tmp3[1]);
> array_tmp4[1] := (array_tmp4_a1[1] / array_tmp4_a2[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_const_0D0[1] + array_tmp4[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_tmp5[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_2D0[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre sqrt 2 $eq_no = 1
> array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/glob__2;
> #emit pre tan $eq_no = 1
> array_tmp4_a1[2] := att(1,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[2] := neg(att(1,array_tmp4_a1,array_tmp3,1));
> array_tmp4[2] := (array_tmp4_a1[2] - ats(2,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := 0;
> array_tmp3[3] := neg(ats(3,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
> #emit pre tan $eq_no = 1
> array_tmp4_a1[3] := att(2,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[3] := neg(att(2,array_tmp4_a1,array_tmp3,1));
> array_tmp4[3] := (array_tmp4_a1[3] - ats(3,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp4[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[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 sqrt ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := 0;
> array_tmp3[4] := neg(ats(4,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
> #emit pre tan $eq_no = 1
> array_tmp4_a1[4] := att(3,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[4] := neg(att(3,array_tmp4_a1,array_tmp3,1));
> array_tmp4[4] := (array_tmp4_a1[4] - ats(4,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp4[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[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 sqrt ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := 0;
> array_tmp3[5] := neg(ats(5,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
> #emit pre tan $eq_no = 1
> array_tmp4_a1[5] := att(4,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[5] := neg(att(4,array_tmp4_a1,array_tmp3,1));
> array_tmp4[5] := (array_tmp4_a1[5] - ats(5,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp4[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[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 sqrt LINEAR $eq_no = 1
> array_tmp3[kkk] := 0;
> array_tmp3[kkk] := neg(ats(kkk,array_tmp3,array_tmp3,2)) /array_tmp3[1] / glob__2;
> array_tmp4_a1[kkk] := att(kkk-1 ,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[kkk] := neg(att(kkk-1,array_tmp4_a1,array_tmp3,1));
> array_tmp4[kkk] := (array_tmp4_a1[kkk] - ats(kkk ,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp5[kkk] := array_tmp4[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp5[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_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
array_tmp1[1] := array_const_2D0[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_3D0[1];
array_tmp3[1] := sqrt(array_tmp2[1]);
array_tmp4_a1[1] := sin(array_tmp3[1]);
array_tmp4_a2[1] := cos(array_tmp3[1]);
array_tmp4[1] := array_tmp4_a1[1]/array_tmp4_a2[1];
array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_2D0[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*glob__2);
array_tmp4_a1[2] := att(1, array_tmp4_a2, array_tmp3, 1);
array_tmp4_a2[2] := neg(att(1, array_tmp4_a1, array_tmp3, 1));
array_tmp4[2] := (
array_tmp4_a1[2] - ats(2, array_tmp4_a2, array_tmp4, 2))/
array_tmp4_a2[1];
array_tmp5[2] := array_tmp4[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp3[3] := 0;
array_tmp3[3] :=
neg(ats(3, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
array_tmp4_a1[3] := att(2, array_tmp4_a2, array_tmp3, 1);
array_tmp4_a2[3] := neg(att(2, array_tmp4_a1, array_tmp3, 1));
array_tmp4[3] := (
array_tmp4_a1[3] - ats(3, array_tmp4_a2, array_tmp4, 2))/
array_tmp4_a2[1];
array_tmp5[3] := array_tmp4[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp3[4] := 0;
array_tmp3[4] :=
neg(ats(4, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
array_tmp4_a1[4] := att(3, array_tmp4_a2, array_tmp3, 1);
array_tmp4_a2[4] := neg(att(3, array_tmp4_a1, array_tmp3, 1));
array_tmp4[4] := (
array_tmp4_a1[4] - ats(4, array_tmp4_a2, array_tmp4, 2))/
array_tmp4_a2[1];
array_tmp5[4] := array_tmp4[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp3[5] := 0;
array_tmp3[5] :=
neg(ats(5, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
array_tmp4_a1[5] := att(4, array_tmp4_a2, array_tmp3, 1);
array_tmp4_a2[5] := neg(att(4, array_tmp4_a1, array_tmp3, 1));
array_tmp4[5] := (
array_tmp4_a1[5] - ats(5, array_tmp4_a2, array_tmp4, 2))/
array_tmp4_a2[1];
array_tmp5[5] := array_tmp4[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp3[kkk] := 0;
array_tmp3[kkk] := neg(ats(kkk, array_tmp3, array_tmp3, 2))/(
array_tmp3[1]*glob__2);
array_tmp4_a1[kkk] := att(kkk - 1, array_tmp4_a2, array_tmp3, 1);
array_tmp4_a2[kkk] :=
neg(att(kkk - 1, array_tmp4_a1, array_tmp3, 1));
array_tmp4[kkk] := (
array_tmp4_a1[kkk] - ats(kkk, array_tmp4_a2, array_tmp4, 2))/
array_tmp4_a2[1];
array_tmp5[kkk] := array_tmp4[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y_set_initial[1, kkk + order_d] then
temporary := c(array_tmp5[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,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 40;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=40;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(40),[]);
> array_norms:= Array(0..(40),[]);
> array_fact_1:= Array(0..(40),[]);
> array_1st_rel_error:= Array(0..(2),[]);
> array_last_rel_error:= Array(0..(2),[]);
> array_est_rel_error:= Array(0..(2),[]);
> array_max_est_error:= Array(0..(2),[]);
> array_type_pole:= Array(0..(2),[]);
> array_type_real_pole:= Array(0..(2),[]);
> array_type_complex_pole:= Array(0..(2),[]);
> array_est_digits:= Array(0..(2),[]);
> array_y:= Array(0..(40),[]);
> array_x:= Array(0..(40),[]);
> array_tmp0:= Array(0..(40),[]);
> array_tmp1:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_tmp3:= Array(0..(40),[]);
> array_tmp4_g:= Array(0..(40),[]);
> array_tmp4_a1:= Array(0..(40),[]);
> array_tmp4_a2:= Array(0..(40),[]);
> array_tmp4:= Array(0..(40),[]);
> array_tmp5:= Array(0..(40),[]);
> array_m1:= Array(0..(40),[]);
> array_y_higher := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..40+ 1),[]);
> array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(40) ,(0..40+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 40) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4_a1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4_a2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=40) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4_g);
> zero_ats_ar(array_tmp4_a1);
> zero_ats_ar(array_tmp4_a2);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> 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_const_3D0);
> array_const_3D0[1] := c(3.0);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_h := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 1000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> array_y_set_initial[1,31] := false;
> array_y_set_initial[1,32] := false;
> array_y_set_initial[1,33] := false;
> array_y_set_initial[1,34] := false;
> array_y_set_initial[1,35] := false;
> array_y_set_initial[1,36] := false;
> array_y_set_initial[1,37] := false;
> array_y_set_initial[1,38] := false;
> array_y_set_initial[1,39] := false;
> array_y_set_initial[1,40] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 40;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/tan_sqrt_linpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=40;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := c(0.1);");
> omniout_str(ALWAYS,"x_end := c(5.0) ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_min_h := c(0.001);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 1;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(-1.5);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(0.5);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);");
> 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_min_h := c(0.001);
> glob_type_given_pole := 1;
> array_given_rad_poles[1,1] := c(-1.5);
> array_given_rad_poles[1,2] := c(0.0);
> array_given_ord_poles[1,1] := c(0.5);
> array_given_ord_poles[1,2] := c(0.0);
> #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 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2016-08-26T17:06:11-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"tan_sqrt_lin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ; ")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 308.maple.seems.ok | ")
> ;
> logitem_str(html_log_file,"tan_sqrt_lin diffeq.mxt")
> ;
> logitem_str(html_log_file,"tan_sqrt_lin maple results")
> ;
> logitem_str(html_log_file,"PROBLEM - Singularity not accurate")
> ;
> 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_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
ATS_MAX_TERMS := 40;
Digits := 32;
max_terms := 40;
glob_html_log := true;
array_y_init := Array(0 .. 40, []);
array_norms := Array(0 .. 40, []);
array_fact_1 := Array(0 .. 40, []);
array_1st_rel_error := Array(0 .. 2, []);
array_last_rel_error := Array(0 .. 2, []);
array_est_rel_error := Array(0 .. 2, []);
array_max_est_error := Array(0 .. 2, []);
array_type_pole := Array(0 .. 2, []);
array_type_real_pole := Array(0 .. 2, []);
array_type_complex_pole := Array(0 .. 2, []);
array_est_digits := Array(0 .. 2, []);
array_y := Array(0 .. 40, []);
array_x := Array(0 .. 40, []);
array_tmp0 := Array(0 .. 40, []);
array_tmp1 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_tmp3 := Array(0 .. 40, []);
array_tmp4_g := Array(0 .. 40, []);
array_tmp4_a1 := Array(0 .. 40, []);
array_tmp4_a2 := Array(0 .. 40, []);
array_tmp4 := Array(0 .. 40, []);
array_tmp5 := Array(0 .. 40, []);
array_m1 := Array(0 .. 40, []);
array_y_higher := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 41, []);
array_y_set_initial := Array(0 .. 2, 0 .. 41, []);
array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
array_fact_2 := Array(0 .. 40, 0 .. 41, []);
term := 1;
while term <= 40 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 40 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp4_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp4_a1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp4_a2[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 40 do
term := 1;
while term <= 40 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4_g);
zero_ats_ar(array_tmp4_a1);
zero_ats_ar(array_tmp4_a2);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
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_const_3D0);
array_const_3D0[1] := c(3.0);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_h := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 1000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
array_y_set_initial[1, 31] := false;
array_y_set_initial[1, 32] := false;
array_y_set_initial[1, 33] := false;
array_y_set_initial[1, 34] := false;
array_y_set_initial[1, 35] := false;
array_y_set_initial[1, 36] := false;
array_y_set_initial[1, 37] := false;
array_y_set_initial[1, 38] := false;
array_y_set_initial[1, 39] := false;
array_y_set_initial[1, 40] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 40;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/tan_sqrt_linpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = tan ( sqrt ( 2.0 \
* x + 3.0 ) ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=40;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := c(0.1);");
omniout_str(ALWAYS, "x_end := c(5.0) ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_min_h := c(0.001);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 1;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(-1.5);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(0.5);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);");
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_min_h := c(0.001);
glob_type_given_pole := 1;
array_given_rad_poles[1, 1] := c(-1.5);
array_given_rad_poles[1, 2] := c(0.);
array_given_ord_poles[1, 1] := c(0.5);
array_given_ord_poles[1, 2] := c(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 ) = tan ( sqrt ( 2.\
0 * x + 3.0 ) ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2016-08-26T17:06:11-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"tan_sqrt_lin");
logitem_str(html_log_file, "diff ( y , x , 1 ) = ta\
n ( sqrt ( 2.0 * x + 3.0 ) ) ; ");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 308.maple.seems.ok | ");
logitem_str(html_log_file, "tan_sqrt_lin diffeq.mxt");
logitem_str(html_log_file, "tan_sqrt_lin maple results");
logitem_str(html_log_file, "PROBLEM - Singularity not accurate")
;
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/tan_sqrt_linpostode.ode#################
diff ( y , x , 1 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(0.1);
x_end := c(5.0) ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_min_h := c(0.001);
glob_type_given_pole := 1;
array_given_rad_poles[1,1] := c(-1.5);
array_given_rad_poles[1,2] := c(0.0);
array_given_ord_poles[1,1] := c(0.5);
array_given_ord_poles[1,2] := c(0.0);
#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
memory used=4.1MB, alloc=40.3MB, time=0.09
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=18.5MB, alloc=40.3MB, time=0.26
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (closed_form) = 0
y[1] (numeric) = -0.044601613960418243968668110698576
absolute error = 0.044601613960418243968668110698576
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) = -0.088066884075519907980802638190262
absolute error = 0.088066884075519907980802638190262
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
memory used=62.8MB, alloc=52.3MB, time=0.77
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (closed_form) = 0
y[1] (numeric) = -0.13045284233220728109182318862601
absolute error = 0.13045284233220728109182318862601
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) = -0.1718122558682538203483354896552
absolute error = 0.1718122558682538203483354896552
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
memory used=107.1MB, alloc=52.3MB, time=1.26
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (closed_form) = 0
y[1] (numeric) = -0.21219404226654027677010426618427
absolute error = 0.21219404226654027677010426618427
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) = -0.25164363549036244560739423708931
