|\^/| Maple 2019 (X86 64 WINDOWS)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2019
\ 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_0D1,
> array_const_0D2,
#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_g,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> 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_0D1,
array_const_0D2, 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_g, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4,
array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6,
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_0D1,
> array_const_0D2,
#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_g,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> 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_0D1,
array_const_0D2, 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_g, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4,
array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6,
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_0D1,
> array_const_0D2,
#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_g,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> 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_0D1,
array_const_0D2, 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_g, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4,
array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6,
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_0D1,
> array_const_0D2,
#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_g,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> 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_0D1,
array_const_0D2, 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_g, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4,
array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6,
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_0D1,
> array_const_0D2,
#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_g,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> 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/float_abs(closed_form_val_y);
> if (c(relerr) > c(glob_prec)) then # if number 6
> glob_good_digits := round(-log10(relerr));
> 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)*29*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 * c(100.0),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_0D1,
array_const_0D2, 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_g, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4,
array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6,
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/float_abs(closed_form_val_y);
if c(glob_prec) < c(relerr) then
glob_good_digits := round(-log10(relerr))
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)*29*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*c(100.0), 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_0D1,
> array_const_0D2,
#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_g,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> 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_0D1,
array_const_0D2, 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_g, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4,
array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6,
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_0D1,
> array_const_0D2,
#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_g,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> 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_0D1,
array_const_0D2, 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_g, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4,
array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6,
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_0D1,
> array_const_0D2,
#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_g,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> 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_0D1[1] * array_x[1];
> #emit pre sin 1 $eq_no = 1
> array_tmp2[1] := sin(array_tmp1[1]);
> array_tmp2_g[1] := cos(array_tmp1[1]);
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D2[1] * array_x[1];
> #emit pre sin 1 $eq_no = 1
> array_tmp4[1] := sin(array_tmp3[1]);
> array_tmp4_g[1] := cos(array_tmp3[1]);
> #emit pre expt FULL - FULL $eq_no = 1 i = 1
> array_tmp5[1] := expt(array_tmp2[1] ,c( array_tmp4[1] )) ;
> array_tmp5_a1[1] := ln(array_tmp2[1] ) ;
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp6[1] := array_const_0D0[1] + array_tmp5[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_tmp6[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_0D1[1] * array_x[2];
> #emit pre sin ID_LINEAR iii = 2 $eq_no = 1
> array_tmp2[2] := array_tmp2_g[1] * array_tmp1[2] / c(1);
> array_tmp2_g[2] := neg(array_tmp2[1]) * array_tmp1[2] / c(1);
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := array_const_0D2[1] * array_x[2];
> #emit pre sin ID_LINEAR iii = 2 $eq_no = 1
> array_tmp4[2] := array_tmp4_g[1] * array_tmp3[2] / c(1);
> array_tmp4_g[2] := neg(array_tmp4[1]) * array_tmp3[2] / c(1);
> #emit pre expt FULL - FULL $eq_no = 1 i = 2
> array_tmp5_a1[2] := (array_tmp2[2] -att(1,array_tmp2,array_tmp5_a1,2))/ array_tmp2[1];
> array_tmp5_a2[1] := ats(2,array_tmp2,array_tmp5_a1,1) * c(1) / glob_h;
> array_tmp5[2] := ats(1,array_tmp5,array_tmp5_a2,1)*glob_h/c(1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp6[2] := array_tmp5[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_tmp6[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sin ID_LINEAR iii = 3 $eq_no = 1
> array_tmp2[3] := array_tmp2_g[2] * array_tmp1[2] / c(2);
> array_tmp2_g[3] := neg(array_tmp2[2]) * array_tmp1[2] / c(2);
> #emit pre sin ID_LINEAR iii = 3 $eq_no = 1
> array_tmp4[3] := array_tmp4_g[2] * array_tmp3[2] / c(2);
> array_tmp4_g[3] := neg(array_tmp4[2]) * array_tmp3[2] / c(2);
> #emit pre expt FULL - FULL $eq_no = 1 i = 3
> array_tmp5_a1[3] := (array_tmp2[3] -att(2,array_tmp2,array_tmp5_a1,2))/ array_tmp2[1];
> array_tmp5_a2[2] := ats(3,array_tmp2,array_tmp5_a1,1) * c(2) / glob_h;
> array_tmp5[3] := ats(2,array_tmp5,array_tmp5_a2,1)*glob_h/c(2);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp6[3] := array_tmp5[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_tmp6[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sin ID_LINEAR iii = 4 $eq_no = 1
> array_tmp2[4] := array_tmp2_g[3] * array_tmp1[2] / c(3);
> array_tmp2_g[4] := neg(array_tmp2[3]) * array_tmp1[2] / c(3);
> #emit pre sin ID_LINEAR iii = 4 $eq_no = 1
> array_tmp4[4] := array_tmp4_g[3] * array_tmp3[2] / c(3);
> array_tmp4_g[4] := neg(array_tmp4[3]) * array_tmp3[2] / c(3);
> #emit pre expt FULL - FULL $eq_no = 1 i = 4
> array_tmp5_a1[4] := (array_tmp2[4] -att(3,array_tmp2,array_tmp5_a1,2))/ array_tmp2[1];
> array_tmp5_a2[3] := ats(4,array_tmp2,array_tmp5_a1,1) * c(3) / glob_h;
> array_tmp5[4] := ats(3,array_tmp5,array_tmp5_a2,1)*glob_h/c(3);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp6[4] := array_tmp5[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_tmp6[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sin ID_LINEAR iii = 5 $eq_no = 1
> array_tmp2[5] := array_tmp2_g[4] * array_tmp1[2] / c(4);
> array_tmp2_g[5] := neg(array_tmp2[4]) * array_tmp1[2] / c(4);
> #emit pre sin ID_LINEAR iii = 5 $eq_no = 1
> array_tmp4[5] := array_tmp4_g[4] * array_tmp3[2] / c(4);
> array_tmp4_g[5] := neg(array_tmp4[4]) * array_tmp3[2] / c(4);
> #emit pre expt FULL - FULL $eq_no = 1 i = 5
> array_tmp5_a1[5] := (array_tmp2[5] -att(4,array_tmp2,array_tmp5_a1,2))/ array_tmp2[1];
> array_tmp5_a2[4] := ats(5,array_tmp2,array_tmp5_a1,1) * c(4) / glob_h;
> array_tmp5[5] := ats(4,array_tmp5,array_tmp5_a2,1)*glob_h/c(4);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp6[5] := array_tmp5[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_tmp6[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit sin LINEAR $eq_no = 1
> array_tmp2[kkk] := array_tmp2_g[kkk - 1] * array_tmp1[2] / c(kkk - 1);
> array_tmp2_g[kkk] := neg(array_tmp2[kkk - 1]) * array_tmp1[2] / c(kkk - 1);
> #emit sin LINEAR $eq_no = 1
> array_tmp4[kkk] := array_tmp4_g[kkk - 1] * array_tmp3[2] / c(kkk - 1);
> array_tmp4_g[kkk] := neg(array_tmp4[kkk - 1]) * array_tmp3[2] / c(kkk - 1);
> #emit expt FULL FULL $eq_no = 1 i = 1
> array_tmp5_a1[kkk] := (array_tmp2[kkk] - att(kkk-1,array_tmp2,array_tmp5_a1,2))/array_tmp2[1];
> array_tmp5_a2[kkk-1] := ats(kkk,array_tmp2,array_tmp5_a1,1) * c(kkk-1)/glob_h;
> array_tmp5[kkk] := ats(kkk-1,array_tmp5,array_tmp5_a2,1) * glob_h/c(kkk-1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp6[kkk] := array_tmp5[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_tmp6[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_0D1,
array_const_0D2, 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_g, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4,
array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6,
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_0D1[1]*array_x[1];
array_tmp2[1] := sin(array_tmp1[1]);
array_tmp2_g[1] := cos(array_tmp1[1]);
array_tmp3[1] := array_const_0D2[1]*array_x[1];
array_tmp4[1] := sin(array_tmp3[1]);
array_tmp4_g[1] := cos(array_tmp3[1]);
array_tmp5[1] := expt(array_tmp2[1], c(array_tmp4[1]));
array_tmp5_a1[1] := ln(array_tmp2[1]);
array_tmp6[1] := array_const_0D0[1] + array_tmp5[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[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_0D1[1]*array_x[2];
array_tmp2[2] := array_tmp2_g[1]*array_tmp1[2]/c(1);
array_tmp2_g[2] := neg(array_tmp2[1])*array_tmp1[2]/c(1);
array_tmp3[2] := array_const_0D2[1]*array_x[2];
array_tmp4[2] := array_tmp4_g[1]*array_tmp3[2]/c(1);
array_tmp4_g[2] := neg(array_tmp4[1])*array_tmp3[2]/c(1);
array_tmp5_a1[2] := (
array_tmp2[2] - att(1, array_tmp2, array_tmp5_a1, 2))/array_tmp2[1]
;
array_tmp5_a2[1] := ats(2, array_tmp2, array_tmp5_a1, 1)*c(1)/glob_h;
array_tmp5[2] := ats(1, array_tmp5, array_tmp5_a2, 1)*glob_h/c(1);
array_tmp6[2] := array_tmp5[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[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_tmp2[3] := array_tmp2_g[2]*array_tmp1[2]/c(2);
array_tmp2_g[3] := neg(array_tmp2[2])*array_tmp1[2]/c(2);
array_tmp4[3] := array_tmp4_g[2]*array_tmp3[2]/c(2);
array_tmp4_g[3] := neg(array_tmp4[2])*array_tmp3[2]/c(2);
array_tmp5_a1[3] := (
array_tmp2[3] - att(2, array_tmp2, array_tmp5_a1, 2))/array_tmp2[1]
;
array_tmp5_a2[2] := ats(3, array_tmp2, array_tmp5_a1, 1)*c(2)/glob_h;
array_tmp5[3] := ats(2, array_tmp5, array_tmp5_a2, 1)*glob_h/c(2);
array_tmp6[3] := array_tmp5[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[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_tmp2[4] := array_tmp2_g[3]*array_tmp1[2]/c(3);
array_tmp2_g[4] := neg(array_tmp2[3])*array_tmp1[2]/c(3);
array_tmp4[4] := array_tmp4_g[3]*array_tmp3[2]/c(3);
array_tmp4_g[4] := neg(array_tmp4[3])*array_tmp3[2]/c(3);
array_tmp5_a1[4] := (
array_tmp2[4] - att(3, array_tmp2, array_tmp5_a1, 2))/array_tmp2[1]
;
array_tmp5_a2[3] := ats(4, array_tmp2, array_tmp5_a1, 1)*c(3)/glob_h;
array_tmp5[4] := ats(3, array_tmp5, array_tmp5_a2, 1)*glob_h/c(3);
array_tmp6[4] := array_tmp5[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[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_tmp2[5] := array_tmp2_g[4]*array_tmp1[2]/c(4);
array_tmp2_g[5] := neg(array_tmp2[4])*array_tmp1[2]/c(4);
array_tmp4[5] := array_tmp4_g[4]*array_tmp3[2]/c(4);
array_tmp4_g[5] := neg(array_tmp4[4])*array_tmp3[2]/c(4);
array_tmp5_a1[5] := (
array_tmp2[5] - att(4, array_tmp2, array_tmp5_a1, 2))/array_tmp2[1]
;
array_tmp5_a2[4] := ats(5, array_tmp2, array_tmp5_a1, 1)*c(4)/glob_h;
array_tmp5[5] := ats(4, array_tmp5, array_tmp5_a2, 1)*glob_h/c(4);
array_tmp6[5] := array_tmp5[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[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_tmp2[kkk] := array_tmp2_g[kkk - 1]*array_tmp1[2]/c(kkk - 1);
array_tmp2_g[kkk] :=
neg(array_tmp2[kkk - 1])*array_tmp1[2]/c(kkk - 1);
array_tmp4[kkk] := array_tmp4_g[kkk - 1]*array_tmp3[2]/c(kkk - 1);
array_tmp4_g[kkk] :=
neg(array_tmp4[kkk - 1])*array_tmp3[2]/c(kkk - 1);
array_tmp5_a1[kkk] := (
array_tmp2[kkk] - att(kkk - 1, array_tmp2, array_tmp5_a1, 2))/
array_tmp2[1];
array_tmp5_a2[kkk - 1] :=
ats(kkk, array_tmp2, array_tmp5_a1, 1)*c(kkk - 1)/glob_h;
array_tmp5[kkk] :=
ats(kkk - 1, array_tmp5, array_tmp5_a2, 1)*glob_h/c(kkk - 1);
array_tmp6[kkk] := array_tmp5[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_tmp6[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_0D1,
> array_const_0D2,
> #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_g,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 30;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(30),[]);
> array_norms:= Array(0..(30),[]);
> array_fact_1:= Array(0..(30),[]);
> array_1st_rel_error:= Array(0..(2),[]);
> array_last_rel_error:= Array(0..(2),[]);
> array_est_rel_error:= Array(0..(2),[]);
> array_max_est_error:= Array(0..(2),[]);
> array_type_pole:= Array(0..(2),[]);
> array_type_real_pole:= Array(0..(2),[]);
> array_type_complex_pole:= Array(0..(2),[]);
> array_est_digits:= Array(0..(2),[]);
> array_y:= Array(0..(30),[]);
> array_x:= Array(0..(30),[]);
> array_tmp0:= Array(0..(30),[]);
> array_tmp1:= Array(0..(30),[]);
> array_tmp2_g:= Array(0..(30),[]);
> array_tmp2:= Array(0..(30),[]);
> array_tmp3:= Array(0..(30),[]);
> array_tmp4_g:= Array(0..(30),[]);
> array_tmp4:= Array(0..(30),[]);
> array_tmp5_c1:= Array(0..(30),[]);
> array_tmp5_a1:= Array(0..(30),[]);
> array_tmp5_a2:= Array(0..(30),[]);
> array_tmp5:= Array(0..(30),[]);
> array_tmp6:= Array(0..(30),[]);
> array_m1:= Array(0..(30),[]);
> array_y_higher := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..30+ 1),[]);
> array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(30) ,(0..30+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 30) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp2_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp4_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp5_c1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp5_a1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp5_a2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp6[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=30) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2_g);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4_g);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5_c1);
> zero_ats_ar(array_tmp5_a1);
> zero_ats_ar(array_tmp5_a2);
> zero_ats_ar(array_tmp5);
> zero_ats_ar(array_tmp6);
> 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_0D1);
> array_const_0D1[1] := c(0.1);
> zero_ats_ar(array_const_0D2);
> array_const_0D2[1] := c(0.2);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_h := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 1000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 30;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############R:\Temp/expt_sin_sinpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = expt ( sin ( 0.1 * x ) , sin ( 0.2 * x ) ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := c(0.1);");
> omniout_str(ALWAYS,"x_end := c(5.0) ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 0;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=12;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=2;");
> omniout_str(ALWAYS,"glob_max_iter:=1000000;");
> 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:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"glob_h_reason:=1;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(c(0.0));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := c(0.1);
