|\^/| Maple 18 (X86 64 WINDOWS)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
# End Function number 7
# Begin Function number 8
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number 0
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
> if (years_int > 0) then # if number 1
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 2
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 8
# Begin Function number 9
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 7
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 7;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 7
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 12
# Begin Function number 13
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 6
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 7
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 8
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 9
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 10
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 11
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 12
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 12
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 19
# Begin Function number 20
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 20
# Begin Function number 21
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 21
# Begin Function number 22
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 12
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 12;
> if (errflag) then # if number 12
> quit;
> fi;# end if 12
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 22
# Begin Function number 23
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 12
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 13
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 13
> fi;# end if 12;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 23
# Begin Function number 24
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 12
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 12;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 24
# Begin Function number 25
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 25
# Begin Function number 26
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 26
# Begin Function number 27
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalf(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalf(in_val); ret end proc
# End Function number 27
# Begin Function number 28
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 12
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 28
# Begin Function number 29
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 29
# Begin Function number 30
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 12
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 13
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 15
> if (rcs > glob__0) then # if number 16
> rad_c := sqrt(rcs) * float_abs(glob_h);
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 16
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> fi;# end if 13
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 12;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := sqrt(rcs)*float_abs(glob_h)
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 30
# Begin Function number 31
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 31
# Begin Function number 32
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 32
# Begin Function number 33
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 12
> if (array_fact_1[nnn] = 0) then # if number 13
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 13;
> else
> ret := factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 33
# Begin Function number 34
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 12
> if (array_fact_2[mmm,nnn] = 0) then # if number 13
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 13;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 34
# Begin Function number 35
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 35
# Begin Function number 36
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 36
# Begin Function number 37
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 37
# Begin Function number 38
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 38
# Begin Function number 39
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 39
# Begin Function number 40
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 40
# Begin Function number 41
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 41
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(1.0) + sin(c(x)));
> end;
exact_soln_y := proc(x) return c(1.0) + sin(c(x)) end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]);
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if (rad_given < glob_least_given_sing) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])*
(array_x[1] - array_given_rad_poles[1, 1])
+ array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if rad_given < glob_least_given_sing then
glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if array_rad_test_poles[1, 1] < glob_least_ratio_sing then
glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_float(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if array_rad_test_poles[1, 2] < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if array_rad_test_poles[1, 3] < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y[1]) < min_size) then # if number 3
> min_size := float_abs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < glob__1) then # if number 3
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y[1]) < min_size then
min_size := float_abs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := float_abs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
> est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
> fi;# end if 3;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 3
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y[no_terms - 3]))
+ c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 3
> if (iter >= 0) then # if number 4
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> closed_form_val_y := evalf(exact_soln_y(ind_var));
> omniout_float(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := float_abs(numeric_val - closed_form_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 5
> relerr := abserr*glob__100/float_abs(closed_form_val_y);
> if (c(relerr) > c(glob_prec)) then # if number 6
> glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 6;
> else
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 5;
> if (glob_good_digits < glob_min_good_digits) then # if number 5
> glob_min_good_digits := glob_good_digits;
> fi;# end if 5;
> if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 5
> glob_min_apfp_est_good_digits := glob_apfp_est_good_digits;
> fi;# end if 5;
> if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 5
> est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*17*ATS_MAX_TERMS/float_abs(numeric_val));
> if (evalf(est_rel_err) > glob_prec) then # if number 6
> glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
> else
> glob_est_digits := Digits;
> fi;# end if 6;
> else
> relerr := glob__m1 ;
> glob_est_digits := -16;
> fi;# end if 5;
> array_est_digits[1] := glob_est_digits;
> if (glob_iter = 1) then # if number 5
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 5;
> array_est_rel_error[1] := est_rel_err;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," ");
> omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," ");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 4;
> #BOTTOM DISPLAY ALOT
> fi;# end if 3;
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
closed_form_val_y := evalf(exact_soln_y(ind_var));
omniout_float(ALWAYS, "y[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := float_abs(numeric_val - closed_form_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if c(glob_prec) < c(float_abs(closed_form_val_y)) then
relerr := abserr*glob__100/float_abs(closed_form_val_y);
if c(glob_prec) < c(relerr) then
glob_good_digits := -int_trunc(log10(c(relerr))) + 3
else glob_good_digits := Digits
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits
then glob_min_apfp_est_good_digits := glob_apfp_est_good_digits
end if;
if glob_prec < evalf(float_abs(numeric_val)) then
est_rel_err := evalf(array_max_est_error[1]*100.0*
sqrt(glob_iter)*17*ATS_MAX_TERMS/float_abs(numeric_val))
;
if glob_prec < evalf(est_rel_err) then
glob_est_digits := -int_trunc(log10(est_rel_err)) + 3
else glob_est_digits := Digits
end if
else relerr := glob__m1; glob_est_digits := -16
end if;
array_est_digits[1] := glob_est_digits;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
array_est_rel_error[1] := est_rel_err;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Desired digits ", 32,
glob_desired_digits_correct, 4, " ");
omniout_int(INFO, "Estimated correct digits ", 32,
glob_est_digits, 4, " ");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr((glob_clock_sec));
> if (c(percent_done) < glob__100) then # if number 3
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 3;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr((left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(glob_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(left_sec);
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 3;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 4
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_rad_test_poles[1,1]) then # if number 6
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,2]) then # if number 8
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 9
> glob_min_pole_est := rad_c;
> fi;# end if 9;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[1,3]) then # if number 10
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 11
> glob_min_pole_est := rad_c;
> fi;# end if 11;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test1
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 10;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 9;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 9
> display_poles();
> fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4],
array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
if
float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_poles() end if
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre cos 1 $eq_no = 1
> array_tmp1[1] := cos(array_x[1]);
> array_tmp1_g[1] := sin(array_x[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre cos ID_LINEAR iii = 2 $eq_no = 1
> array_tmp1[2] := neg(array_tmp1_g[1]) * array_x[2] / c(1);
> array_tmp1_g[2] := array_tmp1[1] * array_x[2] / c(1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre cos ID_LINEAR iii = 3 $eq_no = 1
> array_tmp1[3] := neg(array_tmp1_g[2]) * array_x[2] / c(2);
> array_tmp1_g[3] := array_tmp1[2] * array_x[2] / c(2);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre cos ID_LINEAR iii = 4 $eq_no = 1
> array_tmp1[4] := neg(array_tmp1_g[3]) * array_x[2] / c(3);
> array_tmp1_g[4] := array_tmp1[3] * array_x[2] / c(3);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre cos ID_LINEAR iii = 5 $eq_no = 1
> array_tmp1[5] := neg(array_tmp1_g[4]) * array_x[2] / c(4);
> array_tmp1_g[5] := array_tmp1[4] * array_x[2] / c(4);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit cos LINEAR $eq_no = 1
> array_tmp1[kkk] := neg(array_tmp1_g[kkk - 1]) * array_x[2] / c(kkk - 1);
> array_tmp1_g[kkk] := array_tmp1[kkk - 1] * array_x[2] / c(kkk - 1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp2[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
array_tmp1[1] := cos(array_x[1]);
array_tmp1_g[1] := sin(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := neg(array_tmp1_g[1])*array_x[2]/c(1);
array_tmp1_g[2] := array_tmp1[1]*array_x[2]/c(1);
array_tmp2[2] := array_tmp1[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp1[3] := neg(array_tmp1_g[2])*array_x[2]/c(2);
array_tmp1_g[3] := array_tmp1[2]*array_x[2]/c(2);
array_tmp2[3] := array_tmp1[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp1[4] := neg(array_tmp1_g[3])*array_x[2]/c(3);
array_tmp1_g[4] := array_tmp1[3]*array_x[2]/c(3);
array_tmp2[4] := array_tmp1[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp1[5] := neg(array_tmp1_g[4])*array_x[2]/c(4);
array_tmp1_g[5] := array_tmp1[4]*array_x[2]/c(4);
array_tmp2[5] := array_tmp1[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp1[kkk] := neg(array_tmp1_g[kkk - 1])*array_x[2]/c(kkk - 1)
;
array_tmp1_g[kkk] := array_tmp1[kkk - 1]*array_x[2]/c(kkk - 1);
array_tmp2[kkk] := array_tmp1[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y_set_initial[1, kkk + order_d] then
temporary := c(array_tmp2[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 40;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=40;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(40),[]);
> array_norms:= Array(0..(40),[]);
> array_fact_1:= Array(0..(40),[]);
> array_1st_rel_error:= Array(0..(2),[]);
> array_last_rel_error:= Array(0..(2),[]);
> array_est_rel_error:= Array(0..(2),[]);
> array_max_est_error:= Array(0..(2),[]);
> array_type_pole:= Array(0..(2),[]);
> array_type_real_pole:= Array(0..(2),[]);
> array_type_complex_pole:= Array(0..(2),[]);
> array_est_digits:= Array(0..(2),[]);
> array_y:= Array(0..(40),[]);
> array_x:= Array(0..(40),[]);
> array_tmp0:= Array(0..(40),[]);
> array_tmp1_g:= Array(0..(40),[]);
> array_tmp1:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_m1:= Array(0..(40),[]);
> array_y_higher := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..40+ 1),[]);
> array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(40) ,(0..40+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 40) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp1_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=40) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1_g);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_h := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 1000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> array_y_set_initial[1,31] := false;
> array_y_set_initial[1,32] := false;
> array_y_set_initial[1,33] := false;
> array_y_set_initial[1,34] := false;
> array_y_set_initial[1,35] := false;
> array_y_set_initial[1,36] := false;
> array_y_set_initial[1,37] := false;
> array_y_set_initial[1,38] := false;
> array_y_set_initial[1,39] := false;
> array_y_set_initial[1,40] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 40;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/cospostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = cos ( x ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=40;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := c(0.0);");
> omniout_str(ALWAYS,"x_end := c(5.0) ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := false;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 3;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=100000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.0000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.9999999);");
> 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,"#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(1.0) + sin(c(x)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := c(0.0);
> x_end := c(5.0) ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := false;
> glob_type_given_pole := 3;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=100000;
> glob_upper_ratio_limit:=c(1.0000001);
> glob_lower_ratio_limit:=c(0.9999999);
> glob_look_poles:=true;
> glob_h:=c(0.001);
> glob_display_interval:=c(0.01);
> #END OVERRIDE BLOCK
> #END BLOCK 2
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
> # after second input block
> glob_check_sign := c(my_check_sign(x_start,x_end));
> glob__pi := arccos(glob__m1);
> glob_prec = expt(10.0,c(-Digits));
> if (glob_optimize) then # if number 9
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> found_h := false;
> glob_min_pole_est := glob_larger_float;
> last_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> glob_min_h := float_abs(glob_min_h) * glob_check_sign;
> glob_max_h := float_abs(glob_max_h) * glob_check_sign;
> glob_h := float_abs(glob_min_h) * glob_check_sign;
> glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign));
> display_max := c(x_end) - c(x_start)/glob__10;
> if ((glob_display_interval) > (display_max)) then # if number 10
> glob_display_interval := c(display_max);
> fi;# end if 10;
> chk_data();
> min_value := glob_larger_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := glob_small_float;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> atomall();
> if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> glob_h := glob_check_sign * float_abs(glob_min_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
> glob_h_reason := 2;
> glob_h := glob_display_interval;
> found_h := true;
> fi;# end if 10;
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if ( not found_h) then # if number 10
> est_answer := est_size_answer();
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := test_suggested_h();
> omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
> if (estimated_step_error < est_needed_step_err) then # if number 11
> omniout_str(ALWAYS,"Double H and LOOP");
> glob_h := glob_h*glob__2;
> else
> omniout_str(ALWAYS,"Found H for OPTIMAL");
> found_h := true;
> glob_h_reason := 3;
> glob_h := glob_h/glob__2;
> fi;# end if 11;
> fi;# end if 10;
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 10
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 10;
> if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MAX H");
> glob_h := glob_check_sign * float_abs(glob_max_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> else
> found_h := true;
> glob_h := glob_h * glob_check_sign;
> fi;# end if 9;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 9
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 9;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 9
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> glob_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and (glob_check_sign * array_x[1] < glob_check_sign * x_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1
> #left paren 0001C
> if (reached_interval()) then # if number 10
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 10;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> track_estimated_error();
> atomall();
> track_estimated_error();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if (reached_interval()) then # if number 10
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 10;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 10
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 10;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 10;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = cos ( x ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2015-05-02T17:30:01-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"cos")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = cos ( x ) ; ")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 308.maple.seems.ok | ")
> ;
> logitem_str(html_log_file,"cos diffeq.mxt")
> ;
> logitem_str(html_log_file,"cos maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> fi;# end if 14
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
ATS_MAX_TERMS := 40;
Digits := 32;
max_terms := 40;
glob_html_log := true;
array_y_init := Array(0 .. 40, []);
array_norms := Array(0 .. 40, []);
array_fact_1 := Array(0 .. 40, []);
array_1st_rel_error := Array(0 .. 2, []);
array_last_rel_error := Array(0 .. 2, []);
array_est_rel_error := Array(0 .. 2, []);
array_max_est_error := Array(0 .. 2, []);
array_type_pole := Array(0 .. 2, []);
array_type_real_pole := Array(0 .. 2, []);
array_type_complex_pole := Array(0 .. 2, []);
array_est_digits := Array(0 .. 2, []);
array_y := Array(0 .. 40, []);
array_x := Array(0 .. 40, []);
array_tmp0 := Array(0 .. 40, []);
array_tmp1_g := Array(0 .. 40, []);
array_tmp1 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_m1 := Array(0 .. 40, []);
array_y_higher := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 41, []);
array_y_set_initial := Array(0 .. 2, 0 .. 41, []);
array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