absolute error = 0.25164363549036244560739423708931
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
memory used=151.4MB, alloc=52.3MB, time=1.77
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (closed_form) = 0
y[1] (numeric) = -0.29020330933658473378989857472295
absolute error = 0.29020330933658473378989857472295
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) = -0.32791246419096267736377193497656
absolute error = 0.32791246419096267736377193497656
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
memory used=195.7MB, alloc=52.3MB, time=2.26
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (closed_form) = 0
y[1] (numeric) = -0.36480788197145358510992738182062
absolute error = 0.36480788197145358510992738182062
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) = -0.40092395340288090553292973425444
absolute error = 0.40092395340288090553292973425444
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
memory used=239.9MB, alloc=52.3MB, time=2.75
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (closed_form) = 0
y[1] (numeric) = -0.4362928811500711360799567266717
absolute error = 0.4362928811500711360799567266717
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (closed_form) = 0
y[1] (numeric) = -0.47094486182290834659326127575715
absolute error = 0.47094486182290834659326127575715
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=284.2MB, alloc=52.3MB, time=3.24
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (closed_form) = 0
y[1] (numeric) = -0.50490824943683429630961666167456
absolute error = 0.50490824943683429630961666167456
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=328.6MB, alloc=52.3MB, time=3.73
x[1] = 0.24
y[1] (closed_form) = 0
y[1] (numeric) = -0.53820970255110409348478697127365
absolute error = 0.53820970255110409348478697127365
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (closed_form) = 0
y[1] (numeric) = -0.57087431700247977711210747563124
absolute error = 0.57087431700247977711210747563124
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=372.9MB, alloc=52.3MB, time=4.23
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (closed_form) = 0
y[1] (numeric) = -0.60292574589422435654613996228287
absolute error = 0.60292574589422435654613996228287
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (closed_form) = 0
y[1] (numeric) = -0.63438630828130766960442391062786
absolute error = 0.63438630828130766960442391062786
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=417.3MB, alloc=52.3MB, time=4.72
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (closed_form) = 0
y[1] (numeric) = -0.66527708780618238183074780616251
absolute error = 0.66527708780618238183074780616251
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (closed_form) = 0
y[1] (numeric) = -0.69561802238003815862697045318553
absolute error = 0.69561802238003815862697045318553
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=461.8MB, alloc=52.3MB, time=5.21
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (closed_form) = 0
y[1] (numeric) = -0.7254279858677436651474137013587
absolute error = 0.7254279858677436651474137013587
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (closed_form) = 0
y[1] (numeric) = -0.75472486261715122189802432691986
absolute error = 0.75472486261715122189802432691986
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=506.1MB, alloc=52.3MB, time=5.70
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (closed_form) = 0
y[1] (numeric) = -0.78352561557209731698466338487678
absolute error = 0.78352561557209731698466338487678
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (closed_form) = 0
y[1] (numeric) = -0.81184634862081631015774629824741
absolute error = 0.81184634862081631015774629824741
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=550.5MB, alloc=52.3MB, time=6.20
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (closed_form) = 0
y[1] (numeric) = -0.83970236375553792600365107566092
absolute error = 0.83970236375553792600365107566092
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) = -0.8671082135530416918022340233542
absolute error = 0.8671082135530416918022340233542
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=594.6MB, alloc=52.3MB, time=6.69
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (closed_form) = 0
y[1] (numeric) = -0.89407774942845060385893432451037
absolute error = 0.89407774942845060385893432451037
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) = -0.92062416606434804935435499637115
absolute error = 0.92062416606434804935435499637115
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=638.6MB, alloc=52.3MB, time=7.18
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (closed_form) = 0
y[1] (numeric) = -0.9467600423733719031329955639706
absolute error = 0.9467600423733719031329955639706
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) = -0.9724973793139107477043541082161
absolute error = 0.9724973793139107477043541082161
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=682.8MB, alloc=52.3MB, time=7.67
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (closed_form) = 0
y[1] (numeric) = -0.99784763484466355356923147775142
absolute error = 0.99784763484466355356923147775142
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) = -1.0228217562739998397795689187221
absolute error = 1.0228217562739998397795689187221
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=726.8MB, alloc=52.3MB, time=8.16
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (closed_form) = 0
y[1] (numeric) = -1.0474302102337382252420026464882
absolute error = 1.0474302102337382252420026464882
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=770.8MB, alloc=52.3MB, time=8.65
x[1] = 0.43
y[1] (closed_form) = 0
y[1] (numeric) = -1.0716830104836906236163278139473
absolute error = 1.0716830104836906236163278139473
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) = -1.0955897437327055620855894107106
absolute error = 1.0955897437327055620855894107106
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=814.9MB, alloc=52.3MB, time=9.14
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (closed_form) = 0
y[1] (numeric) = -1.1191595936436507489857870108603
absolute error = 1.1191595936436507489857870108603
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) = -1.1424013631735122980542500026754
absolute error = 1.1424013631735122980542500026754
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=859.0MB, alloc=52.3MB, time=9.63
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (closed_form) = 0
y[1] (numeric) = -1.1653234953853058182534120840624
absolute error = 1.1653234953853058182534120840624
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) = -1.1879340928555765475778349761821
absolute error = 1.1879340928555765475778349761821
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=903.0MB, alloc=52.3MB, time=10.12
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (closed_form) = 0
y[1] (numeric) = -1.2102409357897243177240648102747
absolute error = 1.2102409357897243177240648102747
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) = -1.2322514989470615078646244894321
absolute error = 1.2322514989470615078646244894321
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=947.0MB, alloc=52.3MB, time=10.61
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (closed_form) = 0
y[1] (numeric) = -1.2539729674682565381395192006365
absolute error = 1.2539729674682565381395192006365
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) = -1.2754122516895082812919592417016
absolute error = 1.2754122516895082812919592417016
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=991.1MB, alloc=52.3MB, time=11.10
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (closed_form) = 0
y[1] (numeric) = -1.2965760010203300789027122775235
absolute error = 1.2965760010203300789027122775235
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) = -1.3174706169551013646522199250272
absolute error = 1.3174706169551013646522199250272
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1035.1MB, alloc=52.3MB, time=11.59
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (closed_form) = 0
y[1] (numeric) = -1.3381022652824874021439818345624
absolute error = 1.3381022652824874021439818345624
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) = -1.3584768875513606116982057890793
absolute error = 1.3584768875513606116982057890793
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1079.2MB, alloc=52.3MB, time=12.08
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (closed_form) = 0
y[1] (numeric) = -1.3786002118469164169311276765669
absolute error = 1.3786002118469164169311276765669
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) = -1.3984777629262061251657456858051
absolute error = 1.3984777629262061251657456858051
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1123.4MB, alloc=52.3MB, time=12.57
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (closed_form) = 0
y[1] (numeric) = -1.4181148717582593286186838730083
absolute error = 1.4181148717582593286186838730083
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) = -1.4375166845102947174839089876028
absolute error = 1.4375166845102947174839089876028
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1167.5MB, alloc=52.3MB, time=13.06
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (closed_form) = 0
y[1] (numeric) = -1.4566881710181821217800944739607
absolute error = 1.4566881710181821217800944739607
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) = -1.4756341327762855545237516620306
absolute error = 1.4756341327762855545237516620306
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1211.6MB, alloc=52.3MB, time=13.56
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (closed_form) = 0
y[1] (numeric) = -1.4943592104790563952622792549646
absolute error = 1.4943592104790563952622792549646
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1255.7MB, alloc=52.3MB, time=14.05
x[1] = 0.64
y[1] (closed_form) = 0
y[1] (numeric) = -1.5128678911442304105850613707012
absolute error = 1.5128678911442304105850613707012
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) = -1.531164514845187826148911812969
absolute error = 1.531164514845187826148911812969
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1299.8MB, alloc=52.3MB, time=14.54
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (closed_form) = 0
y[1] (numeric) = -1.5492532810779405440149355555165
absolute error = 1.5492532810779405440149355555165
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) = -1.567138254786295561435075306356
absolute error = 1.567138254786295561435075306356
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1344.0MB, alloc=52.3MB, time=15.03
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (closed_form) = 0
y[1] (numeric) = -1.584823372066991463739438915878
absolute error = 1.584823372066991463739438915878
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) = -1.6023124455750001179831369793599
absolute error = 1.6023124455750001179831369793599
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1388.1MB, alloc=52.3MB, time=15.52
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (closed_form) = 0
y[1] (numeric) = -1.6196091696477145735667011637991
absolute error = 1.6196091696477145735667011637991
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) = -1.6367171251653942920799403400453
absolute error = 1.6367171251653942920799403400453
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1432.2MB, alloc=52.3MB, time=16.01
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (closed_form) = 0
y[1] (numeric) = -1.6536397841639990553498278770467
absolute error = 1.6536397841639990553498278770467
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) = -1.6703805142154032353287563717044
absolute error = 1.6703805142154032353287563717044
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1476.3MB, alloc=52.3MB, time=16.50
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (closed_form) = 0
y[1] (numeric) = -1.6869425825889335488400528080007
absolute error = 1.6869425825889335488400528080007
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) = -1.703329160207207851883631767421
absolute error = 1.703329160207207851883631767421
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1520.4MB, alloc=52.3MB, time=16.99
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (closed_form) = 0
y[1] (numeric) = -1.7195433254083626345586244656457
absolute error = 1.7195433254083626345586244656457
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) = -1.7355880675259360510042187742223
absolute error = 1.7355880675259360510042187742223
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1564.5MB, alloc=52.3MB, time=17.48
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (closed_form) = 0
y[1] (numeric) = -1.7514662902969155863357980037719
absolute error = 1.7514662902969155863357980037719
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) = -1.767180815107759420049499557336
absolute error = 1.767180815107759420049499557336
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1608.7MB, alloc=52.3MB, time=17.99
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (closed_form) = 0
y[1] (numeric) = -1.7827343840875532979701989187487
absolute error = 1.7827343840875532979701989187487
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) = -1.7981296630568658348645274545992
absolute error = 1.7981296630568658348645274545992
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1652.8MB, alloc=52.3MB, time=18.48
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (closed_form) = 0
y[1] (numeric) = -1.8133692443403106102924026570893
absolute error = 1.8133692443403106102924026570893
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) = -1.8284556494503095332978653929769
absolute error = 1.8284556494503095332978653929769
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1696.9MB, alloc=52.3MB, time=18.97
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (closed_form) = 0
y[1] (numeric) = -1.843391331649075411625354908015
absolute error = 1.843391331649075411625354908015
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1741.0MB, alloc=52.3MB, time=19.46
x[1] = 0.85