> x_end := c(5.0) ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_type_given_pole := 0;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=12;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=2;
> glob_max_iter:=1000000;
> glob_upper_ratio_limit:=c(1.000001);
> glob_lower_ratio_limit:=c(0.999999);
> glob_look_poles:=true;
> glob_h:=c(0.001);
> glob_display_interval:=c(0.01);
> glob_h_reason:=1;
> #END OVERRIDE BLOCK
> #END BLOCK 2
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
> # after second input block
> glob_check_sign := c(my_check_sign(x_start,x_end));
> glob__pi := arccos(glob__m1);
> glob_prec = expt(10.0,c(-Digits));
> if (glob_optimize) then # if number 9
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> found_h := false;
> glob_min_pole_est := glob_larger_float;
> last_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> glob_min_h := float_abs(glob_min_h) * glob_check_sign;
> glob_max_h := float_abs(glob_max_h) * glob_check_sign;
> glob_h := float_abs(glob_min_h) * glob_check_sign;
> glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign));
> display_max := c(x_end) - c(x_start)/glob__10;
> if ((glob_display_interval) > (display_max)) then # if number 10
> glob_display_interval := c(display_max);
> fi;# end if 10;
> chk_data();
> min_value := glob_larger_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := glob_small_float;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> atomall();
> if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> glob_h := glob_check_sign * float_abs(glob_min_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
> glob_h_reason := 2;
> glob_h := glob_display_interval;
> found_h := true;
> fi;# end if 10;
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if ( not found_h) then # if number 10
> est_answer := est_size_answer();
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := test_suggested_h();
> omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
> if (estimated_step_error < est_needed_step_err) then # if number 11
> omniout_str(ALWAYS,"Double H and LOOP");
> glob_h := glob_h*glob__2;
> else
> omniout_str(ALWAYS,"Found H for OPTIMAL");
> found_h := true;
> glob_h_reason := 3;
> glob_h := glob_h/glob__2;
> fi;# end if 11;
> fi;# end if 10;
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 10
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 10;
> if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MAX H");
> glob_h := glob_check_sign * float_abs(glob_max_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> else
> found_h := true;
> glob_h := glob_h * glob_check_sign;
> fi;# end if 9;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 9
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 9;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 9
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> glob_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and (glob_check_sign * array_x[1] < glob_check_sign * x_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1
> #left paren 0001C
> if (reached_interval()) then # if number 10
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 10;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> track_estimated_error();
> atomall();
> track_estimated_error();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if (reached_interval()) then # if number 10
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 10;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 10
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 10;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 10;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = expt ( sin ( 0.1 * x ) , sin ( 0.2 * x ) ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2020-05-25T23:47:29-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"expt_sin_sin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = expt ( sin ( 0.1 * x ) , sin ( 0.2 * x ) ) ; ")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 310 | ")
> ;
> logitem_str(html_log_file,"expt_sin_sin diffeq.mxt")
> ;
> logitem_str(html_log_file,"expt_sin_sin maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> fi;# end if 14
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, 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_g, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4,
array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
ATS_MAX_TERMS := 30;
Digits := 32;
max_terms := 30;
glob_html_log := true;
array_y_init := Array(0 .. 30, []);
array_norms := Array(0 .. 30, []);
array_fact_1 := Array(0 .. 30, []);
array_1st_rel_error := Array(0 .. 2, []);
array_last_rel_error := Array(0 .. 2, []);
array_est_rel_error := Array(0 .. 2, []);
array_max_est_error := Array(0 .. 2, []);
array_type_pole := Array(0 .. 2, []);
array_type_real_pole := Array(0 .. 2, []);
array_type_complex_pole := Array(0 .. 2, []);
array_est_digits := Array(0 .. 2, []);
array_y := Array(0 .. 30, []);
array_x := Array(0 .. 30, []);
array_tmp0 := Array(0 .. 30, []);
array_tmp1 := Array(0 .. 30, []);
array_tmp2_g := Array(0 .. 30, []);
array_tmp2 := Array(0 .. 30, []);
array_tmp3 := Array(0 .. 30, []);
array_tmp4_g := Array(0 .. 30, []);
array_tmp4 := Array(0 .. 30, []);
array_tmp5_c1 := Array(0 .. 30, []);
array_tmp5_a1 := Array(0 .. 30, []);
array_tmp5_a2 := Array(0 .. 30, []);
array_tmp5 := Array(0 .. 30, []);
array_tmp6 := Array(0 .. 30, []);
array_m1 := Array(0 .. 30, []);
array_y_higher := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []);
array_y_set_initial := Array(0 .. 2, 0 .. 31, []);
array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
array_fact_2 := Array(0 .. 30, 0 .. 31, []);
term := 1;
while term <= 30 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 30 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 30 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp2_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp4_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp5_c1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp5_a1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp5_a2[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp6[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 30 do
term := 1;
while term <= 30 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2_g);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4_g);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5_c1);
zero_ats_ar(array_tmp5_a1);
zero_ats_ar(array_tmp5_a2);
zero_ats_ar(array_tmp5);
zero_ats_ar(array_tmp6);
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_0D1);
array_const_0D1[1] := c(0.1);
zero_ats_ar(array_const_0D2);
array_const_0D2[1] := c(0.2);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_h := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 1000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 30;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############R:Temp/expt_sin_sinpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = expt ( sin ( 0.1\
* x ) , sin ( 0.2 * x ) ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := c(0.1);");
omniout_str(ALWAYS, "x_end := c(5.0) ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 0;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=12;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=2;");
omniout_str(ALWAYS, "glob_max_iter:=1000000;");
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:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "glob_h_reason:=1;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(c(0.0));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := c(0.1);
x_end := c(5.0);
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 0;
glob_desired_digits_correct := 12;
glob_max_minutes := 3.0;
glob_subiter_method := 2;
glob_max_iter := 1000000;
glob_upper_ratio_limit := c(1.000001);
glob_lower_ratio_limit := c(0.999999);
glob_look_poles := true;
glob_h := c(0.001);
glob_display_interval := c(0.01);
glob_h_reason := 1;
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
glob_check_sign := c(my_check_sign(x_start, x_end));
glob__pi := arccos(glob__m1);
glob_prec = expt(10.0, c(-Digits));
if glob_optimize then
omniout_str(ALWAYS, "START of Optimize");
found_h := false;
glob_min_pole_est := glob_larger_float;
last_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
glob_min_h := float_abs(glob_min_h)*glob_check_sign;
glob_max_h := float_abs(glob_max_h)*glob_check_sign;
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_display_interval :=
c(float_abs(c(glob_display_interval))*glob_check_sign);
display_max := c(x_end) - c(x_start)/glob__10;
if display_max < glob_display_interval then
glob_display_interval := c(display_max)
end if;
chk_data();
min_value := glob_larger_float;
est_answer := est_size_answer();
opt_iter := 1;
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
;
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := glob_small_float;
while opt_iter <= 100 and not found_h do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] :=
array_y_init[it]*expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
atomall();
if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if;
if
glob_check_sign*glob_display_interval <= glob_check_sign*glob_h
then
omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL");
glob_h_reason := 2;
glob_h := glob_display_interval;
found_h := true
end if;
if glob_look_poles then check_for_pole() end if;
if not found_h then
est_answer := est_size_answer();
est_needed_step_err := estimated_needed_step_error(x_start,
x_end, glob_h, est_answer);
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := test_suggested_h();
omniout_float(ALWAYS, "estimated_step_error", 32,
estimated_step_error, 32, "");
if estimated_step_error < est_needed_step_err then
omniout_str(ALWAYS, "Double H and LOOP");
glob_h := glob_h*glob__2
else
omniout_str(ALWAYS, "Found H for OPTIMAL");
found_h := true;
glob_h_reason := 3;
glob_h := glob_h/glob__2
end if
end if;
opt_iter := opt_iter + 1
end do;
if not found_h and opt_iter = 1 then
omniout_str(ALWAYS, "Beginning glob_h too large.");
found_h := false
end if;
if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then
omniout_str(ALWAYS, "SETTING H FOR MAX H");
glob_h := float_abs(glob_max_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if
else found_h := true; glob_h := glob_check_sign*glob_h
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
glob_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
glob_clock_sec - glob_orig_start_sec < glob_max_sec do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
track_estimated_error();
atomall();
track_estimated_error();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then
glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then
omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = expt ( sin ( 0\
.1 * x ) , sin ( 0.2 * x ) ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2020-05-25T23:47:29-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"expt_sin_sin");
logitem_str(html_log_file, "diff ( y , x , 1 ) = e\
xpt ( sin ( 0.1 * x ) , sin ( 0.2 * x ) ) ; ");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 310 | ");
logitem_str(html_log_file, "expt_sin_sin diffeq.mxt");
logitem_str(html_log_file, "expt_sin_sin maple results");
logitem_str(html_log_file, "OK");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
##############ECHO OF PROBLEM#################
##############R:Temp/expt_sin_sinpostode.ode#################
diff ( y , x , 1 ) = expt ( sin ( 0.1 * x ) , sin ( 0.2 * x ) ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(0.1);
x_end := c(5.0) ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 0;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=12;
glob_max_minutes:=(3.0);
glob_subiter_method:=2;
glob_max_iter:=1000000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
glob_h_reason:=1;
#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=4.3MB, alloc=40.3MB, time=0.11
x[1] = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 0
absolute error = 0
relative error = -100 %
Desired digits = 12
Estimated correct digits = -16
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (closed_form) = 0
y[1] (numeric) = 0.0090892809602897921845934385592707
absolute error = 0.0090892809602897921845934385592707
relative error = -100 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (closed_form) = 0
y[1] (numeric) = 0.018114943495478338365806927841686
absolute error = 0.018114943495478338365806927841686
relative error = -100 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=46.1MB, alloc=44.3MB, time=0.33
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (closed_form) = 0
y[1] (numeric) = 0.027079000999840013416337228879153
absolute error = 0.027079000999840013416337228879153
relative error = -100 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (closed_form) = 0
y[1] (numeric) = 0.035983306722272530839021345914699
absolute error = 0.035983306722272530839021345914699
relative error = -100 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (closed_form) = 0
y[1] (numeric) = 0.04482957681002978148214777818092
absolute error = 0.04482957681002978148214777818092
relative error = -100 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (closed_form) = 0
y[1] (numeric) = 0.05361940864992853632617396839943
absolute error = 0.05361940864992853632617396839943
relative error = -100 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=97.8MB, alloc=48.3MB, time=0.58
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (closed_form) = 0
y[1] (numeric) = 0.062354295714632335362597991077209
absolute error = 0.062354295714632335362597991077209
relative error = -100 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (closed_form) = 0
y[1] (numeric) = 0.071035639755737366488322591034392
absolute error = 0.071035639755737366488322591034392
relative error = -100 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (closed_form) = 0
y[1] (numeric) = 0.079664760945279700402255619013675
absolute error = 0.079664760945279700402255619013675
relative error = -100 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (closed_form) = 0
y[1] (numeric) = 0.088242906405151415700153471649259
absolute error = 0.088242906405151415700153471649259
relative error = -100 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=141.3MB, alloc=48.3MB, time=0.84
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (closed_form) = 0
y[1] (numeric) = 0.096771257451675551849061569761731
absolute error = 0.096771257451675551849061569761731
relative error = -100 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (closed_form) = 0
y[1] (numeric) = 0.10525093580317362925936340741509
absolute error = 0.10525093580317362925936340741509
relative error = -100 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (closed_form) = 0
y[1] (numeric) = 0.11368300894106632713723396437902
absolute error = 0.11368300894106632713723396437902
relative error = -100 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=184.9MB, alloc=48.3MB, time=1.09
x[1] = 0.24
y[1] (closed_form) = 0
y[1] (numeric) = 0.12206849477299297745781981616132
absolute error = 0.12206849477299297745781981616132
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (closed_form) = 0
y[1] (numeric) = 0.1304083657150818431277599553768
absolute error = 0.1304083657150818431277599553768
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (closed_form) = 0
y[1] (numeric) = 0.13870355228679671191634028856635
absolute error = 0.13870355228679671191634028856635