array_fact_2 := Array(0 .. 40, 0 .. 41, []);
term := 1;
while term <= 40 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 40 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp1_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 40 do
term := 1;
while term <= 40 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1_g);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_h := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 1000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
array_y_set_initial[1, 31] := false;
array_y_set_initial[1, 32] := false;
array_y_set_initial[1, 33] := false;
array_y_set_initial[1, 34] := false;
array_y_set_initial[1, 35] := false;
array_y_set_initial[1, 36] := false;
array_y_set_initial[1, 37] := false;
array_y_set_initial[1, 38] := false;
array_y_set_initial[1, 39] := false;
array_y_set_initial[1, 40] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 40;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/cospostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = cos ( x ) ; ")
;
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=40;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := c(0.0);");
omniout_str(ALWAYS, "x_end := c(5.0) ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := false;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 3;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=100000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.0000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.9999999);");
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, "#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(1.0) + sin(c(x)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := c(0.);
x_end := c(5.0);
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := false;
glob_type_given_pole := 3;
glob_desired_digits_correct := 8;
glob_max_minutes := 3.0;
glob_subiter_method := 3;
glob_max_iter := 100000;
glob_upper_ratio_limit := c(1.0000001);
glob_lower_ratio_limit := c(0.9999999);
glob_look_poles := true;
glob_h := c(0.001);
glob_display_interval := c(0.01);
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
glob_check_sign := c(my_check_sign(x_start, x_end));
glob__pi := arccos(glob__m1);
glob_prec = expt(10.0, c(-Digits));
if glob_optimize then
omniout_str(ALWAYS, "START of Optimize");
found_h := false;
glob_min_pole_est := glob_larger_float;
last_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
glob_min_h := float_abs(glob_min_h)*glob_check_sign;
glob_max_h := float_abs(glob_max_h)*glob_check_sign;
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_display_interval :=
c(float_abs(c(glob_display_interval))*glob_check_sign);
display_max := c(x_end) - c(x_start)/glob__10;
if display_max < glob_display_interval then
glob_display_interval := c(display_max)
end if;
chk_data();
min_value := glob_larger_float;
est_answer := est_size_answer();
opt_iter := 1;
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
;
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := glob_small_float;
while opt_iter <= 100 and not found_h do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] :=
array_y_init[it]*expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
atomall();
if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if;
if
glob_check_sign*glob_display_interval <= glob_check_sign*glob_h
then
omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL");
glob_h_reason := 2;
glob_h := glob_display_interval;
found_h := true
end if;
if glob_look_poles then check_for_pole() end if;
if not found_h then
est_answer := est_size_answer();
est_needed_step_err := estimated_needed_step_error(x_start,
x_end, glob_h, est_answer);
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := test_suggested_h();
omniout_float(ALWAYS, "estimated_step_error", 32,
estimated_step_error, 32, "");
if estimated_step_error < est_needed_step_err then
omniout_str(ALWAYS, "Double H and LOOP");
glob_h := glob_h*glob__2
else
omniout_str(ALWAYS, "Found H for OPTIMAL");
found_h := true;
glob_h_reason := 3;
glob_h := glob_h/glob__2
end if
end if;
opt_iter := opt_iter + 1
end do;
if not found_h and opt_iter = 1 then
omniout_str(ALWAYS, "Beginning glob_h too large.");
found_h := false
end if;
if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then
omniout_str(ALWAYS, "SETTING H FOR MAX H");
glob_h := float_abs(glob_max_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if
else found_h := true; glob_h := glob_check_sign*glob_h
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
glob_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
glob_clock_sec - glob_orig_start_sec < glob_max_sec do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
track_estimated_error();
atomall();
track_estimated_error();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO,
"diff ( y , x , 1 ) = cos ( x ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2015-05-02T17:30:01-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "cos");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = cos ( x ) ; ");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 308.maple.seems.ok | ");
logitem_str(html_log_file,
"cos diffeq.mxt");
logitem_str(html_log_file,
"cos maple results");
logitem_str(html_log_file, "OK");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
##############ECHO OF PROBLEM#################
##############temp/cospostode.ode#################
diff ( y , x , 1 ) = cos ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(0.0);
x_end := c(5.0) ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := false;
glob_type_given_pole := 3;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=100000;
glob_upper_ratio_limit:=c(1.0000001);
glob_lower_ratio_limit:=c(0.9999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(1.0) + sin(c(x)));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0
y[1] (closed_form) = 1
y[1] (numeric) = 1
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 14
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
memory used=4.1MB, alloc=40.3MB, time=0.13
TOP MAIN SOLVE Loop
x[1] = 0.009999994000001199999885714292066
y[1] (closed_form) = 1.0099998273344678619424400995742
y[1] (numeric) = 1.0099998273344678619424400995738
absolute error = 4e-31
relative error = 3.9603967166574322371005009032587e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.009999
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
memory used=45.6MB, alloc=44.3MB, time=0.55
TOP MAIN SOLVE Loop
x[1] = 0.019999987333335866666425396838766
y[1] (closed_form) = 1.0199986540292021928119442653159
y[1] (numeric) = 1.0199986540292021928119442653157
absolute error = 2e-31
relative error = 1.9607869011391271138381330760294e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01999
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
memory used=87.0MB, alloc=44.3MB, time=0.97
TOP MAIN SOLVE Loop
memory used=128.4MB, alloc=44.3MB, time=1.39
x[1] = 0.029999980666670533332965079385466
y[1] (closed_form) = 1.029995480877865534275374510175
y[1] (numeric) = 1.0299954808778655342753745101747
absolute error = 3e-31
relative error = 2.9126341383974800316084892805719e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02998
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
memory used=169.8MB, alloc=44.3MB, time=1.81
TOP MAIN SOLVE Loop
x[1] = 0.039999974000005199999504761932166
y[1] (closed_form) = 1.0399893082074365685907935371552
y[1] (numeric) = 1.0399893082074365685907935371547
absolute error = 5e-31
relative error = 4.8077417340166525558403471530687e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03996
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
memory used=211.2MB, alloc=44.3MB, time=2.23
TOP MAIN SOLVE Loop
x[1] = 0.049999967333339866666044444478866
y[1] (closed_form) = 1.0499791366448429877270671251367
y[1] (numeric) = 1.0499791366448429877270671251361
absolute error = 6e-31
relative error = 5.7143992586107060597936824083543e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04992
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
memory used=252.7MB, alloc=44.3MB, time=2.66
TOP MAIN SOLVE Loop
x[1] = 0.059999960666674533332584127025566
y[1] (closed_form) = 1.0599639672168978345390985910126
y[1] (numeric) = 1.0599639672168978345390985910123
absolute error = 3e-31
relative error = 2.8302848896618363408042304791255e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05986
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
memory used=294.1MB, alloc=44.3MB, time=3.08
TOP MAIN SOLVE Loop
x[1] = 0.069999954000009199999123809572266
y[1] (closed_form) = 1.0699428014501958557945284594058
y[1] (numeric) = 1.0699428014501958557945284594055
absolute error = 3e-31
relative error = 2.8038882040552195373135437340751e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06977
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
memory used=335.5MB, alloc=44.3MB, time=3.48
TOP MAIN SOLVE Loop
x[1] = 0.079999947333343866665663492118966
y[1] (closed_form) = 1.0799146414709598775131626380085
y[1] (numeric) = 1.0799146414709598775131626380081
absolute error = 4e-31
relative error = 3.7039964515635882418436657103199e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07966
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
memory used=376.9MB, alloc=44.3MB, time=3.92
TOP MAIN SOLVE Loop
x[1] = 0.089999940666678533332203174665666
y[1] (closed_form) = 1.0898784901048272180781128122244
y[1] (numeric) = 1.0898784901048272180781128122238
absolute error = 6e-31
relative error = 5.5052008590635687368994036052564e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08951
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
memory used=418.4MB, alloc=44.3MB, time=4.33
TOP MAIN SOLVE Loop
x[1] = 0.099999934000013199998742857212366
y[1] (closed_form) = 1.0998333509765661605737976383885
y[1] (numeric) = 1.0998333509765661605737976383883
absolute error = 2e-31
relative error = 1.8184573128503114802096391706470e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09933
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
memory used=459.8MB, alloc=44.3MB, time=4.75
TOP MAIN SOLVE Loop
x[1] = 0.10999992733334786666528253975936