y[1] (closed_form) = 0
y[1] (numeric) = -1.8581786783953894421750268097927
absolute error = 1.8581786783953894421750268097927
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (closed_form) = 0
y[1] (numeric) = -1.8728200136823386852791035339481
absolute error = 1.8728200136823386852791035339481
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1785.2MB, alloc=52.3MB, time=19.96
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (closed_form) = 0
y[1] (numeric) = -1.8873176002717969837358742192479
absolute error = 1.8873176002717969837358742192479
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) = -1.9016736418310779462659968401546
absolute error = 1.9016736418310779462659968401546
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1829.4MB, alloc=52.3MB, time=20.45
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (closed_form) = 0
y[1] (numeric) = -1.9158902849768584412326376076082
absolute error = 1.9158902849768584412326376076082
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) = -1.9299696212311636274794958825535
absolute error = 1.9299696212311636274794958825535
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1873.6MB, alloc=52.3MB, time=20.94
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (closed_form) = 0
y[1] (numeric) = -1.9439136888939181357450436118776
absolute error = 1.9439136888939181357450436118776
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) = -1.9577244748363010052127345371501
absolute error = 1.9577244748363010052127345371501
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1917.7MB, alloc=52.3MB, time=21.43
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (closed_form) = 0
y[1] (numeric) = -1.9714039162188929087239098269523
absolute error = 1.9714039162188929087239098269523
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) = -1.9849539021383717225256606250104
absolute error = 1.9849539021383717225256606250104
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=1961.8MB, alloc=52.3MB, time=21.93
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (closed_form) = 0
y[1] (numeric) = -1.9983762752062953787101801275902
absolute error = 1.9983762752062953787101801275902
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) = -2.0116728330633080483259426000564
absolute error = 2.0116728330633080483259426000564
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2005.9MB, alloc=52.3MB, time=22.42
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (closed_form) = 0
y[1] (numeric) = -2.0248453298319160001149415195729
absolute error = 2.0248453298319160001149415195729
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) = -2.0378954775108020074171211174764
absolute error = 2.0378954775108020074171211174764
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2050.0MB, alloc=52.3MB, time=22.91
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (closed_form) = 0
y[1] (numeric) = -2.0508249473134810539235841973584
absolute error = 2.0508249473134810539235841973584
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) = -2.0636353709539445073995358733992
absolute error = 2.0636353709539445073995358733992
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2094.2MB, alloc=52.3MB, time=23.40
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (closed_form) = 0
y[1] (numeric) = -2.0763283418817941427438169986641
absolute error = 2.0763283418817941427438169986641
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) = -2.08890541646923071359763511073
absolute error = 2.08890541646923071359763511073
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2138.4MB, alloc=52.3MB, time=23.89
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (closed_form) = 0
y[1] (numeric) = -2.1013681151521335602725115302266
absolute error = 2.1013681151521335602725115302266
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) = -2.1137179235273474149577499321511
absolute error = 2.1137179235273474149577499321511
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2182.5MB, alloc=52.3MB, time=24.38
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (closed_form) = 0
y[1] (numeric) = -2.1259562934081795816253186571183
absolute error = 2.1259562934081795816253186571183
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=2226.5MB, alloc=52.3MB, time=24.87
x[1] = 1.06
y[1] (closed_form) = 0
y[1] (numeric) = -2.1380846438400045273985195537403
absolute error = 2.1380846438400045273985195537403
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) = -2.1501043620777731616147377080261
absolute error = 2.1501043620777731616147377080261
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2270.7MB, alloc=52.3MB, time=25.36
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (closed_form) = 0
y[1] (numeric) = -2.1620168045271302701324749906087
absolute error = 2.1620168045271302701324749906087
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) = -2.1738232976507553190544265582736
absolute error = 2.1738232976507553190544265582736
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2314.8MB, alloc=52.3MB, time=25.86
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (closed_form) = 0
y[1] (numeric) = -2.1855251388414587765493421715592
absolute error = 2.1855251388414587765493421715592
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) = -2.1971235972634878832471017565474
absolute error = 2.1971235972634878832471017565474
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2359.0MB, alloc=52.3MB, time=26.35
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (closed_form) = 0
y[1] (numeric) = -2.2086199146634221148132374311736
absolute error = 2.2086199146634221148132374311736
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) = -2.2200153061519691315574794252662
absolute error = 2.2200153061519691315574794252662
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2403.2MB, alloc=52.3MB, time=26.84
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (closed_form) = 0
y[1] (numeric) = -2.2313109609579065270052714205248
absolute error = 2.2313109609579065270052714205248
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) = -2.2425080431553529172719104585582
absolute error = 2.2425080431553529172719104585582
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2447.4MB, alloc=52.3MB, time=27.34
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (closed_form) = 0
y[1] (numeric) = -2.2536076923654936206428223657141
absolute error = 2.2536076923654936206428223657141
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) = -2.2646110244338311432347604085993
absolute error = 2.2646110244338311432347604085993
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2491.6MB, alloc=52.3MB, time=27.83
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (closed_form) = 0
y[1] (numeric) = -2.2755191320839787084281684897877
absolute error = 2.2755191320839787084281684897877
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) = -2.2863330855489659553886373249286
absolute error = 2.2863330855489659553886373249286
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2535.8MB, alloc=52.3MB, time=28.32
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (closed_form) = 0
y[1] (numeric) = -2.2970539331809795088780501387022
absolute error = 2.2970539331809795088780501387022
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) = -2.3076827020404172241407023949783
absolute error = 2.3076827020404172241407023949783
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2580.0MB, alloc=52.3MB, time=28.81
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (closed_form) = 0
y[1] (numeric) = -2.3182203984650933834959611086136
absolute error = 2.3182203984650933834959611086136
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) = -2.328668008620392822229037514552
absolute error = 2.328668008620392822229037514552
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2624.2MB, alloc=52.3MB, time=29.30
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (closed_form) = 0
y[1] (numeric) = -2.3390264990311347568354697941747
absolute error = 2.3390264990311347568354697941747
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) = -2.3492968170958718538769070816789
absolute error = 2.3492968170958718538769070816789
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2668.3MB, alloc=52.3MB, time=29.80
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (closed_form) = 0
y[1] (numeric) = -2.3594798915843166960836954977298
absolute error = 2.3594798915843166960836954977298
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=2712.4MB, alloc=52.3MB, time=30.29
x[1] = 1.27
y[1] (closed_form) = 0
y[1] (numeric) = -2.3695766331185561649459854502455
absolute error = 2.3695766331185561649459854502455
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) = -2.3795879346386842639928312745317
absolute error = 2.3795879346386842639928312745317
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=2756.6MB, alloc=52.3MB, time=30.78
x[1] = 1.29
y[1] (closed_form) = 0
y[1] (numeric) = -2.3895146718534554589605406622503
absolute error = 2.3895146718534554589605406622503
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) = -2.3993577036765336208961393938294
absolute error = 2.3993577036765336208961393938294
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2800.6MB, alloc=52.3MB, time=31.28
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (closed_form) = 0
y[1] (numeric) = -2.4091178726488860424066998994759
absolute error = 2.4091178726488860424066998994759
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) = -2.4187960053478476775114018188495
absolute error = 2.4187960053478476775114018188495
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2844.6MB, alloc=52.3MB, time=31.77
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (closed_form) = 0
y[1] (numeric) = -2.4283929127833576585596706698032
absolute error = 2.4283929127833576585596706698032
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) = -2.4379093907818482007048984798336
absolute error = 2.4379093907818482007048984798336
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2888.7MB, alloc=52.3MB, time=32.26
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (closed_form) = 0
y[1] (numeric) = -2.4473462203582451509958268680706
absolute error = 2.4473462203582451509958268680706
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) = -2.4567041680765196147712013242745
absolute error = 2.4567041680765196147712013242745
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2932.9MB, alloc=52.3MB, time=32.75
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (closed_form) = 0
y[1] (numeric) = -2.465983986399211239931799938048
absolute error = 2.465983986399211239931799938048
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) = -2.4751864140263258064922089029557
absolute error = 2.4751864140263258064922089029557
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2977.0MB, alloc=52.3MB, time=33.24
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (closed_form) = 0
y[1] (numeric) = -2.4843121762239927044877527192272
absolute error = 2.4843121762239927044877527192272
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) = -2.4933619851432516407510177278022
absolute error = 2.4933619851432516407510177278022
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=3021.1MB, alloc=52.3MB, time=33.74
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (closed_form) = 0
y[1] (numeric) = -2.502336540129322450016318077394
absolute error = 2.502336540129322450016318077394
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) = -2.5112365280216971566313815436747
absolute error = 2.5112365280216971566313815436747
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=3065.2MB, alloc=52.3MB, time=34.23
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (closed_form) = 0
y[1] (numeric) = -2.5200626234453794006875554782886
absolute error = 2.5200626234453794006875554782886
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) = -2.5288154890935829697597384255494
absolute error = 2.5288154890935829697597384255494
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=3109.3MB, alloc=52.3MB, time=34.72
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (closed_form) = 0
y[1] (numeric) = -2.5374957760021884299664710709659
absolute error = 2.5374957760021884299664710709659
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (closed_form) = 0
y[1] (numeric) = -2.5461041238162446950275307624537
absolute error = 2.5461041238162446950275307624537
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=3153.4MB, alloc=52.3MB, time=35.21
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (closed_form) = 0
y[1] (numeric) = -2.5546411610487907786080616316604
absolute error = 2.5546411610487907786080616316604
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) = -2.563107505332261914461219703797
absolute error = 2.563107505332261914461219703797
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=3197.5MB, alloc=52.3MB, time=35.70
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (closed_form) = 0
y[1] (numeric) = -2.5715037636627336733402219577052
absolute error = 2.5715037636627336733402219577052
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=3241.6MB, alloc=52.3MB, time=36.20
x[1] = 1.5
y[1] (closed_form) = 0
y[1] (numeric) = -2.5798305326372476295248919362842
absolute error = 2.5798305326372476295248919362842
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) = -2.5880883986844525087346822786673
absolute error = 2.5880883986844525087346822786673
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=3285.7MB, alloc=52.3MB, time=36.69
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (closed_form) = 0
y[1] (numeric) = -2.5962779382887855601851113073425
absolute error = 2.5962779382887855601851113073425
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (closed_form) = 0
y[1] (numeric) = -2.6043997182084101168769279335181
absolute error = 2.6043997182084101168769279335181
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=3329.8MB, alloc=52.3MB, time=37.18
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (closed_form) = 0
y[1] (numeric) = -2.612454295687116919382005736081
absolute error = 2.612454295687116919382005736081
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) = -2.6204422186603887600341585900993