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (closed_form) = 0
y[1] (numeric) = 0.1469549462936306473928072016941
absolute error = 0.1469549462936306473928072016941
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=228.4MB, alloc=48.3MB, time=1.36
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (closed_form) = 0
y[1] (numeric) = 0.15516340365885176143955657195036
absolute error = 0.15516340365885176143955657195036
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (closed_form) = 0
y[1] (numeric) = 0.16332974695449086845951921217871
absolute error = 0.16332974695449086845951921217871
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (closed_form) = 0
y[1] (numeric) = 0.17145476767305004005675366204813
absolute error = 0.17145476767305004005675366204813
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (closed_form) = 0
y[1] (numeric) = 0.17953922827445976949959546769428
absolute error = 0.17953922827445976949959546769428
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=272.1MB, alloc=48.3MB, time=1.61
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (closed_form) = 0
y[1] (numeric) = 0.18758386403721859424396096755233
absolute error = 0.18758386403721859424396096755233
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (closed_form) = 0
y[1] (numeric) = 0.19558938473811238489767516155684
absolute error = 0.19558938473811238489767516155684
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (closed_form) = 0
y[1] (numeric) = 0.20355647618120454853020871467531
absolute error = 0.20355647618120454853020871467531
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=315.8MB, alloc=48.3MB, time=1.87
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (closed_form) = 0
y[1] (numeric) = 0.21148580159374049304144646051119
absolute error = 0.21148580159374049304144646051119
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (closed_form) = 0
y[1] (numeric) = 0.21937800290408711985950143891966
absolute error = 0.21937800290408711985950143891966
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (closed_form) = 0
y[1] (numeric) = 0.22723370191472791148009865806123
absolute error = 0.22723370191472791148009865806123
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (closed_form) = 0
y[1] (numeric) = 0.23505350138157588199730991139231
absolute error = 0.23505350138157588199730991139231
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=359.4MB, alloc=48.3MB, time=2.13
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (closed_form) = 0
y[1] (numeric) = 0.24283798600938687664256944973486
absolute error = 0.24283798600938687664256944973486
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (closed_form) = 0
y[1] (numeric) = 0.2505877233718041617876475320905
absolute error = 0.2505877233718041617876475320905
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (closed_form) = 0
y[1] (numeric) = 0.25830326476350179229984784000153
absolute error = 0.25830326476350179229984784000153
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (closed_form) = 0
y[1] (numeric) = 0.26598514599098661887986292972238
absolute error = 0.26598514599098661887986292972238
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=403.1MB, alloc=48.3MB, time=2.39
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (closed_form) = 0
y[1] (numeric) = 0.27363388810784092825342333938073
absolute error = 0.27363388810784092825342333938073
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (closed_form) = 0
y[1] (numeric) = 0.28124999809951839771805728278549
absolute error = 0.28124999809951839771805728278549
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (closed_form) = 0
y[1] (numeric) = 0.28883396952222797091389718339334
absolute error = 0.28883396952222797091389718339334
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=446.8MB, alloc=48.3MB, time=2.64
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (closed_form) = 0
y[1] (numeric) = 0.29638628309993919653916264497479
absolute error = 0.29638628309993919653916264497479
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (closed_form) = 0
y[1] (numeric) = 0.30390740728310677402210939040502
absolute error = 0.30390740728310677402210939040502
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (closed_form) = 0
y[1] (numeric) = 0.31139779877233178441230606099233
absolute error = 0.31139779877233178441230606099233
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (closed_form) = 0
y[1] (numeric) = 0.31885790300984424380014305462572
absolute error = 0.31885790300984424380014305462572
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=490.4MB, alloc=48.3MB, time=2.91
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (closed_form) = 0
y[1] (numeric) = 0.3262881546413994210005585157343
absolute error = 0.3262881546413994210005585157343
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (closed_form) = 0
y[1] (numeric) = 0.33368897795092311929237768121479
absolute error = 0.33368897795092311929237768121479
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (closed_form) = 0
y[1] (numeric) = 0.34106078727001403684919195083592
absolute error = 0.34106078727001403684919195083592
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (closed_form) = 0
y[1] (numeric) = 0.34840398736421033472091036429032
absolute error = 0.34840398736421033472091036429032
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=534.0MB, alloc=48.3MB, time=3.16
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (closed_form) = 0
y[1] (numeric) = 0.35571897379774921084260372836471
absolute error = 0.35571897379774921084260372836471
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (closed_form) = 0
y[1] (numeric) = 0.3630061332783896704396894075211
absolute error = 0.3630061332783896704396894075211
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (closed_form) = 0
y[1] (numeric) = 0.37026584398372729127834884380123
absolute error = 0.37026584398372729127834884380123
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=577.5MB, alloc=48.3MB, time=3.41
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (closed_form) = 0
y[1] (numeric) = 0.37749847587030345861847790265091
absolute error = 0.37749847587030345861847790265091
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (closed_form) = 0
y[1] (numeric) = 0.38470439096669844314552648112602
absolute error = 0.38470439096669844314552648112602
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (closed_form) = 0
y[1] (numeric) = 0.39188394365169622392968336902957
absolute error = 0.39188394365169622392968336902957
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (closed_form) = 0
y[1] (numeric) = 0.39903748091851774167885272547513
absolute error = 0.39903748091851774167885272547513
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=621.1MB, alloc=48.3MB, time=3.67
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (closed_form) = 0
y[1] (numeric) = 0.40616534262603711265272902401475
absolute error = 0.40616534262603711265272902401475
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (closed_form) = 0
y[1] (numeric) = 0.41326786173782120429011342893265
absolute error = 0.41326786173782120429011342893265
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (closed_form) = 0
y[1] (numeric) = 0.42034536454976596713362500853832
absolute error = 0.42034536454976596713362500853832
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (closed_form) = 0
y[1] (numeric) = 0.42739817090704224574944309978074
absolute error = 0.42739817090704224574944309978074
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=664.7MB, alloc=48.3MB, time=3.92
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (closed_form) = 0
y[1] (numeric) = 0.43442659441100876413756418111561
absolute error = 0.43442659441100876413756418111561
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (closed_form) = 0
y[1] (numeric) = 0.44143094261669999346055569893982
absolute error = 0.44143094261669999346055569893982
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (closed_form) = 0
y[1] (numeric) = 0.44841151722145112982910334114332
absolute error = 0.44841151722145112982910334114332
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=708.2MB, alloc=48.3MB, time=4.19
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (closed_form) = 0
y[1] (numeric) = 0.45536861424518096877885187187062
absolute error = 0.45536861424518096877885187187062
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (closed_form) = 0
y[1] (numeric) = 0.46230252420281564734680763030096
absolute error = 0.46230252420281564734680763030096
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (closed_form) = 0
y[1] (numeric) = 0.46921353226930166851643676832811
absolute error = 0.46921353226930166851643676832811
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (closed_form) = 0
y[1] (numeric) = 0.47610191843762500213442117793745
absolute error = 0.47610191843762500213442117793745
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=751.7MB, alloc=48.3MB, time=4.44
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (closed_form) = 0
y[1] (numeric) = 0.48296795767022408349477105432107
absolute error = 0.48296795767022408349477105432107
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (closed_form) = 0
y[1] (numeric) = 0.4898119200441579497803251012351
absolute error = 0.4898119200441579497803251012351
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (closed_form) = 0
y[1] (numeric) = 0.49663407089036633752600932666079
absolute error = 0.49663407089036633752600932666079
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=795.2MB, alloc=48.3MB, time=4.70
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (closed_form) = 0
y[1] (numeric) = 0.50343467092733610784543087197496
absolute error = 0.50343467092733610784543087197496
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (closed_form) = 0
y[1] (numeric) = 0.51021397638946768857044603393836
absolute error = 0.51021397638946768857044603393836
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (closed_form) = 0
y[1] (numeric) = 0.51697223915041616097258738449529
absolute error = 0.51697223915041616097258738449529
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (closed_form) = 0
y[1] (numeric) = 0.52370970684166402747679184436507
absolute error = 0.52370970684166402747679184436507
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=838.7MB, alloc=48.3MB, time=4.95
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (closed_form) = 0
y[1] (numeric) = 0.53042662296656644474667419304515
absolute error = 0.53042662296656644474667419304515
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (closed_form) = 0
y[1] (numeric) = 0.53712322701009467592329399404249
absolute error = 0.53712322701009467592329399404249
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (closed_form) = 0
y[1] (numeric) = 0.54379975454448960056349397080523
absolute error = 0.54379975454448960056349397080523
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (closed_form) = 0
y[1] (numeric) = 0.55045643733102422529954404164893
absolute error = 0.55045643733102422529954404164893
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=882.3MB, alloc=48.3MB, time=5.20
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (closed_form) = 0
y[1] (numeric) = 0.55709350341806217606145662618448
absolute error = 0.55709350341806217606145662618448
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (closed_form) = 0
y[1] (numeric) = 0.56371117723558804577865250086771
absolute error = 0.56371117723558804577865250086771
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (closed_form) = 0
y[1] (numeric) = 0.57030967968637514911571145936615
absolute error = 0.57030967968637514911571145936615
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=925.8MB, alloc=48.3MB, time=5.47
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (closed_form) = 0
y[1] (numeric) = 0.57688922823394663392001684696853
absolute error = 0.57688922823394663392001684696853
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (closed_form) = 0
y[1] (numeric) = 0.58345003698747695951507501536852
absolute error = 0.58345003698747695951507501536852
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (closed_form) = 0
y[1] (numeric) = 0.58999231678377242192509504104528
absolute error = 0.58999231678377242192509504104528
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (closed_form) = 0
y[1] (numeric) = 0.59651627526646163750070896413921
absolute error = 0.59651627526646163750070896413921
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=969.4MB, alloc=48.3MB, time=5.72
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (closed_form) = 0
y[1] (numeric) = 0.60302211696251964546220893655648
absolute error = 0.60302211696251964546220893655648
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (closed_form) = 0
y[1] (numeric) = 0.6095100433562425166807270998489
absolute error = 0.6095100433562425166807270998489
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (closed_form) = 0
y[1] (numeric) = 0.61598025296078302415980153061419
absolute error = 0.61598025296078302415980153061419
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=1012.9MB, alloc=48.3MB, time=5.97
x[1] = 0.93
y[1] (closed_form) = 0
y[1] (numeric) = 0.62243294138735200688589792199746
absolute error = 0.62243294138735200688589792199746
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (closed_form) = 0
y[1] (numeric) = 0.62886830141218451255559449049967
absolute error = 0.62886830141218451255559449049967
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (closed_form) = 0
y[1] (numeric) = 0.63528652304136460830011214251275
absolute error = 0.63528652304136460830011214251275
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (closed_form) = 0
y[1] (numeric) = 0.64168779357359787638500415606101
absolute error = 0.64168779357359787638500415606101
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1056.5MB, alloc=48.3MB, time=6.23
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (closed_form) = 0
y[1] (numeric) = 0.64807229766101604054666335907383
absolute error = 0.64807229766101604054666335907383
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (closed_form) = 0
y[1] (numeric) = 0.65444021736809387663770075376955
absolute error = 0.65444021736809387663770075376955
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (closed_form) = 0
y[1] (numeric) = 0.66079173222875452883219734191757
absolute error = 0.66079173222875452883219734191757
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (closed_form) = 0
y[1] (numeric) = 0.66712701930173556161598239374134
absolute error = 0.66712701930173556161598239374134
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1099.9MB, alloc=48.3MB, time=6.48
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (closed_form) = 0
y[1] (numeric) = 0.67344625322428451142593222248022
absolute error = 0.67344625322428451142593222248022
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (closed_form) = 0
y[1] (numeric) = 0.67974960626424934469029887609705
absolute error = 0.67974960626424934469029887609705
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (closed_form) = 0
y[1] (numeric) = 0.68603724837062606694339889516427
absolute error = 0.68603724837062606694339889516427
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1143.5MB, alloc=48.3MB, time=6.73
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (closed_form) = 0
y[1] (numeric) = 0.69230934722262274752219244848878
absolute error = 0.69230934722262274752219244848878
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (closed_form) = 0