y[1] (closed_form) = 1.1097782286097125127999630197021
y[1] (numeric) = 1.1097782286097125127999630197014
absolute error = 7e-31
relative error = 6.3075665205374688312142489860214e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1091
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
memory used=501.2MB, alloc=44.3MB, time=5.17
TOP MAIN SOLVE Loop
x[1] = 0.11999992066668253333182222230636
y[1] (closed_form) = 1.1197121285261162914020348989319
y[1] (numeric) = 1.1197121285261162914020348989307
absolute error = 1.2e-30
relative error = 1.0717040294808337116885516942810e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1189
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
memory used=542.7MB, alloc=44.3MB, time=5.59
TOP MAIN SOLVE Loop
x[1] = 0.12999991400001719999836190485336
y[1] (closed_form) = 1.1296340573453885755456194891161
y[1] (numeric) = 1.1296340573453885755456194891146
absolute error = 1.5e-30
relative error = 1.3278636477417846354712504491187e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1285
Order of pole (three term test) = 32.98
NO COMPLEX POLE (six term test) for Equation 1
memory used=584.2MB, alloc=44.3MB, time=6.01
TOP MAIN SOLVE Loop
x[1] = 0.13999990733335186666490158740036
y[1] (closed_form) = 1.1395430228842385855459149464962
y[1] (numeric) = 1.1395430228842385855459149464944
absolute error = 1.8e-30
relative error = 1.5795805545315110750642854405192e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1382
Order of pole (three term test) = 32.98
NO COMPLEX POLE (six term test) for Equation 1
memory used=625.5MB, alloc=44.3MB, time=6.44
TOP MAIN SOLVE Loop
x[1] = 0.14999990066668653333144126994736
y[1] (closed_form) = 1.1494380342556910528401968834376
y[1] (numeric) = 1.1494380342556910528401968834358
absolute error = 1.8e-30
relative error = 1.5659826335619517630256876625178e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1478
Order of pole (three term test) = 32.98
NO COMPLEX POLE (six term test) for Equation 1
memory used=666.9MB, alloc=44.3MB, time=6.86
TOP MAIN SOLVE Loop
x[1] = 0.15999989400002119999798095249436
y[1] (closed_form) = 1.1593181019681739596622900939541
y[1] (numeric) = 1.1593181019681739596622900939522
absolute error = 1.9e-30
relative error = 1.6388944473258639075316032006384e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1573
Order of pole (three term test) = 32.97
NO COMPLEX POLE (six term test) for Equation 1
memory used=708.3MB, alloc=44.3MB, time=7.28
TOP MAIN SOLVE Loop
x[1] = 0.16999988733335586666452063504136
y[1] (closed_form) = 1.1691822380244667397408433571984
y[1] (numeric) = 1.1691822380244667397408433571966
absolute error = 1.8e-30
relative error = 1.5395375857243672346729882389711e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1667
Order of pole (three term test) = 32.97
NO COMPLEX POLE (six term test) for Equation 1
memory used=749.7MB, alloc=44.3MB, time=7.70
TOP MAIN SOLVE Loop
x[1] = 0.17999988066669053333106031758836
y[1] (closed_form) = 1.1790294560204990452969869170049
y[1] (numeric) = 1.1790294560204990452969869170034
absolute error = 1.5e-30
relative error = 1.2722328457024744946386058807385e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1761
Order of pole (three term test) = 32.97
NO COMPLEX POLE (six term test) for Equation 1
memory used=791.1MB, alloc=44.3MB, time=8.11
TOP MAIN SOLVE Loop
x[1] = 0.18999987400002519999760000013536
y[1] (closed_form) = 1.1888587712439902005601778454836
y[1] (numeric) = 1.1888587712439902005601778454819
absolute error = 1.7e-30
relative error = 1.4299427662220679176701823285004e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1855
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
memory used=832.5MB, alloc=44.3MB, time=8.53
TOP MAIN SOLVE Loop
x[1] = 0.19999986733335986666413968268236
y[1] (closed_form) = 1.1986692007729194779522326776511
y[1] (numeric) = 1.1986692007729194779522326776492
absolute error = 1.9e-30
relative error = 1.5850911984514594505191416575944e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1947
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
memory used=873.9MB, alloc=44.3MB, time=8.95
TOP MAIN SOLVE Loop
x[1] = 0.20999986066669453333067936522936
y[1] (closed_form) = 1.2084597635738173500071163481272
y[1] (numeric) = 1.2084597635738173500071163481247
absolute error = 2.5e-30
relative error = 2.0687490600486926568304338074961e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2039
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
memory used=915.4MB, alloc=44.3MB, time=9.37
TOP MAIN SOLVE Loop
x[1] = 0.21999985400002919999721904777636
y[1] (closed_form) = 1.2182294805998678879963098294163
y[1] (numeric) = 1.218229480599867887996309829413
absolute error = 3.3e-30
relative error = 2.7088492378094875267792806054255e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.213
Order of pole (three term test) = 32.95
NO COMPLEX POLE (six term test) for Equation 1
memory used=956.7MB, alloc=44.3MB, time=9.80
TOP MAIN SOLVE Loop
x[1] = 0.22999984733336386666375873032336
y[1] (closed_form) = 1.2279773748888124971147257561938
y[1] (numeric) = 1.2279773748888124971147257561906
absolute error = 3.2e-30
relative error = 2.6059112044224306327797672051965e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.222
Order of pole (three term test) = 32.95
NO COMPLEX POLE (six term test) for Equation 1
memory used=998.2MB, alloc=44.3MB, time=10.22
TOP MAIN SOLVE Loop
x[1] = 0.23999984066669853333029841287036
y[1] (closed_form) = 1.2377024716606451979482932249027
y[1] (numeric) = 1.237702471660645197948293224899
absolute error = 3.7e-30
relative error = 2.9894098821953961475353947013938e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2309
Order of pole (three term test) = 32.94
NO COMPLEX POLE (six term test) for Equation 1
memory used=1039.7MB, alloc=44.3MB, time=10.64
TOP MAIN SOLVE Loop
x[1] = 0.24999983400003319999683809541736
y[1] (closed_form) = 1.2474037984150896847895032868446
y[1] (numeric) = 1.2474037984150896847895032868415
absolute error = 3.1e-30
relative error = 2.4851615843552490620996145819682e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2397
Order of pole (three term test) = 32.94
NO COMPLEX POLE (six term test) for Equation 1
memory used=1081.2MB, alloc=44.3MB, time=11.06
TOP MAIN SOLVE Loop
x[1] = 0.25999982733336786666337777796436
y[1] (closed_form) = 1.2570803850288484131893109089377
y[1] (numeric) = 1.2570803850288484131893109089341
absolute error = 3.6e-30
relative error = 2.8637786754722010315094053675604e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2484
Order of pole (three term test) = 32.93
NO COMPLEX POLE (six term test) for Equation 1
memory used=1122.6MB, alloc=44.3MB, time=11.47
TOP MAIN SOLVE Loop
x[1] = 0.26999982066670253332991746051136
y[1] (closed_form) = 1.2667312638526139919306451700887
y[1] (numeric) = 1.2667312638526139919306451700851
absolute error = 3.6e-30
relative error = 2.8419603294948479206839201900866e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2571
Order of pole (three term test) = 32.93
NO COMPLEX POLE (six term test) for Equation 1
memory used=1163.9MB, alloc=44.3MB, time=11.89
TOP MAIN SOLVE Loop
x[1] = 0.27999981400003719999645714305836
y[1] (closed_form) = 1.2763554698078331783781075291109
y[1] (numeric) = 1.2763554698078331783781075291068
absolute error = 4.1e-30
relative error = 3.2122712653217931202537360852113e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2656
Order of pole (three term test) = 32.92
NO COMPLEX POLE (six term test) for Equation 1
memory used=1205.2MB, alloc=44.3MB, time=12.31
TOP MAIN SOLVE Loop
x[1] = 0.28999980733337186666299682560536
y[1] (closed_form) = 1.2859520404832138008978612325019
y[1] (numeric) = 1.285952040483213800897861232498
absolute error = 3.9e-30
relative error = 3.0327725119006168124792187912895e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.274
Order of pole (three term test) = 32.92
NO COMPLEX POLE (six term test) for Equation 1
memory used=1246.6MB, alloc=44.3MB, time=12.75
memory used=1287.9MB, alloc=44.3MB, time=13.17
TOP MAIN SOLVE Loop
x[1] = 0.29999980066670653332953650815236
y[1] (closed_form) = 1.2955200162309649577487594087504
y[1] (numeric) = 1.2955200162309649577487594087463
absolute error = 4.1e-30
relative error = 3.1647523377740333654719332555292e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2823
Order of pole (three term test) = 32.91
NO COMPLEX POLE (six term test) for Equation 1
memory used=1329.2MB, alloc=44.3MB, time=13.58
TOP MAIN SOLVE Loop
x[1] = 0.30999979400004119999607619069936
y[1] (closed_form) = 1.3050584402627608685178544405805
y[1] (numeric) = 1.3050584402627608685178544405765
absolute error = 4.0e-30
relative error = 3.0649968435088920365858261006090e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2905
Order of pole (three term test) = 32.91
NO COMPLEX POLE (six term test) for Equation 1
memory used=1370.6MB, alloc=44.3MB, time=14.00
TOP MAIN SOLVE Loop
x[1] = 0.31999978733337586666261587324636
y[1] (closed_form) = 1.3145663587454187818079096339431
y[1] (numeric) = 1.3145663587454187818079096339391
absolute error = 4.0e-30
relative error = 3.0428285140489031713127826390915e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2986
Order of pole (three term test) = 32.9
NO COMPLEX POLE (six term test) for Equation 1
memory used=1412.1MB, alloc=44.3MB, time=14.42
TOP MAIN SOLVE Loop
x[1] = 0.32999978066671053332915555579336
y[1] (closed_form) = 1.3240428208962813714786325914933
y[1] (numeric) = 1.3240428208962813714786325914892
absolute error = 4.1e-30
relative error = 3.0965765874736559421019992004568e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3066
Order of pole (three term test) = 32.89
NO COMPLEX POLE (six term test) for Equation 1
memory used=1453.4MB, alloc=44.3MB, time=14.84
TOP MAIN SOLVE Loop
x[1] = 0.33999977400004519999569523834036
y[1] (closed_form) = 1.3334868790782940832942086665575
y[1] (numeric) = 1.333486879078294083294208666553
absolute error = 4.5e-30
relative error = 3.3746113820860384299029695058250e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3144
Order of pole (three term test) = 32.89