absolute error = 2.6204422186603887600341585900993
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=3374.0MB, alloc=52.3MB, time=37.67
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (closed_form) = 0
y[1] (numeric) = -2.6283640259558203382378635349785
absolute error = 2.6283640259558203382378635349785
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) = -2.6362202474880778862643486217726
absolute error = 2.6362202474880778862643486217726
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=3418.1MB, alloc=52.3MB, time=38.16
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (closed_form) = 0
y[1] (numeric) = -2.6440114044485761120439569643268
absolute error = 2.6440114044485761120439569643268
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) = -2.651738009490043295601781588511
absolute error = 2.651738009490043295601781588511
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=3462.2MB, alloc=52.3MB, time=38.66
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (closed_form) = 0
y[1] (numeric) = -2.6594005669061389542679967469405
absolute error = 2.6594005669061389542679967469405
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (closed_form) = 0
y[1] (numeric) = -2.6669995728062823447559541701788
absolute error = 2.6669995728062823447559541701788
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=3506.3MB, alloc=52.3MB, time=39.26
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (closed_form) = 0
y[1] (numeric) = -2.674535515285844184508175769422
absolute error = 2.674535515285844184508175769422
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) = -2.6820088745918483379255156807464
absolute error = 2.6820088745918483379255156807464
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=3550.4MB, alloc=52.3MB, time=39.74
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (closed_form) = 0
y[1] (numeric) = -2.6894201232843248134349050311232
absolute error = 2.6894201232843248134349050311232
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) = -2.6967697263934502436497527749833
absolute error = 2.6967697263934502436497527749833
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=3594.5MB, alloc=52.3MB, time=40.24
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (closed_form) = 0
y[1] (numeric) = -2.704058141572607062549065187716
absolute error = 2.704058141572607062549065187716
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) = -2.7112858192474878406096487095735
absolute error = 2.7112858192474878406096487095735
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=3638.6MB, alloc=52.3MB, time=40.73
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (closed_form) = 0
y[1] (numeric) = -2.7184532027613666816504651401574
absolute error = 2.7184532027613666816504651401574
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) = -2.7255607285166552147573527582401
absolute error = 2.7255607285166552147573527582401
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=3682.7MB, alloc=52.3MB, time=41.22
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (closed_form) = 0
y[1] (numeric) = -2.73260882611285652247852598175
absolute error = 2.73260882611285652247852598175
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) = -2.7395979184810263243800040846542
absolute error = 2.7395979184810263243800040846542
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=3726.8MB, alloc=52.3MB, time=41.71
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (closed_form) = 0
y[1] (numeric) = -2.7465284220148468752996022081494
absolute error = 2.7465284220148468752996022081494
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=3770.9MB, alloc=52.3MB, time=42.20
x[1] = 1.73
y[1] (closed_form) = 0
y[1] (numeric) = -2.7534007466984153329005799223752
absolute error = 2.7534007466984153329005799223752
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) = -2.7602152962308447924304148979074
absolute error = 2.7602152962308447924304148979074
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=3814.9MB, alloc=52.3MB, time=42.70
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (closed_form) = 0
y[1] (numeric) = -2.7669724681477727713120203415835
absolute error = 2.7669724681477727713120203415835
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (closed_form) = 0
y[1] (numeric) = -2.7736726539398686460373929183926
absolute error = 2.7736726539398686460373929183926
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=3859.2MB, alloc=52.3MB, time=43.19
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (closed_form) = 0
y[1] (numeric) = -2.7803162391684283928105178059083
absolute error = 2.7803162391684283928105178059083
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) = -2.7869036035781419558040318017497
absolute error = 2.7869036035781419558040318017497
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=3903.4MB, alloc=52.3MB, time=43.69
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (closed_form) = 0
y[1] (numeric) = -2.7934351212071156573368927201039
absolute error = 2.7934351212071156573368927201039
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) = -2.7999111604942292675951231770566
absolute error = 2.7999111604942292675951231770566
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=3947.5MB, alloc=52.3MB, time=44.18
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (closed_form) = 0
y[1] (numeric) = -2.8063320843839046628003927245124
absolute error = 2.8063320843839046628003927245124
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) = -2.8126982504283604153132295425846
absolute error = 2.8126982504283604153132295425846
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=3991.5MB, alloc=52.3MB, time=44.68
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (closed_form) = 0
y[1] (numeric) = -2.8190100108874241725937217156306
absolute error = 2.8190100108874241725937217156306
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) = -2.8252677128259722899989544119496
absolute error = 2.8252677128259722899989544119496
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=4035.7MB, alloc=52.3MB, time=45.17
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (closed_form) = 0
y[1] (numeric) = -2.8314716982090638810399501829406
absolute error = 2.8314716982090638810399501829406
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) = -2.8376223039948342341084926678511
absolute error = 2.8376223039948342341084926678511
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=4079.8MB, alloc=52.3MB, time=45.66
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (closed_form) = 0
y[1] (numeric) = -2.8437198622252104131532022268665
absolute error = 2.8437198622252104131532022268665
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) = -2.8497647001145098078429389569262
absolute error = 2.8497647001145098078429389569262
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=4123.9MB, alloc=52.3MB, time=46.16
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (closed_form) = 0
y[1] (numeric) = -2.8557571401359804230746902564722
absolute error = 2.8557571401359804230746902564722
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) = -2.8616975001063397950872630606118
absolute error = 2.8616975001063397950872630606118
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=4168.0MB, alloc=52.3MB, time=46.65
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (closed_form) = 0
y[1] (numeric) = -2.8675860932683675889022964400748
absolute error = 2.8675860932683675889022964400748
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) = -2.8734232283716051664401587457408
absolute error = 2.8734232283716051664401587457408
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=4212.1MB, alloc=52.3MB, time=47.14
TOP MAIN SOLVE Loop
x[1] = 1.93
y[1] (closed_form) = 0
y[1] (numeric) = -2.8792092097512137136919121289576
absolute error = 2.8792092097512137136919121289576
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) = -2.8849443374050408761367384168364
absolute error = 2.8849443374050408761367384168364
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=4256.3MB, alloc=52.3MB, time=47.64
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (closed_form) = 0
y[1] (numeric) = -2.8906289070689442716631173455475
absolute error = 2.8906289070689442716631173455475
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=4300.5MB, alloc=52.3MB, time=48.13
x[1] = 1.96
y[1] (closed_form) = 0
y[1] (numeric) = -2.8962632102904187271808982385869
absolute error = 2.8962632102904187271808982385869
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) = -2.9018475345005726166070703453076
absolute error = 2.9018475345005726166070703453076
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=4344.6MB, alloc=52.3MB, time=48.62
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (closed_form) = 0
y[1] (numeric) = -2.9073821630844972617796888073887
absolute error = 2.9073821630844972617796888073887
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) = -2.9128673754500719920085391189788
absolute error = 2.9128673754500719920085391189788
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=4388.7MB, alloc=52.3MB, time=49.12
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (closed_form) = 0
y[1] (numeric) = -2.9183034470952461404067881610605
absolute error = 2.9183034470952461404067881610605
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) = -2.923690649673837983952234119546
absolute error = 2.923690649673837983952234119546
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=4432.9MB, alloc=52.3MB, time=49.61
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (closed_form) = 0
y[1] (numeric) = -2.9290292510598894075708368512456
absolute error = 2.9290292510598894075708368512456
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) = -2.9343195154106138886698111789675
absolute error = 2.9343195154106138886698111789675
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=4477.0MB, alloc=52.3MB, time=50.10
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (closed_form) = 0
y[1] (numeric) = -2.9395617032279742557995297003886
absolute error = 2.9395617032279742557995297003886
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) = -2.9447560714189255718920277971778
absolute error = 2.9447560714189255718920277971778
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=4521.2MB, alloc=52.3MB, time=50.60
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (closed_form) = 0
y[1] (numeric) = -2.9499028733543574272772071739512
absolute error = 2.9499028733543574272772071739512
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) = -2.9550023589267688989497737658901
absolute error = 2.9550023589267688989497737658901
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=4565.3MB, alloc=52.3MB, time=51.10
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (closed_form) = 0
y[1] (numeric) = -2.9600547746067084389470151886034
absolute error = 2.9600547746067084389470151886034
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) = -2.9650603634980099948559020874742
absolute error = 2.9650603634980099948559020874742
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=4609.5MB, alloc=52.3MB, time=51.59
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (closed_form) = 0
y[1] (numeric) = -2.9700193653918557381107721935465
absolute error = 2.9700193653918557381107721935465
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) = -2.9749320168196948796373764855792
absolute error = 2.9749320168196948796373764855792
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=4653.6MB, alloc=52.3MB, time=52.08
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (closed_form) = 0
y[1] (numeric) = -2.9797985511050471863644430458959
absolute error = 2.9797985511050471863644430458959
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (closed_form) = 0
y[1] (numeric) = -2.9846191984142189750286329434154
absolute error = 2.9846191984142189750286329434154
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=4697.8MB, alloc=52.3MB, time=52.58
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (closed_form) = 0
y[1] (numeric) = -2.9893941858059585504584261905506
absolute error = 2.9893941858059585504584261905506
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) = -2.9941237372800772730976528837598
absolute error = 2.9941237372800772730976528837598
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=4742.0MB, alloc=52.3MB, time=53.07
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (closed_form) = 0
y[1] (numeric) = -2.9988080738250616839235664716613
absolute error = 2.9988080738250616839235664716613
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) = -3.0034474134647013831720150700658
absolute error = 3.0034474134647013831720150700658
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=4786.2MB, alloc=52.3MB, time=53.56
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (closed_form) = 0
y[1] (numeric) = -3.008041971303756651487009562549
absolute error = 3.008041971303756651487009562549
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=4830.2MB, alloc=52.3MB, time=54.05
x[1] = 2.19
y[1] (closed_form) = 0
y[1] (numeric) = -3.0125919595726891173847987147401
absolute error = 3.0125919595726891173847987147401
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) = -3.0170975876714781124201340655787
absolute error = 3.0170975876714781124201340655787
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=4874.4MB, alloc=52.3MB, time=54.55
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (closed_form) = 0
y[1] (numeric) = -3.0215590622125447143555514155391
absolute error = 3.0215590622125447143555514155391
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) = -3.0259765870628048581866273160167
absolute error = 3.0259765870628048581866273160167
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=4918.5MB, alloc=52.3MB, time=55.04
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (closed_form) = 0
y[1] (numeric) = -3.0303503633848722943218699039187
absolute error = 3.0303503633848722943218699039187
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) = -3.0346805896774315918395507412808
absolute error = 3.0346805896774315918395507412808
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=4962.6MB, alloc=52.3MB, time=55.53