y[1] (numeric) = 0.69856606827729641398015299241924
absolute error = 0.69856606827729641398015299241924
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (closed_form) = 0
y[1] (numeric) = 0.70480757481581661857208032284958
absolute error = 0.70480757481581661857208032284958
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (closed_form) = 0
y[1] (numeric) = 0.71103402798840697560749808452099
absolute error = 0.71103402798840697560749808452099
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1186.9MB, alloc=48.3MB, time=7.00
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (closed_form) = 0
y[1] (numeric) = 0.71724558685801360354389777216956
absolute error = 0.71724558685801360354389777216956
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (closed_form) = 0
y[1] (numeric) = 0.72344240844274717050315162232319
absolute error = 0.72344240844274717050315162232319
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (closed_form) = 0
y[1] (numeric) = 0.7296246477571431282008067788031
absolute error = 0.7296246477571431282008067788031
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (closed_form) = 0
y[1] (numeric) = 0.73579245785228271942907165027594
absolute error = 0.73579245785228271942907165027594
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1230.3MB, alloc=48.3MB, time=7.25
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (closed_form) = 0
y[1] (numeric) = 0.74194598985481545112709955809109
absolute error = 0.74194598985481545112709955809109
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (closed_form) = 0
y[1] (numeric) = 0.74808539300492193210663240128165
absolute error = 0.74808539300492193210663240128165
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (closed_form) = 0
y[1] (numeric) = 0.754210814693254275540349880377
absolute error = 0.754210814693254275540349880377
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1273.8MB, alloc=48.3MB, time=7.50
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (closed_form) = 0
y[1] (numeric) = 0.76032240049688965565441826386829
absolute error = 0.76032240049688965565441826386829
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (closed_form) = 0
y[1] (numeric) = 0.76642029421433108037949149412509
absolute error = 0.76642029421433108037949149412509
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (closed_form) = 0
y[1] (numeric) = 0.7725046378995879920529054740128
absolute error = 0.7725046378995879920529054740128
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (closed_form) = 0
y[1] (numeric) = 0.77857557189536793201176438021567
absolute error = 0.77857557189536793201176438021567
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1317.3MB, alloc=48.3MB, time=7.77
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (closed_form) = 0
y[1] (numeric) = 0.78463323486540919776499480981012
absolute error = 0.78463323486540919776499480981012
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (closed_form) = 0
y[1] (numeric) = 0.7906777638259831793621065562498
absolute error = 0.7906777638259831793621065562498
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (closed_form) = 0
y[1] (numeric) = 0.79670929417659388083277242160507
absolute error = 0.79670929417659388083277242160507
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1360.7MB, alloc=48.3MB, time=8.02
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (closed_form) = 0
y[1] (numeric) = 0.80272795972990100964580025543167
absolute error = 0.80272795972990100964580025543167
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (closed_form) = 0
y[1] (numeric) = 0.80873389274089194874793880786759
absolute error = 0.80873389274089194874793880786759
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (closed_form) = 0
y[1] (numeric) = 0.81472722393532690882294654358859
absolute error = 0.81472722393532690882294654358859
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (closed_form) = 0
y[1] (numeric) = 0.82070808253748059008633595924704
absolute error = 0.82070808253748059008633595924704
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1404.2MB, alloc=48.3MB, time=8.27
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (closed_form) = 0
y[1] (numeric) = 0.82667659629720276051021160562747
absolute error = 0.82667659629720276051021160562747
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (closed_form) = 0
y[1] (numeric) = 0.83263289151631927833391416752438
absolute error = 0.83263289151631927833391416752438
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (closed_form) = 0
y[1] (numeric) = 0.83857709307439424869537184711678
absolute error = 0.83857709307439424869537184711678
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (closed_form) = 0
y[1] (numeric) = 0.84450932445387320499711419013558
absolute error = 0.84450932445387320499711419013558
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1447.6MB, alloc=48.3MB, time=8.53
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (closed_form) = 0
y[1] (numeric) = 0.85042970776462644311802606452304
absolute error = 0.85042970776462644311802606452304
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (closed_form) = 0
y[1] (numeric) = 0.85633836376791090884219148829683
absolute error = 0.85633836376791090884219148829683
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (closed_form) = 0
y[1] (numeric) = 0.86223541189976834406290942580463
absolute error = 0.86223541189976834406290942580463
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1491.1MB, alloc=48.3MB, time=8.78
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (closed_form) = 0
y[1] (numeric) = 0.86812097029387673370670179200259
absolute error = 0.86812097029387673370670179200259
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (closed_form) = 0
y[1] (numeric) = 0.87399515580387146128525840796888
absolute error = 0.87399515580387146128525840796888
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (closed_form) = 0
y[1] (numeric) = 0.87985808402515197499514027793604
absolute error = 0.87985808402515197499514027793604
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (closed_form) = 0
y[1] (numeric) = 0.88570986931618918690769574512857
absolute error = 0.88570986931618918690769574512857
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1534.6MB, alloc=48.3MB, time=9.03
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (closed_form) = 0
y[1] (numeric) = 0.89155062481934827367079407143713
absolute error = 0.89155062481934827367079407143713
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (closed_form) = 0
y[1] (numeric) = 0.89738046248124101700370738981505
absolute error = 0.89738046248124101700370738981505
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (closed_form) = 0
y[1] (numeric) = 0.90319949307262131490407001800436
absolute error = 0.90319949307262131490407001800436
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1578.0MB, alloc=48.3MB, time=9.28
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (closed_form) = 0
y[1] (numeric) = 0.9090078262078370087671426141204
absolute error = 0.9090078262078370087671426141204
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (closed_form) = 0
y[1] (numeric) = 0.91480557036385070647260150496957
absolute error = 0.91480557036385070647260150496957
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (closed_form) = 0
y[1] (numeric) = 0.92059283289884183591285885008576
absolute error = 0.92059283289884183591285885008576
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (closed_form) = 0
y[1] (numeric) = 0.92636972007040173646592252833268
absolute error = 0.92636972007040173646592252833268
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1621.5MB, alloc=48.3MB, time=9.55
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (closed_form) = 0
y[1] (numeric) = 0.93213633705333318665426374500054
absolute error = 0.93213633705333318665426374500054
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (closed_form) = 0
y[1] (numeric) = 0.93789278795706537382785355239235
absolute error = 0.93789278795706537382785355239235
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (closed_form) = 0
y[1] (numeric) = 0.94363917584269493535972681433897
absolute error = 0.94363917584269493535972681433897
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=1664.9MB, alloc=48.3MB, time=9.80
x[1] = 1.47
y[1] (closed_form) = 0
y[1] (numeric) = 0.94937560273966333978505447172224
absolute error = 0.94937560273966333978505447172224
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (closed_form) = 0
y[1] (numeric) = 0.95510216966208052982967469522075
absolute error = 0.95510216966208052982967469522075
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (closed_form) = 0
y[1] (numeric) = 0.96081897662470441667980308053243
absolute error = 0.96081897662470441667980308053243
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (closed_form) = 0
y[1] (numeric) = 0.96652612265858549549588701290979
absolute error = 0.96652612265858549549588701290979
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1708.3MB, alloc=48.3MB, time=10.05
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (closed_form) = 0
y[1] (numeric) = 0.97222370582638554545903413582323
absolute error = 0.97222370582638554545903413582323
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (closed_form) = 0
y[1] (numeric) = 0.97791182323737908297893014890194
absolute error = 0.97791182323737908297893014890194
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (closed_form) = 0
y[1] (numeric) = 0.98359057106214595353864254460227
absolute error = 0.98359057106214595353864254460227
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (closed_form) = 0
y[1] (numeric) = 0.98926004454696317548357572701449
absolute error = 0.98926004454696317548357572701449
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1751.8MB, alloc=48.3MB, time=10.31
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (closed_form) = 0
y[1] (numeric) = 0.99492033802790388738526048271816
absolute error = 0.99492033802790388738526048271816
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (closed_form) = 0
y[1] (numeric) = 1.0005715449446509989570176371478
absolute error = 1.0005715449446509989570176371478
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (closed_form) = 0
y[1] (numeric) = 1.0062137578540329034230094806893
absolute error = 1.0062137578540329034230094806893
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1795.2MB, alloc=48.3MB, time=10.56
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (closed_form) = 0
y[1] (numeric) = 1.0118470684432883763223963154256
absolute error = 1.0118470684432883763223963154256
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (closed_form) = 0
y[1] (numeric) = 1.017471567543067561565031499739
absolute error = 1.017471567543067561565031499739
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (closed_form) = 0
y[1] (numeric) = 1.0230873451401757297631205799871
absolute error = 1.0230873451401757297631205799871
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (closed_form) = 0
y[1] (numeric) = 1.0286944903900662860821703062909
absolute error = 1.0286944903900662860821703062909
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1838.6MB, alloc=48.3MB, time=10.81
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (closed_form) = 0
y[1] (numeric) = 1.0342930916290893047398160653665
absolute error = 1.0342930916290893047398160653665
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (closed_form) = 0
y[1] (numeric) = 1.0398832363865016745050376273834
absolute error = 1.0398832363865016745050376273834
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (closed_form) = 0
y[1] (numeric) = 1.045465011396244753801069326934
absolute error = 1.045465011396244753801069326934
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=1882.0MB, alloc=48.3MB, time=11.06
x[1] = 1.65
y[1] (closed_form) = 0
y[1] (numeric) = 1.0510385026084952549962525438625
absolute error = 1.0510385026084952549962525438625
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (closed_form) = 0
y[1] (numeric) = 1.056603795200994904895677064495
absolute error = 1.056603795200994904895677064495
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (closed_form) = 0
y[1] (numeric) = 1.0621609735901642620537007907607
absolute error = 1.0621609735901642620537007907607
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (closed_form) = 0
y[1] (numeric) = 1.0677101214420059110570676993095
absolute error = 1.0677101214420059110570676993095
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1925.5MB, alloc=48.3MB, time=11.33
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (closed_form) = 0
y[1] (numeric) = 1.073251321682802099136184386701
absolute error = 1.073251321682802099136184386701
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (closed_form) = 0
y[1] (numeric) = 1.0787846565096117311154301430844
absolute error = 1.0787846565096117311154301430844
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (closed_form) = 0
y[1] (numeric) = 1.084310207400571494590270003098
absolute error = 1.084310207400571494590270003098
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (closed_form) = 0
y[1] (numeric) = 1.0898280551250057481077965568099
absolute error = 1.0898280551250057481077965568099
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1968.8MB, alloc=48.3MB, time=11.58
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (closed_form) = 0
y[1] (numeric) = 1.09533827975334967082626984114
absolute error = 1.09533827975334967082626984114
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (closed_form) = 0
y[1] (numeric) = 1.1008409606668900424456219881794
absolute error = 1.1008409606668900424456219881794
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (closed_form) = 0
y[1] (numeric) = 1.1063361765673278969508787528162
absolute error = 1.1063361765673278969508787528162
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2012.2MB, alloc=48.3MB, time=11.84
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (closed_form) = 0
y[1] (numeric) = 1.1118240054861671727184787640436
absolute error = 1.1118240054861671727184787640436
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (closed_form) = 0
y[1] (numeric) = 1.1173045247939333646338978746223
absolute error = 1.1173045247939333646338978746223
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (closed_form) = 0
y[1] (numeric) = 1.1227778112092260708976662541801
absolute error = 1.1227778112092260708976662541801
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (closed_form) = 0
y[1] (numeric) = 1.1282439408076092180027814378124
absolute error = 1.1282439408076092180027814378124
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2055.5MB, alloc=48.3MB, time=12.09
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (closed_form) = 0
y[1] (numeric) = 1.1337029890303426418034236312575
absolute error = 1.1337029890303426418034236312575
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (closed_form) = 0
y[1] (numeric) = 1.139155030692958600522957680036
absolute error = 1.139155030692958600522957680036
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (closed_form) = 0
y[1] (numeric) = 1.1446001399936866968347649757009
absolute error = 1.1446001399936866968347649757009
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2098.8MB, alloc=48.3MB, time=12.34
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (closed_form) = 0
y[1] (numeric) = 1.1500383905217305906646124377047
absolute error = 1.1500383905217305906646124377047
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (closed_form) = 0
y[1] (numeric) = 1.1554698552653997919856938066815