NO COMPLEX POLE (six term test) for Equation 1
memory used=1494.8MB, alloc=44.3MB, time=15.27
TOP MAIN SOLVE Loop
x[1] = 0.34999976733337986666223492088736
y[1] (closed_form) = 1.3428975888947679243343773638571
y[1] (numeric) = 1.3428975888947679243343773638521
absolute error = 5.0e-30
relative error = 3.7232921120329822539123426051209e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3221
Order of pole (three term test) = 32.88
NO COMPLEX POLE (six term test) for Equation 1
memory used=1536.3MB, alloc=44.3MB, time=15.69
TOP MAIN SOLVE Loop
x[1] = 0.35999976066671453332877460343436
y[1] (closed_form) = 1.3522740092838182189817141285627
y[1] (numeric) = 1.352274009283818218981714128558
absolute error = 4.7e-30
relative error = 3.4756269570611511673312575434548e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3297
Order of pole (three term test) = 32.88
NO COMPLEX POLE (six term test) for Equation 1
memory used=1577.7MB, alloc=44.3MB, time=16.11
TOP MAIN SOLVE Loop
x[1] = 0.36999975400004919999531428598136
y[1] (closed_form) = 1.3616152026124698877008091140464
y[1] (numeric) = 1.3616152026124698877008091140412
absolute error = 5.2e-30
relative error = 3.8189937876890576194697885252957e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3371
Order of pole (three term test) = 32.87
NO COMPLEX POLE (six term test) for Equation 1
memory used=1619.1MB, alloc=44.3MB, time=16.53
TOP MAIN SOLVE Loop
x[1] = 0.37999974733338386666185396852836
y[1] (closed_form) = 1.3709202347704198381724329693914
y[1] (numeric) = 1.3709202347704198381724329693859
absolute error = 5.5e-30
relative error = 4.0119037275141346987261548654402e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3445
Order of pole (three term test) = 32.86
NO COMPLEX POLE (six term test) for Equation 1
memory used=1660.4MB, alloc=44.3MB, time=16.94
TOP MAIN SOLVE Loop
x[1] = 0.38999974066671853332839365107536
y[1] (closed_form) = 1.3801881752634470926342127327004
y[1] (numeric) = 1.3801881752634470926342127326946
absolute error = 5.8e-30
relative error = 4.2023255262949268187977799762752e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3516
Order of pole (three term test) = 32.86
NO COMPLEX POLE (six term test) for Equation 1
memory used=1701.8MB, alloc=44.3MB, time=17.36
TOP MAIN SOLVE Loop
x[1] = 0.39999973400005319999493333362236
y[1] (closed_form) = 1.3894180973064613105053797453493
y[1] (numeric) = 1.389418097306461310505379745343
absolute error = 6.3e-30
relative error = 4.5342723059482512029860575227554e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3587
Order of pole (three term test) = 32.85
NO COMPLEX POLE (six term test) for Equation 1
memory used=1743.3MB, alloc=44.3MB, time=17.78
TOP MAIN SOLVE Loop
x[1] = 0.40999972733338786666147301616936
y[1] (closed_form) = 1.3986090779161804015332735457428
y[1] (numeric) = 1.3986090779161804015332735457364
absolute error = 6.4e-30
relative error = 4.5759748746486803345250997326111e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3656
Order of pole (three term test) = 32.84
NO COMPLEX POLE (six term test) for Equation 1
memory used=1784.7MB, alloc=44.3MB, time=18.20
TOP MAIN SOLVE Loop
x[1] = 0.41999972066672253332801269871636
y[1] (closed_form) = 1.4077601980034279617898749815799
y[1] (numeric) = 1.4077601980034279617898749815736
absolute error = 6.3e-30
relative error = 4.4751940060068804459444809967830e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3723
Order of pole (three term test) = 32.83
NO COMPLEX POLE (six term test) for Equation 1
memory used=1826.2MB, alloc=44.3MB, time=18.62
TOP MAIN SOLVE Loop
x[1] = 0.42999971400005719999455238126336
y[1] (closed_form) = 1.4168705424650413028639892740658
y[1] (numeric) = 1.4168705424650413028639892740591
absolute error = 6.7e-30
relative error = 4.7287312419831117233676833611100e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3789
Order of pole (three term test) = 32.83
NO COMPLEX POLE (six term test) for Equation 1
memory used=1867.5MB, alloc=44.3MB, time=19.05
TOP MAIN SOLVE Loop
x[1] = 0.43999970733339186666109206381036
y[1] (closed_form) = 1.4259392002753808835350037779095
y[1] (numeric) = 1.4259392002753808835350037779027
absolute error = 6.8e-30
relative error = 4.7687867748405873718559374233593e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3854
Order of pole (three term test) = 32.82
NO COMPLEX POLE (six term test) for Equation 1
memory used=1909.0MB, alloc=44.3MB, time=19.47
TOP MAIN SOLVE Loop
x[1] = 0.44999970066672653332763174635736
y[1] (closed_form) = 1.434965264577431993073511714562
y[1] (numeric) = 1.4349652645774319930735117145547
absolute error = 7.3e-30
relative error = 5.0872311547901482687485194093515e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3917
Order of pole (three term test) = 32.81
NO COMPLEX POLE (six term test) for Equation 1
memory used=1950.2MB, alloc=44.3MB, time=19.88
TOP MAIN SOLVE Loop
x[1] = 0.45999969400006119999417142890436
y[1] (closed_form) = 1.4439478327734895760885363148617
y[1] (numeric) = 1.4439478327734895760885363148544
absolute error = 7.3e-30
relative error = 5.0555843045786423116230755183730e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3978
Order of pole (three term test) = 32.8
NO COMPLEX POLE (six term test) for Equation 1
memory used=1991.6MB, alloc=44.3MB, time=20.30
TOP MAIN SOLVE Loop
x[1] = 0.46999968733339586666071111145136
y[1] (closed_form) = 1.4528860066154171305265321861528
y[1] (numeric) = 1.4528860066154171305265321861455
absolute error = 7.3e-30
relative error = 5.0244822833731991570886308164190e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4038
Order of pole (three term test) = 32.79
NO COMPLEX POLE (six term test) for Equation 1
memory used=2032.8MB, alloc=44.3MB, time=20.72
TOP MAIN SOLVE Loop
x[1] = 0.47999968066673053332725079399836
y[1] (closed_form) = 1.4617788922944706530196138140953
y[1] (numeric) = 1.4617788922944706530196138140878
absolute error = 7.5e-30
relative error = 5.1307349145175296040952071681369e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4096
Order of pole (three term test) = 32.79
NO COMPLEX POLE (six term test) for Equation 1
memory used=2074.3MB, alloc=44.3MB, time=21.14
TOP MAIN SOLVE Loop
x[1] = 0.48999967400006519999379047654536
y[1] (closed_form) = 1.4706256005306786492753057346478
y[1] (numeric) = 1.4706256005306786492753057346398
absolute error = 8.0e-30
relative error = 5.4398617820288056302491917757802e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4152
Order of pole (three term test) = 32.78
NO COMPLEX POLE (six term test) for Equation 1
memory used=2115.6MB, alloc=44.3MB, time=21.56
TOP MAIN SOLVE Loop
x[1] = 0.49999966733339986666033015909236
y[1] (closed_form) = 1.4794252466617692715931756246604
y[1] (numeric) = 1.4794252466617692715931756246518
absolute error = 8.6e-30
relative error = 5.8130682975739147464792749325567e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4207
Order of pole (three term test) = 32.77
NO COMPLEX POLE (six term test) for Equation 1
memory used=2157.0MB, alloc=44.3MB, time=21.98
TOP MAIN SOLVE Loop
x[1] = 0.50999966066673453332686984163936
y[1] (closed_form) = 1.4881769507316356908805610964114
y[1] (numeric) = 1.4881769507316356908805610964028
absolute error = 8.6e-30
relative error = 5.7788826763994450932295289266742e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4261
Order of pole (three term test) = 32.76
NO COMPLEX POLE (six term test) for Equation 1
memory used=2198.4MB, alloc=44.3MB, time=22.39
TOP MAIN SOLVE Loop
x[1] = 0.51999965400006919999340952418636
y[1] (closed_form) = 1.4968798375783308567157047010742
y[1] (numeric) = 1.4968798375783308567157047010654
absolute error = 8.8e-30
relative error = 5.8788954056838253633907775947043e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4312
Order of pole (three term test) = 32.75
NO COMPLEX POLE (six term test) for Equation 1
memory used=2239.9MB, alloc=44.3MB, time=22.81
TOP MAIN SOLVE Loop
x[1] = 0.52999964733340386665994920673336
y[1] (closed_form) = 1.5055330369215828460673519827781
y[1] (numeric) = 1.5055330369215828460673519827689
absolute error = 9.2e-30
relative error = 6.1107925062950252327253373792713e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4362
Order of pole (three term test) = 32.74
NO COMPLEX POLE (six term test) for Equation 1
memory used=2281.3MB, alloc=44.3MB, time=23.23
TOP MAIN SOLVE Loop
x[1] = 0.53999964066673853332648888928036
y[1] (closed_form) = 1.5141356834498220492205383500886
y[1] (numeric) = 1.5141356834498220492205383500792
absolute error = 9.4e-30
relative error = 6.2081622556988716923646622410379e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.441
Order of pole (three term test) = 32.74
NO COMPLEX POLE (six term test) for Equation 1
memory used=2322.7MB, alloc=44.3MB, time=23.66
TOP MAIN SOLVE Loop
x[1] = 0.54999963400007319999302857182736
y[1] (closed_form) = 1.5226869169067114902740980246259
y[1] (numeric) = 1.5226869169067114902740980246161
absolute error = 9.8e-30
relative error = 6.4359914642915422463778767955981e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4456
Order of pole (three term test) = 32.73
NO COMPLEX POLE (six term test) for Equation 1
memory used=2364.1MB, alloc=44.3MB, time=24.08
TOP MAIN SOLVE Loop
x[1] = 0.55999962733340786665956825437436
y[1] (closed_form) = 1.5311858821771716292614908536028
y[1] (numeric) = 1.5311858821771716292614908535928
absolute error = 1.00e-29
relative error = 6.5308857117864363498109928969694e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4501
Order of pole (three term test) = 32.72
NO COMPLEX POLE (six term test) for Equation 1
memory used=2405.6MB, alloc=44.3MB, time=24.50
TOP MAIN SOLVE Loop
x[1] = 0.56999962066674253332610793692136
y[1] (closed_form) = 1.5396317293728910434978917760803
y[1] (numeric) = 1.5396317293728910434978917760698
absolute error = 1.05e-29
relative error = 6.8198126861653894448908357152619e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4543
Order of pole (three term test) = 32.71
NO COMPLEX POLE (six term test) for Equation 1
memory used=2447.0MB, alloc=44.3MB, time=24.92