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (closed_form) = 0
y[1] (numeric) = -3.0389674618148008218582450936579
absolute error = 3.0389674618148008218582450936579
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) = -3.043211173085703011003236449717
absolute error = 3.043211173085703011003236449717
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=5006.7MB, alloc=52.3MB, time=56.02
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (closed_form) = 0
y[1] (numeric) = -3.0474119142312649270934341630587
absolute error = 3.0474119142312649270934341630587
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (closed_form) = 0
y[1] (numeric) = -3.0515698734822612479041628202115
absolute error = 3.0515698734822612479041628202115
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=5050.9MB, alloc=52.3MB, time=56.52
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (closed_form) = 0
y[1] (numeric) = -3.0556852365956216685950799673458
absolute error = 3.0556852365956216685950799673458
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) = -3.0597581868902180235673718316703
absolute error = 3.0597581868902180235673718316703
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=5095.0MB, alloc=52.3MB, time=57.03
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (closed_form) = 0
y[1] (numeric) = -3.0637889052819480335899294355021
absolute error = 3.0637889052819480335899294355021
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) = -3.0677775703181318384910114440391
absolute error = 3.0677775703181318384910114440391
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=5139.1MB, alloc=52.3MB, time=57.52
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (closed_form) = 0
y[1] (numeric) = -3.0717243582112370390505849351031
absolute error = 3.0717243582112370390505849351031
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) = -3.0756294428719475484689216989689
absolute error = 3.0756294428719475484689216989689
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=5183.1MB, alloc=52.3MB, time=58.01
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (closed_form) = 0
y[1] (numeric) = -3.079492995941591143467318868478
absolute error = 3.079492995941591143467318868478
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (closed_form) = 0
y[1] (numeric) = -3.0833151868239402072528229709595
absolute error = 3.0833151868239402072528229709595
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=5227.3MB, alloc=52.3MB, time=58.51
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (closed_form) = 0
y[1] (numeric) = -3.0870961827163997708232551160476
absolute error = 3.0870961827163997708232551160476
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) = -3.0908361486405965849905233514428
absolute error = 3.0908361486405965849905233514428
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=5271.4MB, alloc=52.3MB, time=59.00
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (closed_form) = 0
y[1] (numeric) = -3.0945352474723825926635287648685
absolute error = 3.0945352474723825926635287648685
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) = -3.0981936399712658189761476782662
absolute error = 3.0981936399712658189761476782662
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=5315.5MB, alloc=52.3MB, time=59.49
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (closed_form) = 0
y[1] (numeric) = -3.1018114848092813554042747979785
absolute error = 3.1018114848092813554042747979785
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=5359.6MB, alloc=52.3MB, time=59.99
x[1] = 2.42
y[1] (closed_form) = 0
y[1] (numeric) = -3.1053889385993147827358769772238
absolute error = 3.1053889385993147827358769772238
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (closed_form) = 0
y[1] (numeric) = -3.1089261559228900562996753616564
absolute error = 3.1089261559228900562996753616564
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=5403.7MB, alloc=52.3MB, time=60.50
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (closed_form) = 0
y[1] (numeric) = -3.1124232893574335648942580296265
absolute error = 3.1124232893574335648942580296265
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) = -3.115880489503025772075000522549
absolute error = 3.115880489503025772075000522549
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=5447.9MB, alloc=52.3MB, time=60.99
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (closed_form) = 0
y[1] (numeric) = -3.1192979050086515545475868628314
absolute error = 3.1192979050086515545475868628314
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) = -3.1226756825979600670917358780492
absolute error = 3.1226756825979600670917358780492
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=5492.0MB, alloc=52.3MB, time=61.48
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (closed_form) = 0
y[1] (numeric) = -3.1260139670945446864151663890763
absolute error = 3.1260139670945446864151663890763
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) = -3.1293129014467533173443356853304
absolute error = 3.1293129014467533173443356853304
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=5536.1MB, alloc=52.3MB, time=61.97
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (closed_form) = 0
y[1] (numeric) = -3.1325726267520390835333426586461
absolute error = 3.1325726267520390835333426586461
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (closed_form) = 0
y[1] (numeric) = -3.1357932822808611711633221966663
absolute error = 3.1357932822808611711633221966663
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=5580.2MB, alloc=52.3MB, time=62.46
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (closed_form) = 0
y[1] (numeric) = -3.1389750055001453476684581114618
absolute error = 3.1389750055001453476684581114618
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) = -3.1421179320963134381269029016005
absolute error = 3.1421179320963134381269029016005
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=5624.3MB, alloc=52.3MB, time=62.96
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (closed_form) = 0
y[1] (numeric) = -3.145222195997890809369274729699
absolute error = 3.145222195997890809369274729699
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) = -3.1482879293977006858659043357138
absolute error = 3.1482879293977006858659043357138
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=5668.3MB, alloc=52.3MB, time=63.45
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (closed_form) = 0
y[1] (numeric) = -3.1513152627746539018462514612324
absolute error = 3.1513152627746539018462514612324
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) = -3.1543043249151424806769509361196
absolute error = 3.1543043249151424806769509361196
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=5712.4MB, alloc=52.3MB, time=63.94
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (closed_form) = 0
y[1] (numeric) = -3.1572552429340452250829695694871
absolute error = 3.1572552429340452250829695694871
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) = -3.1601681422953533001504052189261
absolute error = 3.1601681422953533001504052189261
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=5756.5MB, alloc=52.3MB, time=64.43
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (closed_form) = 0
y[1] (numeric) = -3.1630431468324235950171860369235
absolute error = 3.1630431468324235950171860369235
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) = -3.1658803787678674585633236036235
absolute error = 3.1658803787678674585633236036235
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=5800.6MB, alloc=52.3MB, time=64.93
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (closed_form) = 0
y[1] (numeric) = -3.1686799587330822190855344261574
absolute error = 3.1686799587330822190855344261574
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=5844.7MB, alloc=52.3MB, time=65.42
x[1] = 2.63
y[1] (closed_form) = 0
y[1] (numeric) = -3.1714420057874327177179371718208
absolute error = 3.1714420057874327177179371718208
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) = -3.1741666374370899100827735395362
absolute error = 3.1741666374370899100827735395362
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=5888.8MB, alloc=52.3MB, time=65.91
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (closed_form) = 0
y[1] (numeric) = -3.1768539696535334201697394478588
absolute error = 3.1768539696535334201697394478588
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (closed_form) = 0
y[1] (numeric) = -3.1795041168917247646018312067651
absolute error = 3.1795041168917247646018312067651
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=5932.9MB, alloc=52.3MB, time=66.40
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (closed_form) = 0
y[1] (numeric) = -3.1821171921079578041069236316181
absolute error = 3.1821171921079578041069236316181
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) = -3.1846933067773928220397645699027
absolute error = 3.1846933067773928220397645699027
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=5976.9MB, alloc=52.3MB, time=66.89
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (closed_form) = 0
y[1] (numeric) = -3.1872325709112804770555191729327
absolute error = 3.1872325709112804770555191729327
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) = -3.1897350930738817283947454891519
absolute error = 3.1897350930738817283947454891519
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=6021.1MB, alloc=52.3MB, time=67.38
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (closed_form) = 0
y[1] (numeric) = -3.1922009803990896875763742148151
absolute error = 3.1922009803990896875763742148151
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) = -3.1946303386067592094897093284312
absolute error = 3.1946303386067592094897093284312
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=6065.2MB, alloc=52.3MB, time=67.87
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (closed_form) = 0
y[1] (numeric) = -3.1970232720187498988124852468086
absolute error = 3.1970232720187498988124852468086
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) = -3.1993798835746880742472981475599
absolute error = 3.1993798835746880742472981475599
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=6109.2MB, alloc=52.3MB, time=68.37
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (closed_form) = 0
y[1] (numeric) = -3.2017002748474531031546867380705
absolute error = 3.2017002748474531031546867380705
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) = -3.2039845460583933926627723851689
absolute error = 3.2039845460583933926627723851689
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=6153.3MB, alloc=52.3MB, time=68.86
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (closed_form) = 0
y[1] (numeric) = -3.2062327960922772001491401103127
absolute error = 3.2062327960922772001491401103127
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) = -3.2084451225119833060223439314258
absolute error = 3.2084451225119833060223439314258
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=6197.4MB, alloc=52.3MB, time=69.35
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (closed_form) = 0
y[1] (numeric) = -3.2106216215729364748830591010282
absolute error = 3.2106216215729364748830591010282
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) = -3.2127623882372925173265844494422
absolute error = 3.2127623882372925173265844494422
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=6241.6MB, alloc=52.3MB, time=69.84
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (closed_form) = 0
y[1] (numeric) = -3.2148675161878776537702116078276
absolute error = 3.2148675161878776537702116078276
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) = -3.2169370978418867736648958386568
absolute error = 3.2169370978418867736648958386568
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=6285.7MB, alloc=52.3MB, time=70.34
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (closed_form) = 0
y[1] (numeric) = -3.2189712243643450781974346697023
absolute error = 3.2189712243643450781974346697023
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=6329.7MB, alloc=52.3MB, time=70.83
x[1] = 2.84
y[1] (closed_form) = 0
y[1] (numeric) = -3.220969985681337492026413739094
absolute error = 3.220969985681337492026413739094
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) = -3.2229334704930101296445267890965
absolute error = 3.2229334704930101296445267890965
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=6373.8MB, alloc=52.3MB, time=71.32
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (closed_form) = 0
y[1] (numeric) = -3.2248617662863480045460244094564
absolute error = 3.2248617662863480045460244094564
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) = -3.2267549593477330744279053616543
absolute error = 3.2267549593477330744279053616543
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=6417.8MB, alloc=52.3MB, time=71.81
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (closed_form) = 0
y[1] (numeric) = -3.2286131347752866230962678934034
absolute error = 3.2286131347752866230962678934034
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) = -3.2304363764909998895164594384175
absolute error = 3.2304363764909998895164594384175
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=6461.9MB, alloc=52.3MB, time=72.30
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (closed_form) = 0
y[1] (numeric) = -3.2322247672526567664709368395508
absolute error = 3.2322247672526567664709368395508
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) = -3.2339783886655523055077983321573
absolute error = 3.2339783886655523055077983321573
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=6506.0MB, alloc=52.3MB, time=72.79
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (closed_form) = 0
y[1] (numeric) = -3.2356973211940106812135106139342
absolute error = 3.2356973211940106812135106139342
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) = -3.2373816441727061862651125810739
absolute error = 3.2373816441727061862651125810739
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=6550.2MB, alloc=52.3MB, time=73.29
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (closed_form) = 0