absolute error = 1.1554698552653997919856938066815
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (closed_form) = 0
y[1] (numeric) = 1.1608946066200997334900968122696
absolute error = 1.1608946066200997334900968122696
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (closed_form) = 0
y[1] (numeric) = 1.1663127163961832365111972508476
absolute error = 1.1663127163961832365111972508476
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2142.1MB, alloc=48.3MB, time=12.61
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (closed_form) = 0
y[1] (numeric) = 1.1717242558266663998330691419372
absolute error = 1.1717242558266663998330691419372
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (closed_form) = 0
y[1] (numeric) = 1.1771292955748118599526854719413
absolute error = 1.1771292955748118599526854719413
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (closed_form) = 0
y[1] (numeric) = 1.1825279057415822928600525861099
absolute error = 1.1825279057415822928600525861099
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (closed_form) = 0
y[1] (numeric) = 1.187920155872966951376184261264
absolute error = 1.187920155872966951376184261264
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2185.6MB, alloc=48.3MB, time=12.86
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (closed_form) = 0
y[1] (numeric) = 1.193306114967183958448621692364
absolute error = 1.193306114967183958448621692364
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (closed_form) = 0
y[1] (numeric) = 1.198685851481761005462433919017
absolute error = 1.198685851481761005462433919017
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.93
y[1] (closed_form) = 0
y[1] (numeric) = 1.20405943334049703549825445197
absolute error = 1.20405943334049703549825445197
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2229.1MB, alloc=48.3MB, time=13.11
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (closed_form) = 0
y[1] (numeric) = 1.2094269279403074244782977417689
absolute error = 1.2094269279403074244782977417689
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (closed_form) = 0
y[1] (numeric) = 1.2147884021579551082100795417549
absolute error = 1.2147884021579551082100795417549
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (closed_form) = 0
y[1] (numeric) = 1.220143922356670040392467488295
absolute error = 1.220143922356670040392467488295
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (closed_form) = 0
y[1] (numeric) = 1.2254935543926593056194039431709
absolute error = 1.2254935543926593056194039431709
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2272.5MB, alloc=48.3MB, time=13.36
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (closed_form) = 0
y[1] (numeric) = 1.2308373636215101522356920755224
absolute error = 1.2308373636215101522356920755224
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (closed_form) = 0
y[1] (numeric) = 1.2361754149044881525018388572195
absolute error = 1.2361754149044881525018388572195
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (closed_form) = 0
y[1] (numeric) = 1.2415077726147326418489054262829
absolute error = 1.2415077726147326418489054262829
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2315.9MB, alloc=48.3MB, time=13.63
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (closed_form) = 0
y[1] (numeric) = 1.2468345006433515349898911971793
absolute error = 1.2468345006433515349898911971793
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (closed_form) = 0
y[1] (numeric) = 1.2521556624054175642439936093079
absolute error = 1.2521556624054175642439936093079
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (closed_form) = 0
y[1] (numeric) = 1.2574713208458679345690123502852
absolute error = 1.2574713208458679345690123502852
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (closed_form) = 0
y[1] (numeric) = 1.2627815384453093404322296061378
absolute error = 1.2627815384453093404322296061378
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2359.3MB, alloc=48.3MB, time=13.88
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (closed_form) = 0
y[1] (numeric) = 1.2680863772257302417303791069138
absolute error = 1.2680863772257302417303791069138
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (closed_form) = 0
y[1] (numeric) = 1.2733858987561222494458680291176
absolute error = 1.2733858987561222494458680291176
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (closed_form) = 0
y[1] (numeric) = 1.278680164158012426552172368011
absolute error = 1.278680164158012426552172368011
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=2402.7MB, alloc=48.3MB, time=14.13
x[1] = 2.08
y[1] (closed_form) = 0
y[1] (numeric) = 1.2839692341109082658110258367132
absolute error = 1.2839692341109082658110258367132
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (closed_form) = 0
y[1] (numeric) = 1.2892531688576570634941274831227
absolute error = 1.2892531688576570634941274831227
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (closed_form) = 0
y[1] (numeric) = 1.2945320282097213666707183820752
absolute error = 1.2945320282097213666707183820752
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (closed_form) = 0
y[1] (numeric) = 1.2998058715523721314892187008499
absolute error = 1.2998058715523721314892187008499
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2446.1MB, alloc=48.3MB, time=14.38
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (closed_form) = 0
y[1] (numeric) = 1.3050747578498011908073834449286
absolute error = 1.3050747578498011908073834449286
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (closed_form) = 0
y[1] (numeric) = 1.3103387456501545915537893917712
absolute error = 1.3103387456501545915537893917712
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (closed_form) = 0
y[1] (numeric) = 1.3155978930904883252979583120767
absolute error = 1.3155978930904883252979583120767
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (closed_form) = 0
y[1] (numeric) = 1.3208522579016479396324358938517
absolute error = 1.3208522579016479396324358938517
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2489.4MB, alloc=48.3MB, time=14.64
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (closed_form) = 0
y[1] (numeric) = 1.3261018974130734830943420240461
absolute error = 1.3261018974130734830943420240461
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (closed_form) = 0
y[1] (numeric) = 1.3313468685575312024441705800654
absolute error = 1.3313468685575312024441705800654
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (closed_form) = 0
y[1] (numeric) = 1.3365872278757733781450037868618
absolute error = 1.3365872278757733781450037868618
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2532.7MB, alloc=48.3MB, time=14.89
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (closed_form) = 0
y[1] (numeric) = 1.341823031521127651816001432691
absolute error = 1.341823031521127651816001432691
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (closed_form) = 0
y[1] (numeric) = 1.3470543352640171682412926583803
absolute error = 1.3470543352640171682412926583803
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (closed_form) = 0
y[1] (numeric) = 1.3522811944964128241715376224598
absolute error = 1.3522811944964128241715376224598
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (closed_form) = 0
y[1] (numeric) = 1.3575036642362188866337323836949
absolute error = 1.3575036642362188866337323836949
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2576.1MB, alloc=48.3MB, time=15.14
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (closed_form) = 0
y[1] (numeric) = 1.3627217991315932147395514656717
absolute error = 1.3627217991315932147395514656717
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (closed_form) = 0
y[1] (numeric) = 1.3679356534652032910288235722634
absolute error = 1.3679356534652032910288235722634
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (closed_form) = 0
y[1] (numeric) = 1.3731452811584192411786612787765
absolute error = 1.3731452811584192411786612787765
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2619.5MB, alloc=48.3MB, time=15.39
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (closed_form) = 0
y[1] (numeric) = 1.3783507357754449944272044927474
absolute error = 1.3783507357754449944272044927474
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (closed_form) = 0
y[1] (numeric) = 1.3835520705273887112815907602295
absolute error = 1.3835520705273887112815907602295
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (closed_form) = 0
y[1] (numeric) = 1.3887493382762735799811133302135
absolute error = 1.3887493382762735799811133302135
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (closed_form) = 0
y[1] (numeric) = 1.3939425915389900587477995581896
absolute error = 1.3939425915389900587477995581896
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2662.9MB, alloc=48.3MB, time=15.66
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (closed_form) = 0
y[1] (numeric) = 1.399131882491190617057786853712
absolute error = 1.399131882491190617057786853712
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (closed_form) = 0
y[1] (numeric) = 1.4043172629711280059885319986976
absolute error = 1.4043172629711280059885319986976
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (closed_form) = 0
y[1] (numeric) = 1.4094987844834380651203685144185
absolute error = 1.4094987844834380651203685144185
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=2706.3MB, alloc=48.3MB, time=15.91
x[1] = 2.33
y[1] (closed_form) = 0
y[1] (numeric) = 1.4146764982028680514781716688089
absolute error = 1.4146764982028680514781716688089
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (closed_form) = 0
y[1] (numeric) = 1.4198504549779514545724626283979
absolute error = 1.4198504549779514545724626283979
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (closed_form) = 0
y[1] (numeric) = 1.4250207053346302407223347512275
absolute error = 1.4250207053346302407223347512275
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (closed_form) = 0
y[1] (numeric) = 1.4301872994798254494988378427295
absolute error = 1.4301872994798254494988378427295
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2749.7MB, alloc=48.3MB, time=16.16
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (closed_form) = 0
y[1] (numeric) = 1.4353502873049570453011797582308
absolute error = 1.4353502873049570453011797582308
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (closed_form) = 0
y[1] (numeric) = 1.4405097183894139077540954595558
absolute error = 1.4405097183894139077540954595558
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (closed_form) = 0
y[1] (numeric) = 1.4456656420039748257782952033016
absolute error = 1.4456656420039748257782952033016
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (closed_form) = 0
y[1] (numeric) = 1.4508181071141813418228279520054
absolute error = 1.4508181071141813418228279520054
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2793.1MB, alloc=48.3MB, time=16.41
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (closed_form) = 0
y[1] (numeric) = 1.4559671623836632748447455046576
absolute error = 1.4559671623836632748447455046576
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (closed_form) = 0
y[1] (numeric) = 1.4611128561774177331643421239842
absolute error = 1.4611128561774177331643421239842
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (closed_form) = 0
y[1] (numeric) = 1.4662552365650424113006245138069
absolute error = 1.4662552365650424113006245138069
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2836.4MB, alloc=48.3MB, time=16.67
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (closed_form) = 0
y[1] (numeric) = 1.4713943513239239482891088055366
absolute error = 1.4713943513239239482891088055366
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (closed_form) = 0
y[1] (numeric) = 1.4765302479423821087905203310246
absolute error = 1.4765302479423821087905203310246
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (closed_form) = 0
y[1] (numeric) = 1.4816629736227705325028538738309
absolute error = 1.4816629736227705325028538738309
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (closed_form) = 0
y[1] (numeric) = 1.4867925752845347819792780370707
absolute error = 1.4867925752845347819792780370707
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2879.9MB, alloc=48.3MB, time=16.92
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (closed_form) = 0
y[1] (numeric) = 1.4919190995672284039196407452356
absolute error = 1.4919190995672284039196407452356
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (closed_form) = 0
y[1] (numeric) = 1.497042592833487704333306239201
absolute error = 1.497042592833487704333306239201
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (closed_form) = 0
y[1] (numeric) = 1.502163101171965923655516364721
absolute error = 1.502163101171965923655516364721
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2923.3MB, alloc=48.3MB, time=17.17
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (closed_form) = 0
y[1] (numeric) = 1.5072806704002274839285342156133
absolute error = 1.5072806704002274839285342156133
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (closed_form) = 0
y[1] (numeric) = 1.5123953460676029665229230296289
absolute error = 1.5123953460676029665229230296289
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (closed_form) = 0
y[1] (numeric) = 1.517507173458005465564166345662
absolute error = 1.517507173458005465564166345662
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (closed_form) = 0
y[1] (numeric) = 1.5226161975927089492364667967157
absolute error = 1.5226161975927089492364667967157
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2966.7MB, alloc=48.3MB, time=17.44
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (closed_form) = 0
y[1] (numeric) = 1.5277224632330892484502715560453
absolute error = 1.5277224632330892484502715560453
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (closed_form) = 0
y[1] (numeric) = 1.5328260148833282799744345933434
absolute error = 1.5328260148833282799744345933434
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (closed_form) = 0
y[1] (numeric) = 1.5379268967930820990397734876319
absolute error = 1.5379268967930820990397734876319
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (closed_form) = 0
y[1] (numeric) = 1.5430251529601133646101981752085
absolute error = 1.5430251529601133646101981752085
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3010.0MB, alloc=48.3MB, time=17.69
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (closed_form) = 0
y[1] (numeric) = 1.548120827132888788982911166545
absolute error = 1.548120827132888788982911166545
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (closed_form) = 0
y[1] (numeric) = 1.5532139628131421321129694057072
absolute error = 1.5532139628131421321129694057072
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (closed_form) = 0
y[1] (numeric) = 1.5583046032584032900525504171179
absolute error = 1.5583046032584032900525504171179
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3053.3MB, alloc=48.3MB, time=17.94
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (closed_form) = 0
y[1] (numeric) = 1.5633927914844940161445926384532
absolute error = 1.5633927914844940161445926384532
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (closed_form) = 0
y[1] (numeric) = 1.5684785702679908031073069412942
absolute error = 1.5684785702679908031073069412942