memory used=2488.4MB, alloc=44.3MB, time=25.34
TOP MAIN SOLVE Loop
x[1] = 0.57999961400007719999264761946836
y[1] (closed_form) = 1.548023613917314437168068125661
y[1] (numeric) = 1.5480236139173144371680681256502
absolute error = 1.08e-29
relative error = 6.9766377611452038353433026325551e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4584
Order of pole (three term test) = 32.7
NO COMPLEX POLE (six term test) for Equation 1
memory used=2529.9MB, alloc=44.3MB, time=25.77
TOP MAIN SOLVE Loop
x[1] = 0.58999960733341186665918730201536
y[1] (closed_form) = 1.556360696630099480436240626846
y[1] (numeric) = 1.5563606966300994804362406268352
absolute error = 1.08e-29
relative error = 6.9392654436626639467249799045039e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4623
Order of pole (three term test) = 32.69
NO COMPLEX POLE (six term test) for Equation 1
memory used=2571.4MB, alloc=44.3MB, time=26.19
TOP MAIN SOLVE Loop
x[1] = 0.59999960066674653332572698456236
y[1] (closed_form) = 1.564642143811034032475658281804
y[1] (numeric) = 1.564642143811034032475658281793
absolute error = 1.10e-29
relative error = 7.0303615708618539398641310781183e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.466
Order of pole (three term test) = 32.68
NO COMPLEX POLE (six term test) for Equation 1
memory used=2612.8MB, alloc=44.3MB, time=26.59
TOP MAIN SOLVE Loop
x[1] = 0.60999959400008119999226666710936
y[1] (closed_form) = 1.5728671273234053567767037467753
y[1] (numeric) = 1.5728671273234053567767037467644
absolute error = 1.09e-29
relative error = 6.9300195869366621602850776893383e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4695
Order of pole (three term test) = 32.67
NO COMPLEX POLE (six term test) for Equation 1
memory used=2654.1MB, alloc=44.3MB, time=27.01
TOP MAIN SOLVE Loop
x[1] = 0.61999958733341586665880634965636
y[1] (closed_form) = 1.5810348246768129918925882062651
y[1] (numeric) = 1.5810348246768129918925882062543
absolute error = 1.08e-29
relative error = 6.8309690788801445022423946506033e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4729
Order of pole (three term test) = 32.66
NO COMPLEX POLE (six term test) for Equation 1
memory used=2695.5MB, alloc=44.3MB, time=27.44
TOP MAIN SOLVE Loop
x[1] = 0.62999958066675053332534603220336
y[1] (closed_form) = 1.5891444191094169964156131973061
y[1] (numeric) = 1.5891444191094169964156131972949
absolute error = 1.12e-29
relative error = 7.0478175962614313956395471825375e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.476
Order of pole (three term test) = 32.65
NO COMPLEX POLE (six term test) for Equation 1
memory used=2736.8MB, alloc=44.3MB, time=27.86
TOP MAIN SOLVE Loop
x[1] = 0.63999957400008519999188571475036
y[1] (closed_form) = 1.5971950996696133434390079773313
y[1] (numeric) = 1.5971950996696133434390079773199
absolute error = 1.14e-29
relative error = 7.1375125069931274478288366716071e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.479
Order of pole (three term test) = 32.64
NO COMPLEX POLE (six term test) for Equation 1
memory used=2778.3MB, alloc=44.3MB, time=28.28
TOP MAIN SOLVE Loop
x[1] = 0.64999956733341986665842539729736
y[1] (closed_form) = 1.6051860612971282970438487190493
y[1] (numeric) = 1.6051860612971282970438487190381
absolute error = 1.12e-29
relative error = 6.9773842858748956513132104358725e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = 32.63
NO COMPLEX POLE (six term test) for Equation 1
memory used=2819.7MB, alloc=44.3MB, time=28.70
TOP MAIN SOLVE Loop
x[1] = 0.65999956066675453332496507984436
y[1] (closed_form) = 1.61311650490352366145180165977
y[1] (numeric) = 1.613116504903523661451801659758
absolute error = 1.20e-29
relative error = 7.4390163162565180353124804994749e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4844
Order of pole (three term test) = 32.62
NO COMPLEX POLE (six term test) for Equation 1
memory used=2861.1MB, alloc=44.3MB, time=29.13
TOP MAIN SOLVE Loop
x[1] = 0.66999955400008919999150476239136
y[1] (closed_form) = 1.6209856374521048523965962634628
y[1] (numeric) = 1.6209856374521048523965962634507
absolute error = 1.21e-29
relative error = 7.4645942076445559138241584610394e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4867
Order of pole (three term test) = 32.61
NO COMPLEX POLE (six term test) for Equation 1
memory used=2902.5MB, alloc=44.3MB, time=29.53
TOP MAIN SOLVE Loop
x[1] = 0.67999954733342386665804444493836
y[1] (closed_form) = 1.6287926720372237999843353120038
y[1] (numeric) = 1.6287926720372237999843353119915
absolute error = 1.23e-29
relative error = 7.5516056838687082087161437857258e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4889
Order of pole (three term test) = 32.6
NO COMPLEX POLE (six term test) for Equation 1
memory used=2943.9MB, alloc=44.3MB, time=29.95
TOP MAIN SOLVE Loop
x[1] = 0.68999954066675853332458412748536
y[1] (closed_form) = 1.6365368279629687528290149652144
y[1] (numeric) = 1.6365368279629687528290149652019
absolute error = 1.25e-29
relative error = 7.6380804797158207588813470348920e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4909
Order of pole (three term test) = 32.59
NO COMPLEX POLE (six term test) for Equation 1
memory used=2985.3MB, alloc=44.3MB, time=30.37
TOP MAIN SOLVE Loop
x[1] = 0.69999953400009319999112381003236
y[1] (closed_form) = 1.6442173308212331145589076493069
y[1] (numeric) = 1.6442173308212331145589076492943
absolute error = 1.26e-29
relative error = 7.6632205267576820512280063821719e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4927
Order of pole (three term test) = 32.58
NO COMPLEX POLE (six term test) for Equation 1
memory used=3026.7MB, alloc=44.3MB, time=30.80
TOP MAIN SOLVE Loop
x[1] = 0.70999952733342786665766349257936
y[1] (closed_form) = 1.6518334125691555058856232815093
y[1] (numeric) = 1.6518334125691555058856232814965
absolute error = 1.28e-29
relative error = 7.7489654238751005867679857063080e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4943
Order of pole (three term test) = 32.58
NO COMPLEX POLE (six term test) for Equation 1
memory used=3068.3MB, alloc=44.3MB, time=31.22
TOP MAIN SOLVE Loop
x[1] = 0.71999952066676253332420317512636
y[1] (closed_form) = 1.6593843116059233083045002587098
y[1] (numeric) = 1.659384311605923308304500258697
absolute error = 1.28e-29
relative error = 7.7137043603915854635729898661173e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4957
Order of pole (three term test) = 32.57
NO COMPLEX POLE (six term test) for Equation 1
memory used=3109.7MB, alloc=44.3MB, time=31.64
TOP MAIN SOLVE Loop
x[1] = 0.72999951400009719999074285767336
y[1] (closed_form) = 1.6668692728489320091461992071186
y[1] (numeric) = 1.6668692728489320091461992071054
absolute error = 1.32e-29
relative error = 7.9190373324473136768350866417104e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4969
Order of pole (three term test) = 32.56
NO COMPLEX POLE (six term test) for Equation 1
memory used=3151.1MB, alloc=44.3MB, time=32.06
TOP MAIN SOLVE Loop
x[1] = 0.73999950733343186665728254022036
y[1] (closed_form) = 1.6742875478092927321186146475802
y[1] (numeric) = 1.674287547809292732118614647567
absolute error = 1.32e-29
relative error = 7.8839504105919126401555904798538e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4979
Order of pole (three term test) = 32.55
NO COMPLEX POLE (six term test) for Equation 1
memory used=3192.6MB, alloc=44.3MB, time=32.48
TOP MAIN SOLVE Loop
x[1] = 0.74999950066676653332382222276736
y[1] (closed_form) = 1.6816383946666804026590406153193
y[1] (numeric) = 1.6816383946666804026590406153064
absolute error = 1.29e-29
relative error = 7.6710903134183759728171210105768e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4987
Order of pole (three term test) = 32.54
NO COMPLEX POLE (six term test) for Equation 1
memory used=3234.1MB, alloc=44.3MB, time=32.91
TOP MAIN SOLVE Loop
x[1] = 0.75999949400010119999036190531436
y[1] (closed_form) = 1.6889210783435150633524078645042
y[1] (numeric) = 1.688921078343515063352407864491
absolute error = 1.32e-29
relative error = 7.8156405111282587442964761282430e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4994
Order of pole (three term test) = 32.53
NO COMPLEX POLE (six term test) for Equation 1
memory used=3275.5MB, alloc=44.3MB, time=33.33
TOP MAIN SOLVE Loop
x[1] = 0.76999948733343586665690158786136
y[1] (closed_form) = 1.6961348705784689213557590626311
y[1] (numeric) = 1.6961348705784689213557590626176
absolute error = 1.35e-29
relative error = 7.9592727171488480137989170000299e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4998
Order of pole (three term test) = 32.52
NO COMPLEX POLE (six term test) for Equation 1
memory used=3317.0MB, alloc=44.3MB, time=33.75
TOP MAIN SOLVE Loop
x[1] = 0.77999948066677053332344127040836
y[1] (closed_form) = 1.7032790499992917771952759669598
y[1] (numeric) = 1.7032790499992917771952759669458
absolute error = 1.40e-29
relative error = 8.2194400265803898632281573265353e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5
Order of pole (three term test) = 32.51
NO COMPLEX POLE (six term test) for Equation 1
memory used=3358.3MB, alloc=44.3MB, time=34.17
TOP MAIN SOLVE Loop
x[1] = 0.78999947400010519998998095295536
y[1] (closed_form) = 1.710352902194947552463376425481
y[1] (numeric) = 1.7103529021949475524633764254663
absolute error = 1.47e-29
relative error = 8.5947174884990377626189656185833e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5
Order of pole (three term test) = 32.5
NO COMPLEX POLE (six term test) for Equation 1
memory used=3399.7MB, alloc=44.3MB, time=34.59
TOP MAIN SOLVE Loop
x[1] = 0.79999946733343986665652063550236
y[1] (closed_form) = 1.7173557197870547028328431036791
y[1] (numeric) = 1.7173557197870547028328431036645
absolute error = 1.46e-29
relative error = 8.5014419737166287759197776236514e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4998
Order of pole (three term test) = 32.49
NO COMPLEX POLE (six term test) for Equation 1
memory used=3441.0MB, alloc=44.3MB, time=35.02
TOP MAIN SOLVE Loop
x[1] = 0.80999946066677453332306031804936
y[1] (closed_form) = 1.7242868025006233724157412278513