y[1] (numeric) = -3.2390314358177907491516935455841
absolute error = 3.2390314358177907491516935455841
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (closed_form) = 0
y[1] (numeric) = -3.2406467732378313888455940296946
absolute error = 3.2406467732378313888455940296946
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=6594.3MB, alloc=52.3MB, time=73.78
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (closed_form) = 0
y[1] (numeric) = -3.2422277324445609449956898728895
absolute error = 3.2422277324445609449956898728895
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) = -3.2437743883634453483551162471957
absolute error = 3.2437743883634453483551162471957
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=6638.4MB, alloc=52.3MB, time=74.27
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (closed_form) = 0
y[1] (numeric) = -3.2452868148440706240923231782778
absolute error = 3.2452868148440706240923231782778
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) = -3.2467650846703527503174639245414
absolute error = 3.2467650846703527503174639245414
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=6682.5MB, alloc=52.3MB, time=74.76
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (closed_form) = 0
y[1] (numeric) = -3.2482092695705734255373640400991
absolute error = 3.2482092695705734255373640400991
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) = -3.2496194402272447317847390822555
absolute error = 3.2496194402272447317847390822555
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=6726.6MB, alloc=52.3MB, time=75.25
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (closed_form) = 0
y[1] (numeric) = -3.2509956662868056148053851359331
absolute error = 3.2509956662868056148053851359331
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (closed_form) = 0
y[1] (numeric) = -3.2523380163691530388865988065146
absolute error = 3.2523380163691530388865988065146
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=6770.6MB, alloc=52.3MB, time=75.74
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (closed_form) = 0
y[1] (numeric) = -3.2536465580770106116282640767192
absolute error = 3.2536465580770106116282640767192
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=6814.7MB, alloc=52.3MB, time=76.23
x[1] = 3.05
y[1] (closed_form) = 0
y[1] (numeric) = -3.2549213580051374131533319345492
absolute error = 3.2549213580051374131533319345492
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) = -3.2561624817493797048865192605413
absolute error = 3.2561624817493797048865192605413
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=6858.7MB, alloc=52.3MB, time=76.72
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (closed_form) = 0
y[1] (numeric) = -3.2573699939155681350598740485777
absolute error = 3.2573699939155681350598740485777
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) = -3.2585439581282630014934665020118
absolute error = 3.2585439581282630014934665020118
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=6902.9MB, alloc=52.3MB, time=77.22
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (closed_form) = 0
y[1] (numeric) = -3.2596844370393500769120674423546
absolute error = 3.2596844370393500769120674423546
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (closed_form) = 0
y[1] (numeric) = -3.2607914923364894480585531004585
absolute error = 3.2607914923364894480585531004585
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=6947.0MB, alloc=52.3MB, time=77.70
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (closed_form) = 0
y[1] (numeric) = -3.2618651847514197671172682064436
absolute error = 3.2618651847514197671172682064436
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) = -3.262905574068120262432045664074
absolute error = 3.262905574068120262432045664074
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=6991.0MB, alloc=52.3MB, time=78.20
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (closed_form) = 0
y[1] (numeric) = -3.2639127191308328051613650094324
absolute error = 3.2639127191308328051613650094324
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) = -3.2648866778519462793255310914586
absolute error = 3.2648866778519462793255310914586
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=7035.2MB, alloc=52.3MB, time=78.68
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (closed_form) = 0
y[1] (numeric) = -3.2658275072197454546369896769965
absolute error = 3.2658275072197454546369896769965
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) = -3.2667352633060265145350818510363
absolute error = 3.2667352633060265145350818510363
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=7079.2MB, alloc=52.3MB, time=79.18
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (closed_form) = 0
y[1] (numeric) = -3.2676100012735813459416524866331
absolute error = 3.2676100012735813459416524866331
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (closed_form) = 0
y[1] (numeric) = -3.2684517753835526523857847731846
absolute error = 3.2684517753835526523857847731846
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=7123.2MB, alloc=52.3MB, time=79.66
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (closed_form) = 0
y[1] (numeric) = -3.2692606390026619082871578790266
absolute error = 3.2692606390026619082871578790266
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) = -3.2700366446103121293115275069956
absolute error = 3.2700366446103121293115275069956
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=7167.2MB, alloc=52.3MB, time=80.15
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (closed_form) = 0
y[1] (numeric) = -3.2707798438055673917927778240023
absolute error = 3.2707798438055673917927778240023
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) = -3.2714902873140109932287915938152
absolute error = 3.2714902873140109932287915938152
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=7211.3MB, alloc=52.3MB, time=80.64
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (closed_form) = 0
y[1] (numeric) = -3.2721680249944841057786487891566
absolute error = 3.2721680249944841057786487891566
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=7255.3MB, alloc=52.3MB, time=81.13
x[1] = 3.24
y[1] (closed_form) = 0
y[1] (numeric) = -3.2728131058457067354926974048519
absolute error = 3.2728131058457067354926974048519
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (closed_form) = 0
y[1] (numeric) = -3.27342557801278276167181627041
absolute error = 3.27342557801278276167181627041
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=7299.3MB, alloc=52.3MB, time=81.62
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (closed_form) = 0
y[1] (numeric) = -3.2740054887935907932553277749787
absolute error = 3.2740054887935907932553277749787
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) = -3.2745528846450625424567645039243
absolute error = 3.2745528846450625424567645039243
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=7343.4MB, alloc=52.3MB, time=82.11
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (closed_form) = 0
y[1] (numeric) = -3.2750678111893503799819007409649
absolute error = 3.2750678111893503799819007409649
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) = -3.2755503132198857010535685670335
absolute error = 3.2755503132198857010535685670335
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=7387.5MB, alloc=52.3MB, time=82.60
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (closed_form) = 0
y[1] (numeric) = -3.2760004347073296971127996278011
absolute error = 3.2760004347073296971127996278011
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) = -3.2764182188054180944463304145708
absolute error = 3.2764182188054180944463304145708
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=7431.6MB, alloc=52.3MB, time=83.09
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (closed_form) = 0
y[1] (numeric) = -3.2768037078567013880875790340325
absolute error = 3.2768037078567013880875790340325
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (closed_form) = 0
y[1] (numeric) = -3.277156943398182067133461412464
absolute error = 3.277156943398182067133461412464
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=7475.7MB, alloc=52.3MB, time=83.58
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (closed_form) = 0
y[1] (numeric) = -3.2774779661668502960949837711242
absolute error = 3.2774779661668502960949837711242
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) = -3.2777668161051194860380322766823
absolute error = 3.2777668161051194860380322766823
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=7519.7MB, alloc=52.3MB, time=84.07
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (closed_form) = 0
y[1] (numeric) = -3.2780235323661631590552585228526
absolute error = 3.2780235323661631590552585228526
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) = -3.2782481533191544800239672722212
absolute error = 3.2782481533191544800239672722212
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=7563.7MB, alloc=52.3MB, time=84.56
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (closed_form) = 0
y[1] (numeric) = -3.2784407165544098006324308861875
absolute error = 3.2784407165544098006324308861875
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) = -3.2786012588884375322824936722173
absolute error = 3.2786012588884375322824936722173
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=7607.8MB, alloc=52.3MB, time=85.05
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (closed_form) = 0
y[1] (numeric) = -3.2787298163688936366845168679254
absolute error = 3.2787298163688936366845168679254
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) = -3.2788264242794449957368837220098
absolute error = 3.2788264242794449957368837220098
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=7651.8MB, alloc=52.3MB, time=85.53
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (closed_form) = 0
y[1] (numeric) = -3.2788911171445418956120591312256
absolute error = 3.2788911171445418956120591312256
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=7695.7MB, alloc=52.3MB, time=86.02
x[1] = 3.43
y[1] (closed_form) = 0
y[1] (numeric) = -3.2789239287341008338405851737072
absolute error = 3.2789239287341008338405851737072
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) = -3.2789248920680988325797674282475
absolute error = 3.2789248920680988325797674282475
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=7739.7MB, alloc=52.3MB, time=86.51
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (closed_form) = 0
y[1] (numeric) = -3.2788940394210804161619000510958
absolute error = 3.2788940394210804161619000510958
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) = -3.2788314023265783864247704089058
absolute error = 3.2788314023265783864247704089058
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=7783.7MB, alloc=52.3MB, time=87.00
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (closed_form) = 0
y[1] (numeric) = -3.2787370115814495052222938106994
absolute error = 3.2787370115814495052222938106994
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (closed_form) = 0
y[1] (numeric) = -3.2786108972501261698831996164368
absolute error = 3.2786108972501261698831996164368
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=7827.7MB, alloc=52.3MB, time=87.49
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (closed_form) = 0
y[1] (numeric) = -3.2784530886687851442187829597768
absolute error = 3.2784530886687851442187829597768
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) = -3.2782636144494343849652204716403
absolute error = 3.2782636144494343849652204716403
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=7871.8MB, alloc=52.3MB, time=87.98
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (closed_form) = 0
y[1] (numeric) = -3.278042502483918981270491286473
absolute error = 3.278042502483918981270491286473
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) = -3.2777897799478472029895035561185
absolute error = 3.2777897799478472029895035561185
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=7915.8MB, alloc=52.3MB, time=88.46
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (closed_form) = 0
y[1] (numeric) = -3.2775054733044376321228401602546
absolute error = 3.2775054733044376321228401602546
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) = -3.2771896083082883307141166270345
absolute error = 3.2771896083082883307141166270345
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=7959.8MB, alloc=52.3MB, time=88.95
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (closed_form) = 0
y[1] (numeric) = -3.2768422100090689778980656214409
absolute error = 3.2768422100090689778980656214409
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) = -3.2764633027551368885561589007993
absolute error = 3.2764633027551368885561589007993
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=8003.8MB, alloc=52.3MB, time=89.44
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (closed_form) = 0
y[1] (numeric) = -3.2760529101970778061791320182909
absolute error = 3.2760529101970778061791320182909
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) = -3.2756110552911723430467140544522
absolute error = 3.2756110552911723430467140544522
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=8047.9MB, alloc=52.3MB, time=89.93
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (closed_form) = 0
y[1] (numeric) = -3.2751377603027889217049440874913
absolute error = 3.2751377603027889217049440874913
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) = -3.2746330468097040529416659410267
absolute error = 3.2746330468097040529416659410267
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=8092.0MB, alloc=52.3MB, time=90.42
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (closed_form) = 0
y[1] (numeric) = -3.274096935705350767022342414002
absolute error = 3.274096935705350767022342414002
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=8136.0MB, alloc=52.3MB, time=90.91
x[1] = 3.62
y[1] (closed_form) = 0
y[1] (numeric) = -3.2735294472019959968426441470289
absolute error = 3.2735294472019959968426441470289
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) = -3.2729306008338476938729796835148