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (closed_form) = 0
y[1] (numeric) = 1.5735619821486554438838132677442
absolute error = 1.5735619821486554438838132677442
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (closed_form) = 0
y[1] (numeric) = 1.5786430694318337791034710100219
absolute error = 1.5786430694318337791034710100219
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3096.8MB, alloc=48.3MB, time=18.19
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (closed_form) = 0
y[1] (numeric) = 1.5837218741908231292021634773661
absolute error = 1.5837218741908231292021634773661
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (closed_form) = 0
y[1] (numeric) = 1.5887984382692088996718696481165
absolute error = 1.5887984382692088996718696481165
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (closed_form) = 0
y[1] (numeric) = 1.5938728032831708385494931959151
absolute error = 1.5938728032831708385494931959151
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3140.1MB, alloc=48.3MB, time=18.45
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (closed_form) = 0
y[1] (numeric) = 1.598945010623759416105475034068
absolute error = 1.598945010623759416105475034068
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (closed_form) = 0
y[1] (numeric) = 1.6040151014591427877487138540634
absolute error = 1.6040151014591427877487138540634
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (closed_form) = 0
y[1] (numeric) = 1.6090831167368247924204433145705
absolute error = 1.6090831167368247924204433145705
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (closed_form) = 0
y[1] (numeric) = 1.614149097185834430200804770735
absolute error = 1.614149097185834430200804770735
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3183.4MB, alloc=48.3MB, time=18.70
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (closed_form) = 0
y[1] (numeric) = 1.6192130833188872544929018273865
absolute error = 1.6192130833188872544929018273865
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (closed_form) = 0
y[1] (numeric) = 1.6242751154345191059752647188557
absolute error = 1.6242751154345191059752647188557
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (closed_form) = 0
y[1] (numeric) = 1.6293352336191926075201670200314
absolute error = 1.6293352336191926075201670200314
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3226.8MB, alloc=48.3MB, time=18.95
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (closed_form) = 0
y[1] (numeric) = 1.6343934777493768314575396348209
absolute error = 1.6343934777493768314575396348209
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (closed_form) = 0
y[1] (numeric) = 1.639449887493600542917864817193
absolute error = 1.639449887493600542917864817193
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (closed_form) = 0
y[1] (numeric) = 1.6445045023144794155080815860387
absolute error = 1.6445045023144794155080815860387
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (closed_form) = 0
y[1] (numeric) = 1.6495573614707176082579926124209
absolute error = 1.6495573614707176082579926124209
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3270.2MB, alloc=48.3MB, time=19.20
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (closed_form) = 0
y[1] (numeric) = 1.654608504019084085616850714901
absolute error = 1.654608504019084085616850714901
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (closed_form) = 0
y[1] (numeric) = 1.6596579688163640552767558085282
absolute error = 1.6596579688163640552767558085282
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (closed_form) = 0
y[1] (numeric) = 1.664705794521285891747358218894
absolute error = 1.664705794521285891747358218894
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (closed_form) = 0
y[1] (numeric) = 1.6697520195964239069013982233251
absolute error = 1.6697520195964239069013982233251
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3313.6MB, alloc=48.3MB, time=19.45
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (closed_form) = 0
y[1] (numeric) = 1.6747966823100773221491764322974
absolute error = 1.6747966823100773221491764322974
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (closed_form) = 0
y[1] (numeric) = 1.679839820738125790478609158449
absolute error = 1.679839820738125790478609158449
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (closed_form) = 0
y[1] (numeric) = 1.6848814727658618103126400852256
absolute error = 1.6848814727658618103126400852256
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3356.8MB, alloc=48.3MB, time=19.72
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (closed_form) = 0
y[1] (numeric) = 1.689921676089800366984112961157
absolute error = 1.689921676089800366984112961157
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (closed_form) = 0
y[1] (numeric) = 1.6949604682194661316065111147558
absolute error = 1.6949604682194661316065111147558
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (closed_form) = 0
y[1] (numeric) = 1.6999978864791585412240796191663
absolute error = 1.6999978864791585412240796191663
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (closed_form) = 0
y[1] (numeric) = 1.7050339680096950783536933663785
absolute error = 1.7050339680096950783536933663785
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3400.3MB, alloc=48.3MB, time=19.97
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (closed_form) = 0
y[1] (numeric) = 1.7100687497701330623804320027271
absolute error = 1.7100687497701330623804320027271
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (closed_form) = 0
y[1] (numeric) = 1.7151022685394702597362653323933
absolute error = 1.7151022685394702597362653323933
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (closed_form) = 0
y[1] (numeric) = 1.7201345609183246143737144447955
absolute error = 1.7201345609183246143737144447955
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3443.6MB, alloc=48.3MB, time=20.22
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (closed_form) = 0
y[1] (numeric) = 1.7251656633305933947410854026205
absolute error = 1.7251656633305933947410854026205
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (closed_form) = 0
y[1] (numeric) = 1.7301956120250920482701993426985
absolute error = 1.7301956120250920482701993426985
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (closed_form) = 0
y[1] (numeric) = 1.7352244430771730492988630980685
absolute error = 1.7352244430771730492988630980685
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (closed_form) = 0
y[1] (numeric) = 1.7402521923903250213661058694359
absolute error = 1.7402521923903250213661058694359
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3486.9MB, alloc=48.3MB, time=20.48
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (closed_form) = 0
y[1] (numeric) = 1.7452788956977524099359859845826
absolute error = 1.7452788956977524099359859845826
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (closed_form) = 0
y[1] (numeric) = 1.7503045885639359768231492730139
absolute error = 1.7503045885639359768231492730139
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (closed_form) = 0
y[1] (numeric) = 1.7553293063861743829079629242732
absolute error = 1.7553293063861743829079629242732
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=3530.2MB, alloc=48.3MB, time=20.73
x[1] = 3.01
y[1] (closed_form) = 0
y[1] (numeric) = 1.7603530843961071211386838427635
absolute error = 1.7603530843961071211386838427635
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (closed_form) = 0
y[1] (numeric) = 1.7653759576612190573205366407639
absolute error = 1.7653759576612190573205366407639
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (closed_form) = 0
y[1] (numeric) = 1.770397961086326831784620150455
absolute error = 1.770397961086326831784620150455
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (closed_form) = 0
y[1] (numeric) = 1.7754191294150473707111360285485
absolute error = 1.7754191294150473707111360285485
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3573.6MB, alloc=48.3MB, time=20.98
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (closed_form) = 0
y[1] (numeric) = 1.7804394972312487516494970637988
absolute error = 1.7804394972312487516494970637988
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (closed_form) = 0
y[1] (numeric) = 1.7854590989604836636304379990931
absolute error = 1.7854590989604836636304379990931
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (closed_form) = 0
y[1] (numeric) = 1.790477968871405698200381733689
absolute error = 1.790477968871405698200381733689
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (closed_form) = 0
y[1] (numeric) = 1.7954961410771687037241227188665
absolute error = 1.7954961410771687037241227188665
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3616.9MB, alloc=48.3MB, time=21.23
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (closed_form) = 0
y[1] (numeric) = 1.8005136495368094313965401325785
absolute error = 1.8005136495368094313965401325785
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (closed_form) = 0
y[1] (numeric) = 1.8055305280566136975757564185035
absolute error = 1.8055305280566136975757564185035
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (closed_form) = 0
y[1] (numeric) = 1.8105468102914662832971685054926
absolute error = 1.8105468102914662832971685054926
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3660.2MB, alloc=48.3MB, time=21.50
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (closed_form) = 0
y[1] (numeric) = 1.8155625297461847881484007603871
absolute error = 1.8155625297461847881484007603871
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (closed_form) = 0
y[1] (numeric) = 1.8205777197768376520778052329188
absolute error = 1.8205777197768376520778052329188
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (closed_form) = 0
y[1] (numeric) = 1.8255924135920465551720530301597
absolute error = 1.8255924135920465551720530301597
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (closed_form) = 0
y[1] (numeric) = 1.8306066442542734019700487504861
absolute error = 1.8306066442542734019700487504861
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3703.5MB, alloc=48.3MB, time=21.75
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (closed_form) = 0
y[1] (numeric) = 1.8356204446810920934793257230965
absolute error = 1.8356204446810920934793257230965
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (closed_form) = 0
y[1] (numeric) = 1.8406338476464452867257499870146
absolute error = 1.8406338476464452867257499870146
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (closed_form) = 0
y[1] (numeric) = 1.8456468857818863383963197947014
absolute error = 1.8456468857818863383963197947014
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3746.9MB, alloc=48.3MB, time=22.00
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (closed_form) = 0
y[1] (numeric) = 1.8506595915778066259266758136184
absolute error = 1.8506595915778066259266758136184
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (closed_form) = 0
y[1] (numeric) = 1.8556719973846484362382515524279
absolute error = 1.8556719973846484362382515524279
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (closed_form) = 0
y[1] (numeric) = 1.8606841354141036092434448434468
absolute error = 1.8606841354141036092434448434468
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (closed_form) = 0
y[1] (numeric) = 1.8656960377402981202094640492757
absolute error = 1.8656960377402981202094640492757
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3790.2MB, alloc=48.3MB, time=22.25
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (closed_form) = 0
y[1] (numeric) = 1.870707736300962782101314266893
absolute error = 1.870707736300962782101314266893
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (closed_form) = 0
y[1] (numeric) = 1.8757192628985902461104881661371
absolute error = 1.8757192628985902461104881661371
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (closed_form) = 0
y[1] (numeric) = 1.8807306492015784757170930832783
absolute error = 1.8807306492015784757170930832783
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=3833.5MB, alloc=48.3MB, time=22.52
x[1] = 3.26
y[1] (closed_form) = 0
y[1] (numeric) = 1.8857419267453608668281904771727
absolute error = 1.8857419267453608668281904771727
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (closed_form) = 0
y[1] (numeric) = 1.8907531269335231837828849232351
absolute error = 1.8907531269335231837828849232351
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (closed_form) = 0
y[1] (numeric) = 1.8957642810389074783140449415168
absolute error = 1.8957642810389074783140449415168
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (closed_form) = 0
y[1] (numeric) = 1.9007754202047031559063622198284
absolute error = 1.9007754202047031559063622198284
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3876.9MB, alloc=48.3MB, time=22.76
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (closed_form) = 0
y[1] (numeric) = 1.9057865754455253513896811564356
absolute error = 1.9057865754455253513896811564356
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (closed_form) = 0
y[1] (numeric) = 1.9107977776484807730541051994045
absolute error = 1.9107977776484807730541051994045
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (closed_form) = 0
y[1] (numeric) = 1.9158090575742211720682837176653
absolute error = 1.9158090575742211720682837176653
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (closed_form) = 0
y[1] (numeric) = 1.9208204458579845915235013580718
absolute error = 1.9208204458579845915235013580718
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3920.3MB, alloc=48.3MB, time=23.02
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (closed_form) = 0
y[1] (numeric) = 1.925831973010624547012753351697
absolute error = 1.925831973010624547012753351697
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (closed_form) = 0
y[1] (numeric) = 1.9308436694196272882849407858686
absolute error = 1.9308436694196272882849407858686
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (closed_form) = 0
y[1] (numeric) = 1.9358555653501172891887280091005
absolute error = 1.9358555653501172891887280091005
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3963.6MB, alloc=48.3MB, time=23.27
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (closed_form) = 0
y[1] (numeric) = 1.9408676909458511108375608267485
absolute error = 1.9408676909458511108375608267485
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (closed_form) = 0
y[1] (numeric) = 1.945880076230199780685961317215
absolute error = 1.945880076230199780685961317215
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (closed_form) = 0
y[1] (numeric) = 1.9508927511071198280066263181727
absolute error = 1.9508927511071198280066263181727
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (closed_form) = 0
y[1] (numeric) = 1.9559057453621131140972157342908
absolute error = 1.9559057453621131140972157342908
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4006.9MB, alloc=48.3MB, time=23.53
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (closed_form) = 0
y[1] (numeric) = 1.9609190886631755934241975649092
absolute error = 1.9609190886631755934241975649092
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (closed_form) = 0
y[1] (numeric) = 1.9659328105617351398279121079057
absolute error = 1.9659328105617351398279121079057
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (closed_form) = 0