y[1] (numeric) = 1.7242868025006233724157412278361
absolute error = 1.52e-29
relative error = 8.8152388442319501098578612010763e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4994
Order of pole (three term test) = 32.48
NO COMPLEX POLE (six term test) for Equation 1
memory used=3482.4MB, alloc=44.3MB, time=35.42
TOP MAIN SOLVE Loop
x[1] = 0.81999945400010919998960000059636
y[1] (closed_form) = 1.731145457234082215820068343705
y[1] (numeric) = 1.73114545723408221582006834369
absolute error = 1.50e-29
relative error = 8.6647831569081883100424670765834e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4988
Order of pole (three term test) = 32.47
NO COMPLEX POLE (six term test) for Equation 1
memory used=3523.8MB, alloc=44.3MB, time=35.84
TOP MAIN SOLVE Loop
x[1] = 0.82999944733344386665613968314336
y[1] (closed_form) = 1.7379309981285878852896226648029
y[1] (numeric) = 1.7379309981285878852896226647877
absolute error = 1.52e-29
relative error = 8.7460319289818928988207730414859e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.498
Order of pole (three term test) = 32.46
NO COMPLEX POLE (six term test) for Equation 1
memory used=3565.2MB, alloc=44.3MB, time=36.27
TOP MAIN SOLVE Loop
x[1] = 0.83999944066677853332267936569036
y[1] (closed_form) = 1.7446427466366102520453748434461
y[1] (numeric) = 1.7446427466366102520453748434306
absolute error = 1.55e-29
relative error = 8.8843403784995520408890057308995e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.497
Order of pole (three term test) = 32.45
NO COMPLEX POLE (six term test) for Equation 1
memory used=3606.7MB, alloc=44.3MB, time=36.69
TOP MAIN SOLVE Loop
x[1] = 0.84999943400011319998921904823736
y[1] (closed_form) = 1.7512800315897865033725077263133
y[1] (numeric) = 1.7512800315897865033725077262978
absolute error = 1.55e-29
relative error = 8.8506690651462095267619683660384e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4958
Order of pole (three term test) = 32.44
NO COMPLEX POLE (six term test) for Equation 1
memory used=3648.1MB, alloc=44.3MB, time=37.11
TOP MAIN SOLVE Loop
x[1] = 0.85999942733344786665575873078436
y[1] (closed_form) = 1.7578421892660373301090073406376
y[1] (numeric) = 1.7578421892660373301090073406217
absolute error = 1.59e-29
relative error = 9.0451805611963522586414779471473e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4944
Order of pole (three term test) = 32.43
NO COMPLEX POLE (six term test) for Equation 1
memory used=3689.6MB, alloc=44.3MB, time=37.53
TOP MAIN SOLVE Loop
x[1] = 0.86999942066678253332229841333136
y[1] (closed_form) = 1.7643285634559384929819348927076
y[1] (numeric) = 1.7643285634559384929819348926913
absolute error = 1.63e-29
relative error = 9.2386420180557647533182700549534e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4929
Order of pole (three term test) = 32.42
NO COMPLEX POLE (six term test) for Equation 1
memory used=3731.1MB, alloc=44.3MB, time=37.95
TOP MAIN SOLVE Loop
x[1] = 0.87999941400011719998883809587836
y[1] (closed_form) = 1.7707385055283411306989049957094
y[1] (numeric) = 1.7707385055283411306989049956934
absolute error = 1.60e-29
relative error = 9.0357779819251328949247677534447e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4911
Order of pole (three term test) = 32.41
NO COMPLEX POLE (six term test) for Equation 1
memory used=3772.6MB, alloc=44.3MB, time=38.38
memory used=3813.9MB, alloc=44.3MB, time=38.80
TOP MAIN SOLVE Loop
x[1] = 0.88999940733345186665537777842536
y[1] (closed_form) = 1.7770713744952342478273936108082
y[1] (numeric) = 1.7770713744952342478273936107922
absolute error = 1.60e-29
relative error = 9.0035775881791453725608897627997e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4891
Order of pole (three term test) = 32.4
NO COMPLEX POLE (six term test) for Equation 1
memory used=3855.3MB, alloc=44.3MB, time=39.22
TOP MAIN SOLVE Loop
x[1] = 0.89999940066678653332191746097236
y[1] (closed_form) = 1.7833265370758428962757878467011
y[1] (numeric) = 1.7833265370758428962757878466851
absolute error = 1.60e-29
relative error = 8.9719968089722526103083598636737e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4869
Order of pole (three term test) = 32.39
NO COMPLEX POLE (six term test) for Equation 1
memory used=3896.8MB, alloc=44.3MB, time=39.62
TOP MAIN SOLVE Loop
x[1] = 0.90999939400012119998845714351936
y[1] (closed_form) = 1.7895033677599556406199907630466
y[1] (numeric) = 1.7895033677599556406199907630302
absolute error = 1.64e-29
relative error = 9.1645538619628345180060360824091e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4846
Order of pole (three term test) = 32.38
NO COMPLEX POLE (six term test) for Equation 1
memory used=3938.2MB, alloc=44.3MB, time=40.05
TOP MAIN SOLVE Loop
x[1] = 0.91999938733345586665499682606636
y[1] (closed_form) = 1.7956012488704749745902647459647
y[1] (numeric) = 1.7956012488704749745902647459484
absolute error = 1.63e-29
relative error = 9.0777392866336742071202349838609e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.482
Order of pole (three term test) = 32.37
NO COMPLEX POLE (six term test) for Equation 1
memory used=3979.6MB, alloc=44.3MB, time=40.47
TOP MAIN SOLVE Loop
x[1] = 0.92999938066679053332153650861336
y[1] (closed_form) = 1.8016195706251844337371298566764
y[1] (numeric) = 1.8016195706251844337371298566603
absolute error = 1.61e-29
relative error = 8.9364038127167432149398525027628e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4792
Order of pole (three term test) = 32.36
NO COMPLEX POLE (six term test) for Equation 1
memory used=4020.9MB, alloc=44.3MB, time=40.89
TOP MAIN SOLVE Loop
x[1] = 0.93999937400012519998807619116036
y[1] (closed_form) = 1.8075577311977262276247584591315
y[1] (numeric) = 1.807557731197726227624758459115
absolute error = 1.65e-29
relative error = 9.1283391480208760954824687432672e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4763
Order of pole (three term test) = 32.35
NO COMPLEX POLE (six term test) for Equation 1
memory used=4062.4MB, alloc=44.3MB, time=41.31
TOP MAIN SOLVE Loop
x[1] = 0.94999936733345986665461587370736
y[1] (closed_form) = 1.8134151367777832938475915223917
y[1] (numeric) = 1.8134151367777832938475915223747
absolute error = 1.70e-29
relative error = 9.3745770922630098477084175551672e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4732
Order of pole (three term test) = 32.34
NO COMPLEX POLE (six term test) for Equation 1
memory used=4103.7MB, alloc=44.3MB, time=41.73
TOP MAIN SOLVE Loop
x[1] = 0.95999936066679453332115555625436
y[1] (closed_form) = 1.8191912016304597557229506164988
y[1] (numeric) = 1.8191912016304597557229506164813
absolute error = 1.75e-29
relative error = 9.6196595411826597744895475187165e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4698
Order of pole (three term test) = 32.33
NO COMPLEX POLE (six term test) for Equation 1
memory used=4145.2MB, alloc=44.3MB, time=42.16
TOP MAIN SOLVE Loop
x[1] = 0.96999935400012919998769523880136
y[1] (closed_form) = 1.8248853481548538456712771486098
y[1] (numeric) = 1.8248853481548538456712771485921
absolute error = 1.77e-29
relative error = 9.6992394716174988258678178182953e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4663
Order of pole (three term test) = 32.32
NO COMPLEX POLE (six term test) for Equation 1
memory used=4186.7MB, alloc=44.3MB, time=42.58
TOP MAIN SOLVE Loop
x[1] = 0.97999934733346386665423492134836
y[1] (closed_form) = 1.8304970069418174370482810110446
y[1] (numeric) = 1.8304970069418174370482810110267
absolute error = 1.79e-29
relative error = 9.7787649649890706476121218470744e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4626
Order of pole (three term test) = 32.31
NO COMPLEX POLE (six term test) for Equation 1
memory used=4228.2MB, alloc=44.3MB, time=43.02
TOP MAIN SOLVE Loop
x[1] = 0.98999934066679853332077460389536
y[1] (closed_form) = 1.8360256168308964085316493475843
y[1] (numeric) = 1.8360256168308964085316493475662
absolute error = 1.81e-29
relative error = 9.8582502521080377296420055544889e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4587
Order of pole (three term test) = 32.3
NO COMPLEX POLE (six term test) for Equation 1
memory used=4269.6MB, alloc=44.3MB, time=43.42
TOP MAIN SOLVE Loop
x[1] = 0.99999933400013319998731428644236
y[1] (closed_form) = 1.8414706249664461470809188306326
y[1] (numeric) = 1.8414706249664461470809188306144
absolute error = 1.82e-29
relative error = 9.8834050096952408991237772863609e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4546
Order of pole (three term test) = 32.29
NO COMPLEX POLE (six term test) for Equation 1
memory used=4311.0MB, alloc=44.3MB, time=43.84
TOP MAIN SOLVE Loop
x[1] = 1.0099993273334678666538539689923
y[1] (closed_form) = 1.8468314868529165779744601636427
y[1] (numeric) = 1.8468314868529165779744601636229
absolute error = 1.98e-29
relative error = 1.0721064775509153367027991498332e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4504
Order of pole (three term test) = 32.28
NO COMPLEX POLE (six term test) for Equation 1
memory used=4352.4MB, alloc=44.3MB, time=44.27
TOP MAIN SOLVE Loop
x[1] = 1.0199993206668025333203936515423
y[1] (closed_form) = 1.852107666409301193474013025698
y[1] (numeric) = 1.8521076664093011934740130256763
absolute error = 2.17e-29
relative error = 1.1716381500687806703658248855964e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.446
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
memory used=4393.8MB, alloc=44.3MB, time=44.69
TOP MAIN SOLVE Loop
x[1] = 1.0299993140001371999869333340923
y[1] (closed_form) = 1.8572986360227446352665387896946
y[1] (numeric) = 1.8572986360227446352665387896713
absolute error = 2.33e-29
relative error = 1.2545101551301987948498092971871e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4414
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
memory used=4435.3MB, alloc=44.3MB, time=45.11
TOP MAIN SOLVE Loop
x[1] = 1.0399993073334718666534730166423
y[1] (closed_form) = 1.8624038766013034699769672200156
y[1] (numeric) = 1.8624038766013034699769672199909
absolute error = 2.47e-29