absolute error = 3.2729306008338476938729796835148
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=8180.1MB, alloc=52.3MB, time=91.40
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (closed_form) = 0
y[1] (numeric) = -3.2723004154600924403050779517852
absolute error = 3.2723004154600924403050779517852
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) = -3.2716389092678643036539448672246
absolute error = 3.2716389092678643036539448672246
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=8224.2MB, alloc=52.3MB, time=91.90
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (closed_form) = 0
y[1] (numeric) = -3.2709460997751456632122155749594
absolute error = 3.2709460997751456632122155749594
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) = -3.2702220038336007211905220110143
absolute error = 3.2702220038336007211905220110143
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=8268.3MB, alloc=52.3MB, time=92.38
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (closed_form) = 0
y[1] (numeric) = -3.2694666376313423950995809895334
absolute error = 3.2694666376313423950995809895334
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) = -3.2686800166956332719300447759963
absolute error = 3.2686800166956332719300447759963
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=8312.2MB, alloc=52.3MB, time=92.88
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (closed_form) = 0
y[1] (numeric) = -3.2678621558955212889576776645128
absolute error = 3.2678621558955212889576776645128
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) = -3.2670130694444107905372268248006
absolute error = 3.2670130694444107905372268248006
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=8356.3MB, alloc=52.3MB, time=93.37
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (closed_form) = 0
y[1] (numeric) = -3.2661327709025695950417020164455
absolute error = 3.2661327709025695950417020164455
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) = -3.2652212731795726911480804416229
absolute error = 3.2652212731795726911480804416229
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=8400.3MB, alloc=52.3MB, time=93.86
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (closed_form) = 0
y[1] (numeric) = -3.2642785885366831679592746263743
absolute error = 3.2642785885366831679592746263743
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) = -3.2633047285891709689792538498131
absolute error = 3.2633047285891709689792538498131
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=8444.4MB, alloc=52.3MB, time=94.35
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (closed_form) = 0
y[1] (numeric) = -3.2622997043085700457173465468533
absolute error = 3.2622997043085700457173465468533
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (closed_form) = 0
y[1] (numeric) = -3.2612635260248744726829636229379
absolute error = 3.2612635260248744726829636229379
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=8488.5MB, alloc=52.3MB, time=94.84
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (closed_form) = 0
y[1] (numeric) = -3.2601962034286740717373961108558
absolute error = 3.2601962034286740717373961108558
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) = -3.2590977455732300801892105770288
absolute error = 3.2590977455732300801892105770288
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=8532.5MB, alloc=52.3MB, time=95.33
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (closed_form) = 0
y[1] (numeric) = -3.2579681608764913836484739919435
absolute error = 3.2579681608764913836484739919435
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) = -3.2568074571230518214870909069156
absolute error = 3.2568074571230518214870909069156
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=8576.6MB, alloc=52.3MB, time=95.82
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (closed_form) = 0
y[1] (numeric) = -3.2556156414660490597825532744328
absolute error = 3.2556156414660490597825532744328
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=8620.6MB, alloc=52.3MB, time=96.31
x[1] = 3.83
y[1] (closed_form) = 0
y[1] (numeric) = -3.2543927204290055138451262268399
absolute error = 3.2543927204290055138451262268399
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) = -3.2531386999076117898387728770342
absolute error = 3.2531386999076117898387728770342
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=8664.7MB, alloc=52.3MB, time=96.80
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (closed_form) = 0
y[1] (numeric) = -3.2518535851714531025989178872746
absolute error = 3.2518535851714531025989178872746
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) = -3.250537380865679114520528992591
absolute error = 3.250537380865679114520528992591
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=8708.7MB, alloc=52.3MB, time=97.30
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (closed_form) = 0
y[1] (numeric) = -3.2491900910126176283331262259616
absolute error = 3.2491900910126176283331262259616
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) = -3.2478117190133325546904781333961
absolute error = 3.2478117190133325546904781333961
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=8752.8MB, alloc=52.3MB, time=97.78
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (closed_form) = 0
y[1] (numeric) = -3.2464022676491265637772771867406
absolute error = 3.2464022676491265637772771867406
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) = -3.2449617390829888185684609564321
absolute error = 3.2449617390829888185684609564321
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=8796.9MB, alloc=52.3MB, time=98.28
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (closed_form) = 0
y[1] (numeric) = -3.2434901348609881759646103043509
absolute error = 3.2434901348609881759646103043509
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (closed_form) = 0
y[1] (numeric) = -3.2419874559136122307646479281982
absolute error = 3.2419874559136122307646479281982
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=8841.0MB, alloc=52.3MB, time=98.77
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (closed_form) = 0
y[1] (numeric) = -3.2404537025570525663206025237618
absolute error = 3.2404537025570525663206025237618
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) = -3.2388888744944365647443009885237
absolute error = 3.2388888744944365647443009885237
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=8885.0MB, alloc=52.3MB, time=99.26
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (closed_form) = 0
y[1] (numeric) = -3.237292970817006118698389170138
absolute error = 3.237292970817006118698389170138
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) = -3.2356659900052435761000242476461
absolute error = 3.2356659900052435761000242476461
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=8929.1MB, alloc=52.3MB, time=99.75
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (closed_form) = 0
y[1] (numeric) = -3.2340079299299452384909679835583
absolute error = 3.2340079299299452384909679835583
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) = -3.2323187878532427233787520031253
absolute error = 3.2323187878532427233787520031253
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=8973.3MB, alloc=52.3MB, time=100.24
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (closed_form) = 0
y[1] (numeric) = -3.2305985604295724905262670030454
absolute error = 3.2305985604295724905262670030454
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (closed_form) = 0
y[1] (numeric) = -3.228847243706593821957799056768
absolute error = 3.228847243706593821957799056768
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=9017.3MB, alloc=52.3MB, time=100.73
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (closed_form) = 0
y[1] (numeric) = -3.2270648331260555353545161174163
absolute error = 3.2270648331260555353545161174163
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) = -3.2252513235246117005280789105629
memory used=9061.4MB, alloc=52.3MB, time=101.27
absolute error = 3.2252513235246117005280789105629
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) = -3.2234067091345866187838574141858
absolute error = 3.2234067091345866187838574141858
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=9105.4MB, alloc=52.3MB, time=101.76
x[1] = 4.04
y[1] (closed_form) = 0
y[1] (numeric) = -3.2215309835846893152116820454823
absolute error = 3.2215309835846893152116820454823
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) = -3.2196241399006777842687107893003
absolute error = 3.2196241399006777842687107893003
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=9149.5MB, alloc=52.3MB, time=102.25
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (closed_form) = 0
y[1] (numeric) = -3.2176861705059732194424694291774
absolute error = 3.2176861705059732194424694291774
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) = -3.2157170672222244482990958551702
absolute error = 3.2157170672222244482990958551702
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=9193.5MB, alloc=52.3MB, time=102.74
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (closed_form) = 0
y[1] (numeric) = -3.2137168212698227848290178126438
absolute error = 3.2137168212698227848290178126438
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) = -3.2116854232683675016964939241826
absolute error = 3.2116854232683675016964939241826
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=9237.6MB, alloc=52.3MB, time=103.23
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (closed_form) = 0
y[1] (numeric) = -3.2096228632370821157774769120228
absolute error = 3.2096228632370821157774769120228
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) = -3.2075291305951816712289895424899
absolute error = 3.2075291305951816712289895424899
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=9281.7MB, alloc=52.3MB, time=103.72
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (closed_form) = 0
y[1] (numeric) = -3.2054042141621911952695574118317
absolute error = 3.2054042141621911952695574118317
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) = -3.2032481021582154928611817788374
absolute error = 3.2032481021582154928611817788374
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=9325.8MB, alloc=52.3MB, time=104.21
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (closed_form) = 0
y[1] (numeric) = -3.2010607822041604375658660672751
absolute error = 3.2010607822041604375658660672751
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (closed_form) = 0
y[1] (numeric) = -3.1988422413219059070008780256024
absolute error = 3.1988422413219059070008780256024
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=9369.8MB, alloc=52.3MB, time=104.70
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (closed_form) = 0
y[1] (numeric) = -3.1965924659344305025338216732178
absolute error = 3.1965924659344305025338216732178
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) = -3.1943114418658881841383326016689
absolute error = 3.1943114418658881841383326016689
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=9413.9MB, alloc=52.3MB, time=105.20
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (closed_form) = 0
y[1] (numeric) = -3.1919991543416369426709566479069
absolute error = 3.1919991543416369426709566479069
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) = -3.1896555879882196232267198500443
absolute error = 3.1896555879882196232267198500443
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=9458.0MB, alloc=52.3MB, time=105.69
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (closed_form) = 0
y[1] (numeric) = -3.1872807268332970046822746497297
absolute error = 3.1872807268332970046822746497297
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) = -3.1848745543055332320385730983634
absolute error = 3.1848745543055332320385730983634
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=9502.0MB, alloc=52.3MB, time=106.18
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (closed_form) = 0
y[1] (numeric) = -3.1824370532344336897270624072749
absolute error = 3.1824370532344336897270624072749
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) = -3.1799682058501353956417407075438
absolute error = 3.1799682058501353956417407075438
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=9546.1MB, alloc=52.3MB, time=106.67
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (closed_form) = 0
y[1] (numeric) = -3.1774679937831499873013982624236
absolute error = 3.1774679937831499873013982624236
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=9590.2MB, alloc=52.3MB, time=107.16
x[1] = 4.25
y[1] (closed_form) = 0
y[1] (numeric) = -3.174936398064059363229374945055
absolute error = 3.174936398064059363229374945055
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) = -3.1723733991231640343595870245361
absolute error = 3.1723733991231640343595870245361
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=9634.3MB, alloc=52.3MB, time=107.65
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (closed_form) = 0
y[1] (numeric) = -3.1697789767900842320348375058537
absolute error = 3.1697789767900842320348375058537
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) = -3.1671531102933138109539693324793
absolute error = 3.1671531102933138109539693324793
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=9678.4MB, alloc=52.3MB, time=108.14
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (closed_form) = 0
y[1] (numeric) = -3.1644957782597269772457159030359
absolute error = 3.1644957782597269772457159030359
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (closed_form) = 0
y[1] (numeric) = -3.1618069587140378636966348924304
absolute error = 3.1618069587140378636966348924304
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=9722.6MB, alloc=52.3MB, time=108.64
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (closed_form) = 0
y[1] (numeric) = -3.1590866290782129660357845041615
absolute error = 3.1590866290782129660357845041615
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) = -3.1563347661708364460773388992167
absolute error = 3.1563347661708364460773388992167