y[1] (numeric) = 1.9709469404935785698673402243528
absolute error = 1.9709469404935785698673402243528
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4050.2MB, alloc=48.3MB, time=23.78
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (closed_form) = 0
y[1] (numeric) = 1.9759615077797679933741403064439
absolute error = 1.9759615077797679933741403064439
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (closed_form) = 0
y[1] (numeric) = 1.9809765416275466193126040565144
absolute error = 1.9809765416275466193126040565144
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (closed_form) = 0
y[1] (numeric) = 1.9859920711312341431045381882149
absolute error = 1.9859920711312341431045381882149
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (closed_form) = 0
y[1] (numeric) = 1.9910081252731118396749905319179
absolute error = 1.9910081252731118396749905319179
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4093.5MB, alloc=48.3MB, time=24.03
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (closed_form) = 0
y[1] (numeric) = 1.9960247329242974846055041545925
absolute error = 1.9960247329242974846055041545925
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (closed_form) = 0
y[1] (numeric) = 2.0010419228456102239455175110104
absolute error = 2.0010419228456102239455175110104
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (closed_form) = 0
y[1] (numeric) = 2.0060597236884255114289635663194
absolute error = 2.0060597236884255114289635663194
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=4136.8MB, alloc=48.3MB, time=24.30
x[1] = 3.51
y[1] (closed_form) = 0
y[1] (numeric) = 2.0110781639955202300714028211206
absolute error = 2.0110781639955202300714028211206
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (closed_form) = 0
y[1] (numeric) = 2.0160972722019081133825157018866
absolute error = 2.0160972722019081133825157018866
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (closed_form) = 0
y[1] (numeric) = 2.0211170766356655797188548649251
absolute error = 2.0211170766356655797188548649251
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (closed_form) = 0
y[1] (numeric) = 2.0261376055187480916218077844006
absolute error = 2.0261376055187480916218077844006
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4180.1MB, alloc=48.3MB, time=24.55
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (closed_form) = 0
y[1] (numeric) = 2.0311588869677971503351485479334
absolute error = 2.0311588869677971503351485479334
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (closed_form) = 0
y[1] (numeric) = 2.0361809489949380340747825215172
absolute error = 2.0361809489949380340747825215172
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (closed_form) = 0
y[1] (numeric) = 2.0412038195085683870297390444224
absolute error = 2.0412038195085683870297390444224
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (closed_form) = 0
y[1] (numeric) = 2.0462275263141377645075889403
absolute error = 2.0462275263141377645075889403
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4223.4MB, alloc=48.3MB, time=24.80
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (closed_form) = 0
y[1] (numeric) = 2.0512520971149182380987112181645
absolute error = 2.0512520971149182380987112181645
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (closed_form) = 0
y[1] (numeric) = 2.0562775595127661632216748785378
absolute error = 2.0562775595127661632216748785378
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (closed_form) = 0
y[1] (numeric) = 2.0613039410088752099259170813761
absolute error = 2.0613039410088752099259170813761
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4266.7MB, alloc=48.3MB, time=25.05
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (closed_form) = 0
y[1] (numeric) = 2.0663312690045207563673794770972
absolute error = 2.0663312690045207563673794770972
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (closed_form) = 0
y[1] (numeric) = 2.0713595708017957429373129246124
absolute error = 2.0713595708017957429373129246124
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (closed_form) = 0
y[1] (numeric) = 2.076388873604338083613590786858
absolute error = 2.076388873604338083613590786858
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (closed_form) = 0
y[1] (numeric) = 2.0814192045180497297171068910485
absolute error = 2.0814192045180497297171068910485
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4310.1MB, alloc=48.3MB, time=25.31
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (closed_form) = 0
y[1] (numeric) = 2.0864505905518074798927109095814
absolute error = 2.0864505905518074798927109095814
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (closed_form) = 0
y[1] (numeric) = 2.0914830586181656287941963988204
absolute error = 2.0914830586181656287941963988204
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (closed_form) = 0
y[1] (numeric) = 2.0965166355340505456356600161164
absolute error = 2.0965166355340505456356600161164
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4353.4MB, alloc=48.3MB, time=25.56
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (closed_form) = 0
y[1] (numeric) = 2.1015513480214472724766592150709
absolute error = 2.1015513480214472724766592150709
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (closed_form) = 0
y[1] (numeric) = 2.106587222708078230835584158527
absolute error = 2.106587222708078230835584158527
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (closed_form) = 0
y[1] (numeric) = 2.1116242861280741239741110897735
absolute error = 2.1116242861280741239741110897735
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (closed_form) = 0
y[1] (numeric) = 2.1166625647226371209651113808503
absolute error = 2.1166625647226371209651113808503
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4396.7MB, alloc=48.3MB, time=25.81
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (closed_form) = 0
y[1] (numeric) = 2.121702084840696407446554144548
absolute error = 2.121702084840696407446554144548
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (closed_form) = 0
y[1] (numeric) = 2.1267428727395561867743704493705
absolute error = 2.1267428727395561867743704493705
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (closed_form) = 0
y[1] (numeric) = 2.131784954585536214117561987079
absolute error = 2.131784954585536214117561987079
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (closed_form) = 0
y[1] (numeric) = 2.136828356454604944888662859085
absolute error = 2.136828356454604944888662859085
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4440.1MB, alloc=48.3MB, time=26.08
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (closed_form) = 0
y[1] (numeric) = 2.1418731043330053777716342995937
absolute error = 2.1418731043330053777716342995937
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (closed_form) = 0
y[1] (numeric) = 2.1469192241178736714970307581274
absolute error = 2.1469192241178736714970307581274
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (closed_form) = 0
y[1] (numeric) = 2.1519667416178506134204715437427
absolute error = 2.1519667416178506134204715437427
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4483.3MB, alloc=48.3MB, time=26.33
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (closed_form) = 0
y[1] (numeric) = 2.1570156825536860168847423328449
absolute error = 2.1570156825536860168847423328449
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (closed_form) = 0
y[1] (numeric) = 2.1620660725588361232878996539236
absolute error = 2.1620660725588361232878996539236
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (closed_form) = 0
y[1] (numeric) = 2.1671179371800540837392304533987
absolute error = 2.1671179371800540837392304533987
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (closed_form) = 0
y[1] (numeric) = 2.1721713018779735941615063933522
absolute error = 2.1721713018779735941615063933522
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4526.6MB, alloc=48.3MB, time=26.58
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (closed_form) = 0
y[1] (numeric) = 2.1772261920276857566913537566789
absolute error = 2.1772261920276857566913537566789
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (closed_form) = 0
y[1] (numeric) = 2.1822826329193092392394264482991
absolute error = 2.1822826329193092392394264482991
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (closed_form) = 0
y[1] (numeric) = 2.1873406497585538040981197262777
absolute error = 2.1873406497585538040981197262777
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4569.9MB, alloc=48.3MB, time=26.83
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (closed_form) = 0
y[1] (numeric) = 2.1924002676672772755265004009338
absolute error = 2.1924002676672772755265004009338
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (closed_form) = 0
y[1] (numeric) = 2.1974615116840360152996658671239
absolute error = 2.1974615116840360152996658671239
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (closed_form) = 0
y[1] (numeric) = 2.202524406764628974282596042865
absolute error = 2.202524406764628974282596042865
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (closed_form) = 0
y[1] (numeric) = 2.207588977782635387176451489576
absolute error = 2.207588977782635387176451489576
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4613.2MB, alloc=48.3MB, time=27.09
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (closed_form) = 0
y[1] (numeric) = 2.2126552495299461766879258185407
absolute error = 2.2126552495299461766879258185407
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (closed_form) = 0
y[1] (numeric) = 2.2177232467172891324894146656185
absolute error = 2.2177232467172891324894146656185
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (closed_form) = 0
y[1] (numeric) = 2.2227929939747479294691562219032
absolute error = 2.2227929939747479294691562219032
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4656.5MB, alloc=48.3MB, time=27.34
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (closed_form) = 0
y[1] (numeric) = 2.2278645158522750489158740559592
absolute error = 2.2278645158522750489158740559592
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (closed_form) = 0
y[1] (numeric) = 2.232937836820198665441561479186
absolute error = 2.232937836820198665441561479186
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (closed_form) = 0
y[1] (numeric) = 2.2380129812697235616186428081144
absolute error = 2.2380129812697235616186428081144
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (closed_form) = 0
y[1] (numeric) = 2.2430899735134261314935903609277
absolute error = 2.2430899735134261314935903609277
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4699.9MB, alloc=48.3MB, time=27.59
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (closed_form) = 0
y[1] (numeric) = 2.2481688377857435333379315484621
absolute error = 2.2481688377857435333379315484621
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (closed_form) = 0
y[1] (numeric) = 2.2532495982434570512092173936779
absolute error = 2.2532495982434570512092173936779
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (closed_form) = 0
y[1] (numeric) = 2.2583322789661697241187162948696
absolute error = 2.2583322789661697241187162948696
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (closed_form) = 0
y[1] (numeric) = 2.2634169039567783008391234340125
absolute error = 2.2634169039567783008391234340125
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4743.2MB, alloc=48.3MB, time=27.86
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (closed_form) = 0
y[1] (numeric) = 2.2685034971419395776342199582736
absolute error = 2.2685034971419395776342199582736
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (closed_form) = 0
y[1] (numeric) = 2.2735920823725311754529643040359
absolute error = 2.2735920823725311754529643040359
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (closed_form) = 0
y[1] (numeric) = 2.2786826834241068124027424042651
absolute error = 2.2786826834241068124027424042651
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4786.5MB, alloc=48.3MB, time=28.11
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (closed_form) = 0
y[1] (numeric) = 2.2837753239973461266002397836108
absolute error = 2.2837753239973461266002397836108
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (closed_form) = 0
y[1] (numeric) = 2.2888700277184991037934265170798
absolute error = 2.2888700277184991037934265170798
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (closed_form) = 0
y[1] (numeric) = 2.2939668181398251634542694868941
absolute error = 2.2939668181398251634542694868941
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (closed_form) = 0
y[1] (numeric) = 2.2990657187400269563588129733159
absolute error = 2.2990657187400269563588129733159
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4829.7MB, alloc=48.3MB, time=28.36
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (closed_form) = 0
y[1] (numeric) = 2.3041667529246789259990098035783
absolute error = 2.3041667529246789259990098035783
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (closed_form) = 0
y[1] (numeric) = 2.3092699440266506855089562093041
absolute error = 2.3092699440266506855089562093041
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (closed_form) = 0
y[1] (numeric) = 2.3143753153065252611368029818503
absolute error = 2.3143753153065252611368029818503
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4873.0MB, alloc=48.3MB, time=28.61
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (closed_form) = 0
y[1] (numeric) = 2.3194828899530122526524057862211
absolute error = 2.3194828899530122526524057862211
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (closed_form) = 0
y[1] (numeric) = 2.3245926910833559604495643834665
absolute error = 2.3245926910833559604495643834665
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (closed_form) = 0
y[1] (numeric) = 2.3297047417437385284803131954412
absolute error = 2.3297047417437385284803131954412
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (closed_form) = 0
y[1] (numeric) = 2.3348190649096781515469966175535
absolute error = 2.3348190649096781515469966175535
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4916.3MB, alloc=48.3MB, time=28.86
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (closed_form) = 0
y[1] (numeric) = 2.3399356834864223948756274820357
absolute error = 2.3399356834864223948756274820357
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (closed_form) = 0
y[1] (numeric) = 2.345054620309336673301125007268
absolute error = 2.345054620309336673301125007268
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (closed_form) = 0
y[1] (numeric) = 2.350175898144287936811301453469
absolute error = 2.350175898144287936811301453469
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=4959.5MB, alloc=48.3MB, time=29.13
x[1] = 4.19
y[1] (closed_form) = 0
y[1] (numeric) = 2.3552995396880236086217595947436
absolute error = 2.3552995396880236086217595947436
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (closed_form) = 0
y[1] (numeric) = 2.3604255675685458213880240369952
absolute error = 2.3604255675685458213880240369952
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (closed_form) = 0
y[1] (numeric) = 2.3655540043454809966041092932128
absolute error = 2.3655540043454809966041092932128
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (closed_form) = 0
y[1] (numeric) = 2.3706848725104448116881801499294
absolute error = 2.3706848725104448116881801499294