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=9766.7MB, alloc=52.3MB, time=109.13
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (closed_form) = 0
y[1] (numeric) = -3.1535513462064282994416810321006
absolute error = 3.1535513462064282994416810321006
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) = -3.1507363447947153775132111872437
absolute error = 3.1507363447947153775132111872437
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=9810.8MB, alloc=52.3MB, time=109.62
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (closed_form) = 0
y[1] (numeric) = -3.1478897369398552452467370287615
absolute error = 3.1478897369398552452467370287615
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) = -3.1450114970396128484014478538491
absolute error = 3.1450114970396128484014478538491
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=9855.0MB, alloc=52.3MB, time=110.12
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (closed_form) = 0
y[1] (numeric) = -3.1421015988844899557597157609239
absolute error = 3.1421015988844899557597157609239
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (closed_form) = 0
y[1] (numeric) = -3.1391600156568073338749141537344
absolute error = 3.1391600156568073338749141537344
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=9899.0MB, alloc=52.3MB, time=110.61
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (closed_form) = 0
y[1] (numeric) = -3.1361867199297396038857135918249
absolute error = 3.1361867199297396038857135918249
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) = -3.1331816836663027219315291927417
absolute error = 3.1331816836663027219315291927417
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=9943.1MB, alloc=52.3MB, time=111.10
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (closed_form) = 0
y[1] (numeric) = -3.1301448782182940167025827572474
absolute error = 3.1301448782182940167025827572474
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) = -3.1270762743251847096560430373161
absolute error = 3.1270762743251847096560430373161
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=9987.2MB, alloc=52.3MB, time=111.59
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (closed_form) = 0
y[1] (numeric) = -3.1239758421129648354245608716475
absolute error = 3.1239758421129648354245608716475
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) = -3.1208435510929404719328682319107
absolute error = 3.1208435510929404719328682319107
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=10031.4MB, alloc=52.3MB, time=112.08
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (closed_form) = 0
y[1] (numeric) = -3.1176793701604831817196106216856
absolute error = 3.1176793701604831817196106216856
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=10075.4MB, alloc=52.3MB, time=112.58
x[1] = 4.46
y[1] (closed_form) = 0
y[1] (numeric) = -3.1144832675937315579328818565903
absolute error = 3.1144832675937315579328818565903
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) = -3.1112552110522447604266811114831
absolute error = 3.1112552110522447604266811114831
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=10119.5MB, alloc=52.3MB, time=113.07
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (closed_form) = 0
y[1] (numeric) = -3.107995167575607919329366245599
absolute error = 3.107995167575607919329366245599
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) = -3.1047031035819892753817856598671
absolute error = 3.1047031035819892753817856598671
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=10163.7MB, alloc=52.3MB, time=113.56
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (closed_form) = 0
y[1] (numeric) = -3.1013789848666489182497819496518
absolute error = 3.1013789848666489182497819496518
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) = -3.0980227766003989759008197777749
absolute error = 3.0980227766003989759008197777749
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=10207.9MB, alloc=52.3MB, time=114.05
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (closed_form) = 0
y[1] (numeric) = -3.0946344433280150999952387774338
absolute error = 3.0946344433280150999952387774338
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (closed_form) = 0
y[1] (numeric) = -3.0912139489665990840767056002084
absolute error = 3.0912139489665990840767056002084
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=10252.1MB, alloc=52.3MB, time=114.54
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (closed_form) = 0
y[1] (numeric) = -3.0877612568038924431514667181364
absolute error = 3.0877612568038924431514667181364
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) = -3.0842763294965407750196070489383
absolute error = 3.0842763294965407750196070489383
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=10296.2MB, alloc=52.3MB, time=115.04
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (closed_form) = 0
y[1] (numeric) = -3.0807591290683087154613121274867
absolute error = 3.0807591290683087154613121274867
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) = -3.0772096169082452910847170073329
absolute error = 3.0772096169082452910847170073329
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=10340.3MB, alloc=52.3MB, time=115.53
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (closed_form) = 0
y[1] (numeric) = -3.0736277537687994653068962737005
absolute error = 3.0736277537687994653068962737005
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) = -3.0700134997638856645634876591939
absolute error = 3.0700134997638856645634876591939
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=10384.4MB, alloc=52.3MB, time=116.02
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (closed_form) = 0
y[1] (numeric) = -3.0663668143668990634229151189157
absolute error = 3.0663668143668990634229151189157
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) = -3.0626876564086803988157402713152
absolute error = 3.0626876564086803988157402713152
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=10428.6MB, alloc=52.3MB, time=116.52
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (closed_form) = 0
y[1] (numeric) = -3.0589759840754300750758632694492
absolute error = 3.0589759840754300750758632694492
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) = -3.055231754906571312925638758686
absolute error = 3.055231754906571312925638758686
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=10472.7MB, alloc=52.3MB, time=117.02
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (closed_form) = 0
y[1] (numeric) = -3.0514549257925620869189757212909
absolute error = 3.0514549257925620869189757212909
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) = -3.0476454529726555871826395090871
absolute error = 3.0476454529726555871826395090871
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=10516.9MB, alloc=52.3MB, time=117.54
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (closed_form) = 0
y[1] (numeric) = -3.0438032920326089325637385875943
absolute error = 3.0438032920326089325637385875943
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (closed_form) = 0
y[1] (numeric) = -3.0399283979023398534982052540397
absolute error = 3.0399283979023398534982052540397
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=10561.0MB, alloc=52.3MB, time=118.04
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (closed_form) = 0
y[1] (numeric) = -3.0360207248535310540583949310397
absolute error = 3.0360207248535310540583949310397
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=10605.1MB, alloc=52.3MB, time=118.54
x[1] = 4.69
y[1] (closed_form) = 0
y[1] (numeric) = -3.0320802264971819537151357961425
absolute error = 3.0320802264971819537151357961425
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) = -3.0281068557811075003580386729582
absolute error = 3.0281068557811075003580386729582
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=10649.3MB, alloc=52.3MB, time=119.03
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (closed_form) = 0
y[1] (numeric) = -3.0241005649873837370549802619157
absolute error = 3.0241005649873837370549802619157
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) = -3.0200613057297397958947285071881
absolute error = 3.0200613057297397958947285071881
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=10693.3MB, alloc=52.3MB, time=119.52
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (closed_form) = 0
y[1] (numeric) = -3.0159890289508959830429871542725
absolute error = 3.0159890289508959830429871542725
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) = -3.0118836849198476098489684961727
absolute error = 3.0118836849198476098489684961727
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=10737.4MB, alloc=52.3MB, time=120.02
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (closed_form) = 0
y[1] (numeric) = -3.0077452232290942154642000171282
absolute error = 3.0077452232290942154642000171282
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) = -3.0035735927918138169748418858118
absolute error = 3.0035735927918138169748418858118
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=10781.5MB, alloc=52.3MB, time=120.51
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (closed_form) = 0
y[1] (numeric) = -2.9993687418389818135005152008312
absolute error = 2.9993687418389818135005152008312
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) = -2.995130617916434161073658848341
absolute error = 2.995130617916434161073658848341
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=10825.6MB, alloc=52.3MB, time=121.01
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (closed_form) = 0
y[1] (numeric) = -2.9908591678818744253808539066946
absolute error = 2.9908591678818744253808539066946
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) = -2.9865543379018243096184503239454
absolute error = 2.9865543379018243096184503239454
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=10869.7MB, alloc=52.3MB, time=121.50
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (closed_form) = 0
y[1] (numeric) = -2.9822160734485172447862348347489
absolute error = 2.9822160734485172447862348347489
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (closed_form) = 0
y[1] (numeric) = -2.977844319296734619711786273486
absolute error = 2.977844319296734619711786273486
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=10913.8MB, alloc=52.3MB, time=122.00
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (closed_form) = 0
y[1] (numeric) = -2.9734390195205842179615284521104
absolute error = 2.9734390195205842179615284521104
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) = -2.9690001174902204185492234312927
absolute error = 2.9690001174902204185492234312927
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=10958.0MB, alloc=52.3MB, time=122.49
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (closed_form) = 0
y[1] (numeric) = -2.9645275558685057069956176627102
absolute error = 2.9645275558685057069956176627102
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) = -2.9600212766076130328209835064126
absolute error = 2.9600212766076130328209835064126
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=11002.1MB, alloc=52.3MB, time=122.99
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (closed_form) = 0
y[1] (numeric) = -2.9554812209455685389621659713795
absolute error = 2.9554812209455685389621659713795
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) = -2.9509073294027341778941781639098
absolute error = 2.9509073294027341778941781639098
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=11046.3MB, alloc=52.3MB, time=123.48
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (closed_form) = 0
y[1] (numeric) = -2.9462995417782297184000683155124
absolute error = 2.9462995417782297184000683155124
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (closed_form) = 0
y[1] (numeric) = -2.9416577971462936359683347630795
absolute error = 2.9416577971462936359683347630795
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=11090.4MB, alloc=52.3MB, time=123.98
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (closed_form) = 0
y[1] (numeric) = -2.9369820338525823687011685292477
absolute error = 2.9369820338525823687011685292477
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
memory used=11134.6MB, alloc=52.3MB, time=124.47
x[1] = 4.92
y[1] (closed_form) = 0
y[1] (numeric) = -2.9322721895104074093857775156209
absolute error = 2.9322721895104074093857775156209
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) = -2.9275282009969096930114570739461
absolute error = 2.9275282009969096930114570739461
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=11178.8MB, alloc=52.3MB, time=124.96
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (closed_form) = 0
y[1] (numeric) = -2.9227500044491707275033264333754
absolute error = 2.9227500044491707275033264333754
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) = -2.917937535260259903786097241445
absolute error = 2.917937535260259903786097241445
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=11222.8MB, alloc=52.3MB, time=125.45
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (closed_form) = 0
y[1] (numeric) = -2.9130907280752174094841661822506
absolute error = 2.9130907280752174094841661822506
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (closed_form) = 0
y[1] (numeric) = -2.9082095167869721586039520655826
absolute error = 2.9082095167869721586039520655826
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=11267.0MB, alloc=52.3MB, time=125.95
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (closed_form) = 0
y[1] (numeric) = -2.9032938345321941374268878168601
absolute error = 2.9032938345321941374268878168601
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) = -2.8983436136870805545629215093772
absolute error = 2.8983436136870805545629215093772
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=11311.2MB, alloc=52.3MB, time=126.44
Finished!
diff ( y , x , 1 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ;
Iterations = 4900
Total Elapsed Time = 2 Minutes 6 Seconds
Elapsed Time(since restart) = 2 Minutes 6 Seconds
Time to Timeout = 53 Seconds
Percent Done = 100 %
> quit
memory used=11317.1MB, alloc=52.3MB, time=126.51