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5002.7MB, alloc=48.3MB, time=29.37
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (closed_form) = 0
y[1] (numeric) = 2.3758181944874025987158417830581
absolute error = 2.3758181944874025987158417830581
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (closed_form) = 0
y[1] (numeric) = 2.3809539926330252182297675941205
absolute error = 2.3809539926330252182297675941205
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (closed_form) = 0
y[1] (numeric) = 2.386092289237040451030693791513
absolute error = 2.386092289237040451030693791513
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (closed_form) = 0
y[1] (numeric) = 2.3912331065225799503391458976455
absolute error = 2.3912331065225799503391458976455
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5046.0MB, alloc=48.3MB, time=29.62
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (closed_form) = 0
y[1] (numeric) = 2.3963764666465217962094807370395
absolute error = 2.3963764666465217962094807370395
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (closed_form) = 0
y[1] (numeric) = 2.4015223916998286935777976678152
absolute error = 2.4015223916998286935777976678152
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (closed_form) = 0
y[1] (numeric) = 2.4066709037078818548328669210181
absolute error = 2.4066709037078818548328669210181
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5089.1MB, alloc=48.3MB, time=29.87
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (closed_form) = 0
y[1] (numeric) = 2.4118220246308106073143153653629
absolute error = 2.4118220246308106073143153653629
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (closed_form) = 0
y[1] (numeric) = 2.4169757763638177656647776198981
absolute error = 2.4169757763638177656647776198981
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (closed_form) = 0
y[1] (numeric) = 2.4221321807375008084924422894794
absolute error = 2.4221321807375008084924422894794
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (closed_form) = 0
y[1] (numeric) = 2.4272912595181688983372805401321
absolute error = 2.4272912595181688983372805401321
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5132.3MB, alloc=48.3MB, time=30.13
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (closed_form) = 0
y[1] (numeric) = 2.4324530344081557834781208053473
absolute error = 2.4324530344081557834781208053473
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (closed_form) = 0
y[1] (numeric) = 2.4376175270461286196685148156748
absolute error = 2.4376175270461286196685148156748
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (closed_form) = 0
y[1] (numeric) = 2.4427847590073927494469141768089
absolute error = 2.4427847590073927494469141768089
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5175.5MB, alloc=48.3MB, time=30.37
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (closed_form) = 0
y[1] (numeric) = 2.4479547518041924762309332546388
absolute error = 2.4479547518041924762309332546388
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (closed_form) = 0
y[1] (numeric) = 2.4531275268860078699763050500956
absolute error = 2.4531275268860078699763050500956
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (closed_form) = 0
y[1] (numeric) = 2.4583031056398476407584359325944
absolute error = 2.4583031056398476407584359325944
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (closed_form) = 0
y[1] (numeric) = 2.463481509390538116218128357782
absolute error = 2.463481509390538116218128357782
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5218.7MB, alloc=48.3MB, time=30.64
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (closed_form) = 0
y[1] (numeric) = 2.4686627594010083584029657313001
absolute error = 2.4686627594010083584029657313001
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (closed_form) = 0
y[1] (numeric) = 2.4738468768725714551319399631261
absolute error = 2.4738468768725714551319399631261
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (closed_form) = 0
y[1] (numeric) = 2.4790338829452020206130513759352
absolute error = 2.4790338829452020206130513759352
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5262.0MB, alloc=48.3MB, time=30.89
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (closed_form) = 0
y[1] (numeric) = 2.4842237986978099396517256589558
absolute error = 2.4842237986978099396517256589558
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (closed_form) = 0
y[1] (numeric) = 2.4894166451485103894018784165326
absolute error = 2.4894166451485103894018784165326
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (closed_form) = 0
y[1] (numeric) = 2.4946124432548901722312211803537
absolute error = 2.4946124432548901722312211803537
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (closed_form) = 0
y[1] (numeric) = 2.4998112139142703928978518450257
absolute error = 2.4998112139142703928978518450257
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5305.3MB, alloc=48.3MB, time=31.14
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (closed_form) = 0
y[1] (numeric) = 2.505012977963965512866217300068
absolute error = 2.505012977963965512866217300068
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (closed_form) = 0
y[1] (numeric) = 2.5102177561815388142270881283072
absolute error = 2.5102177561815388142270881283072
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (closed_form) = 0
y[1] (numeric) = 2.5154255692850543053281577585428
absolute error = 2.5154255692850543053281577585428
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5348.5MB, alloc=48.3MB, time=31.39
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (closed_form) = 0
y[1] (numeric) = 2.5206364379333250998691860813829
absolute error = 2.5206364379333250998691860813829
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (closed_form) = 0
y[1] (numeric) = 2.525850382726158300868166456909
absolute error = 2.525850382726158300868166456909
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (closed_form) = 0
y[1] (numeric) = 2.5310674242045964205627229399016
absolute error = 2.5310674242045964205627229399016
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (closed_form) = 0
y[1] (numeric) = 2.536287582851155366973760554425
absolute error = 2.536287582851155366973760554425
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5391.8MB, alloc=48.3MB, time=31.64
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (closed_form) = 0
y[1] (numeric) = 2.5415108790900590275262161202387
absolute error = 2.5415108790900590275262161202387
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (closed_form) = 0
y[1] (numeric) = 2.5467373332874704797945124198081
absolute error = 2.5467373332874704797945124198081
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (closed_form) = 0
y[1] (numeric) = 2.5519669657517198591179277151002
absolute error = 2.5519669657517198591179277151002
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=5435.0MB, alloc=48.3MB, time=31.91
x[1] = 4.58
y[1] (closed_form) = 0
y[1] (numeric) = 2.5571997967335289125134804365786
absolute error = 2.5571997967335289125134804365786
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (closed_form) = 0
y[1] (numeric) = 2.5624358464262322680010212449883
absolute error = 2.5624358464262322680010212449883
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (closed_form) = 0
y[1] (numeric) = 2.5676751349659954481469488691873
absolute error = 2.5676751349659954481469488691873
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (closed_form) = 0
y[1] (numeric) = 2.5729176824320296563292506717607
absolute error = 2.5729176824320296563292506717607
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5478.3MB, alloc=48.3MB, time=32.16
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (closed_form) = 0
y[1] (numeric) = 2.5781635088468033639273435465784
absolute error = 2.5781635088468033639273435465784
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (closed_form) = 0
y[1] (numeric) = 2.5834126341762507263453864793533
absolute error = 2.5834126341762507263453864793533
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (closed_form) = 0
y[1] (numeric) = 2.5886650783299768554872850625502
absolute error = 2.5886650783299768554872850625502
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (closed_form) = 0
y[1] (numeric) = 2.5939208611614599760154437736627
absolute error = 2.5939208611614599760154437736627
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5521.6MB, alloc=48.3MB, time=32.41
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (closed_form) = 0
y[1] (numeric) = 2.5991800024682504924433783670371
absolute error = 2.5991800024682504924433783670371
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (closed_form) = 0
y[1] (numeric) = 2.6044425219921669938345138798713
absolute error = 2.6044425219921669938345138798713
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (closed_form) = 0
y[1] (numeric) = 2.6097084394194892226058001964025
absolute error = 2.6097084394194892226058001964025
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5564.9MB, alloc=48.3MB, time=32.66
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (closed_form) = 0
y[1] (numeric) = 2.6149777743811480336651146105673
absolute error = 2.6149777743811480336651146105673
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (closed_form) = 0
y[1] (numeric) = 2.6202505464529123698457281918354
absolute error = 2.6202505464529123698457281918354
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (closed_form) = 0
y[1] (numeric) = 2.625526775155573279339329841618
absolute error = 2.625526775155573279339329841618
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (closed_form) = 0
y[1] (numeric) = 2.6308064799551250005711695933366
absolute error = 2.6308064799551250005711695933366
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5608.2MB, alloc=48.3MB, time=32.92
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (closed_form) = 0
y[1] (numeric) = 2.6360896802629431397067428176863
absolute error = 2.6360896802629431397067428176863
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (closed_form) = 0
y[1] (numeric) = 2.6413763954359599657290323813082
absolute error = 2.6413763954359599657290323813082
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (closed_form) = 0
y[1] (numeric) = 2.6466666447768368477786002643152
absolute error = 2.6466666447768368477786002643152
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5651.5MB, alloc=48.3MB, time=33.17
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (closed_form) = 0
y[1] (numeric) = 2.6519604475341338592057184006779
absolute error = 2.6519604475341338592057184006779
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (closed_form) = 0
y[1] (numeric) = 2.6572578229024765725441962164045
absolute error = 2.6572578229024765725441962164045
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (closed_form) = 0
y[1] (numeric) = 2.6625587900227200693805460575168
absolute error = 2.6625587900227200693805460575168
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (closed_form) = 0
y[1] (numeric) = 2.6678633679821101888595748620453
absolute error = 2.6678633679821101888595748620453
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5694.7MB, alloc=48.3MB, time=33.44
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (closed_form) = 0
y[1] (numeric) = 2.6731715758144420383383493451012
absolute error = 2.6731715758144420383383493451012
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (closed_form) = 0
y[1] (numeric) = 2.6784834325002157894747017927147
absolute error = 2.6784834325002157894747017927147
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (closed_form) = 0
y[1] (numeric) = 2.6837989569667897828139742932942
absolute error = 2.6837989569667897828139742932942
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (closed_form) = 0
y[1] (numeric) = 2.689118168088530963718491689579
absolute error = 2.689118168088530963718491689579
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5737.9MB, alloc=48.3MB, time=33.69
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (closed_form) = 0
y[1] (numeric) = 2.6944410846869626722682593272019
absolute error = 2.6944410846869626722682593272019
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (closed_form) = 0
y[1] (numeric) = 2.6997677255309098095485532155536
absolute error = 2.6997677255309098095485532155536
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (closed_form) = 0
y[1] (numeric) = 2.7050981093366414025303606835121
absolute error = 2.7050981093366414025303606835121
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5781.1MB, alloc=48.3MB, time=33.94
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (closed_form) = 0
y[1] (numeric) = 2.7104322547680105895429929468984
absolute error = 2.7104322547680105895429929468984
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (closed_form) = 0
y[1] (numeric) = 2.7157701804365920481345818912423
absolute error = 2.7157701804365920481345818912423
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (closed_form) = 0
y[1] (numeric) = 2.7211119049018168869155472284346
absolute error = 2.7211119049018168869155472284346
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (closed_form) = 0
y[1] (numeric) = 2.726457446671105022782433141985
absolute error = 2.726457446671105022782433141985
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5824.2MB, alloc=48.3MB, time=34.19
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (closed_form) = 0
y[1] (numeric) = 2.7318068241999950647247224294566
absolute error = 2.7318068241999950647247224294566
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (closed_form) = 0
y[1] (numeric) = 2.7371600558922717252252985091385
absolute error = 2.7371600558922717252252985091385
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (closed_form) = 0
y[1] (numeric) = 2.7425171601000907800760996856281
absolute error = 2.7425171601000907800760996856281
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5867.5MB, alloc=48.3MB, time=34.44
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (closed_form) = 0
y[1] (numeric) = 2.7478781551241015972441546350589
absolute error = 2.7478781551241015972441546350589
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (closed_form) = 0
y[1] (numeric) = 2.7532430592135672552395626970129
absolute error = 2.7532430592135672552395626970129
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (closed_form) = 0
y[1] (numeric) = 2.7586118905664822712560474088218
absolute error = 2.7586118905664822712560474088218
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (closed_form) = 0
y[1] (numeric) = 2.7639846673296879591764275795349
absolute error = 2.7639846673296879591764275795349
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5910.7MB, alloc=48.3MB, time=34.70
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (closed_form) = 0
y[1] (numeric) = 2.7693614075989854373596784826332
absolute error = 2.7693614075989854373596784826332
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (closed_form) = 0
y[1] (numeric) = 2.7747421294192463059531584612627
absolute error = 2.7747421294192463059531584612627
relative error = -100 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = -16
h = 0.001
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = expt ( sin ( 0.1 * x ) , sin ( 0.2 * x ) ) ;
Iterations = 4900
Total Elapsed Time = 34 Seconds
Elapsed Time(since restart) = 34 Seconds
Time to Timeout = 2 Minutes 25 Seconds
Percent Done = 100 %
> quit
memory used=5945.6MB, alloc=48.3MB, time=34.89