relative error = 1.3262429438814835863301197901523e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4366
Order of pole (three term test) = 32.26
NO COMPLEX POLE (six term test) for Equation 1
memory used=4476.7MB, alloc=44.3MB, time=45.53
TOP MAIN SOLVE Loop
x[1] = 1.0499993006668065333200126991923
y[1] (closed_form) = 1.8674228776258548817252876904773
y[1] (numeric) = 1.8674228776258548817252876904512
absolute error = 2.61e-29
relative error = 1.3976480802881773446420445528310e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4316
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 1
memory used=4518.1MB, alloc=44.3MB, time=45.95
TOP MAIN SOLVE Loop
x[1] = 1.0599992940001411999865523817423
y[1] (closed_form) = 1.8723551372011480909089073529936
y[1] (numeric) = 1.8723551372011480909089073529657
absolute error = 2.79e-29
relative error = 1.4901019280832452683928910299010e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4265
Order of pole (three term test) = 32.24
NO COMPLEX POLE (six term test) for Equation 1
memory used=4559.5MB, alloc=44.3MB, time=46.38
TOP MAIN SOLVE Loop
x[1] = 1.0699992873334758666530920642923
y[1] (closed_form) = 1.8772001621059933941177474670801
y[1] (numeric) = 1.8772001621059933941177474670506
absolute error = 2.95e-29
relative error = 1.5714893166695947224760627269640e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4212
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 1
memory used=4601.0MB, alloc=44.3MB, time=46.80
TOP MAIN SOLVE Loop
x[1] = 1.0799992806668105333196317468423
y[1] (closed_form) = 1.8819574678425838063266021979682
y[1] (numeric) = 1.8819574678425838063266021979369
absolute error = 3.13e-29
relative error = 1.6631619223510574146934093468470e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4157
Order of pole (three term test) = 32.22
NO COMPLEX POLE (six term test) for Equation 1
memory used=4642.5MB, alloc=44.3MB, time=47.22
TOP MAIN SOLVE Loop
x[1] = 1.0899992740001451999861714293923
y[1] (closed_form) = 1.8866265786849443732482179847882
y[1] (numeric) = 1.886626578684944373248217984755
absolute error = 3.32e-29
relative error = 1.7597547058380653831428977673427e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4101
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
memory used=4683.9MB, alloc=44.3MB, time=47.63
TOP MAIN SOLVE Loop
x[1] = 1.0999992673334798666527111119423
y[1] (closed_form) = 1.8912070277265043089626922604681
y[1] (numeric) = 1.8912070277265043089626922604334
absolute error = 3.47e-29
relative error = 1.8348070566189815491052294176692e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4042
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
memory used=4725.3MB, alloc=44.3MB, time=48.05
TOP MAIN SOLVE Loop
x[1] = 1.1099992606668145333192507944923
y[1] (closed_form) = 1.8956983569267872016554147419412
y[1] (numeric) = 1.8956983569267872016554147419053
absolute error = 3.59e-29
relative error = 1.8937612025047756883358323389486e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3983
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 1
memory used=4766.7MB, alloc=44.3MB, time=48.47
TOP MAIN SOLVE Loop
x[1] = 1.1199992540001491999857904770423
y[1] (closed_form) = 1.9001001171572146184881111253115
y[1] (numeric) = 1.9001001171572146184881111252737
absolute error = 3.78e-29
relative error = 1.9893688579185757368016633665290e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3922
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
memory used=4807.9MB, alloc=44.3MB, time=48.89
memory used=4848.9MB, alloc=44.3MB, time=49.30
TOP MAIN SOLVE Loop
x[1] = 1.1299992473334838666523301595923
y[1] (closed_form) = 1.9044118682460185292867786673725
y[1] (numeric) = 1.9044118682460185292867786673334
absolute error = 3.91e-29
relative error = 2.0531273015018265160517199834196e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3859
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
memory used=4890.1MB, alloc=44.3MB, time=49.72
TOP MAIN SOLVE Loop
x[1] = 1.1399992406668185333188698421423
y[1] (closed_form) = 1.9086331790222580578475599750674
y[1] (numeric) = 1.9086331790222580578475599750268
absolute error = 4.06e-29
relative error = 2.1271766857159162788908817512220e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3794
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
memory used=4931.2MB, alloc=44.3MB, time=50.14
TOP MAIN SOLVE Loop
x[1] = 1.1499992340001531999854095246923
y[1] (closed_form) = 1.9127636273589361592279737185584
y[1] (numeric) = 1.9127636273589361592279737185169
absolute error = 4.15e-29
relative error = 2.1696355684733225754338250035870e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3729
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
memory used=4972.4MB, alloc=44.3MB, time=50.55
TOP MAIN SOLVE Loop
x[1] = 1.1599992273334878666519492072423
y[1] (closed_form) = 1.9168028002152119113974523809025
y[1] (numeric) = 1.9168028002152119113974523808601
absolute error = 4.24e-29
relative error = 2.2120168018973822638512342493389e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3661
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
memory used=5013.6MB, alloc=44.3MB, time=50.97
TOP MAIN SOLVE Loop
x[1] = 1.1699992206668225333184888897923
y[1] (closed_form) = 1.9207502936777042000588269917564
y[1] (numeric) = 1.9207502936777042000588269917124
absolute error = 4.40e-29
relative error = 2.2907714836660105844089302630221e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3592
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
memory used=5054.7MB, alloc=44.3MB, time=51.39
TOP MAIN SOLVE Loop
x[1] = 1.1799992140001571999850285723423
y[1] (closed_form) = 1.9246057130008826663122033825109
y[1] (numeric) = 1.9246057130008826663122033824661
absolute error = 4.48e-29
relative error = 2.3277495072040999256488972690417e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3522
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
memory used=5095.9MB, alloc=44.3MB, time=51.81
TOP MAIN SOLVE Loop
x[1] = 1.1899992073334918666515682548923
y[1] (closed_form) = 1.9283686726465418781055079531453
y[1] (numeric) = 1.9283686726465418781055079530993
absolute error = 4.60e-29
relative error = 2.3854359725139300262550650028634e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.345
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
memory used=5137.0MB, alloc=44.3MB, time=52.23
TOP MAIN SOLVE Loop
x[1] = 1.1999992006668265333181079374423
y[1] (closed_form) = 1.932038796322354778092716061782
y[1] (numeric) = 1.9320387963223547780927160617353
absolute error = 4.67e-29
relative error = 2.4171357267200677626523067929383e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3377
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
memory used=5178.1MB, alloc=44.3MB, time=52.66
TOP MAIN SOLVE Loop
x[1] = 1.2099991940001611999846476199923
y[1] (closed_form) = 1.9356157170195015525922453515251
y[1] (numeric) = 1.9356157170195015525922453514771
absolute error = 4.80e-29
relative error = 2.4798310727664128818987894124011e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3303
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
memory used=5219.3MB, alloc=44.3MB, time=53.08
TOP MAIN SOLVE Loop
x[1] = 1.2199991873334958666511873025423
y[1] (closed_form) = 1.9390990770493701587949925577568
y[1] (numeric) = 1.9390990770493701587949925577077
absolute error = 4.91e-29
relative error = 2.5321037269902169299589123095066e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3227
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
memory used=5260.4MB, alloc=44.3MB, time=53.48
TOP MAIN SOLVE Loop
x[1] = 1.2299991806668305333177269850923
y[1] (closed_form) = 1.9424885280793248402047699824
y[1] (numeric) = 1.9424885280793248402047699823499
absolute error = 5.01e-29
relative error = 2.5791658110607941176865455025246e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.315
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
memory used=5301.7MB, alloc=44.3MB, time=53.91
TOP MAIN SOLVE Loop
x[1] = 1.2399991740001651999842666676423
y[1] (closed_form) = 1.9457837311675390534941736417077
y[1] (numeric) = 1.9457837311675390534941736416564
absolute error = 5.13e-29
relative error = 2.6364697771020104952138353582693e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3072
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
memory used=5342.9MB, alloc=44.3MB, time=54.33
TOP MAIN SOLVE Loop
x[1] = 1.2499991673334998666508063501923
y[1] (closed_form) = 1.9489843567968893235168691534158
y[1] (numeric) = 1.9489843567968893235168691533631
absolute error = 5.27e-29
relative error = 2.7039724467881943461175233433731e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2992
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5384.0MB, alloc=44.3MB, time=54.75
TOP MAIN SOLVE Loop
x[1] = 1.2599991606668345333173460327423
y[1] (closed_form) = 1.9520900849079066371235580226381
y[1] (numeric) = 1.9520900849079066371235580225842
absolute error = 5.39e-29
relative error = 2.7611430648981975389877772401492e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2912
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
memory used=5425.0MB, alloc=44.3MB, time=55.16
TOP MAIN SOLVE Loop
x[1] = 1.2699991540001691999838857152923
y[1] (closed_form) = 1.9551006049307820806740955767975
y[1] (numeric) = 1.9551006049307820806740955767429
absolute error = 5.46e-29
relative error = 2.7926951616862215376397167508718e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.283
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
memory used=5466.2MB, alloc=44.3MB, time=55.58
TOP MAIN SOLVE Loop
x[1] = 1.2799991473335038666504253978423
y[1] (closed_form) = 1.9580156158164235207129479584238
y[1] (numeric) = 1.9580156158164235207129479583687
absolute error = 5.51e-29
relative error = 2.8140735730049446750617655734337e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2747
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
memory used=5507.4MB, alloc=44.3MB, time=56.00
TOP MAIN SOLVE Loop
x[1] = 1.2899991406668385333169650803923
y[1] (closed_form) = 1.9608348260665602221699419306148
y[1] (numeric) = 1.9608348260665602221699419305587
absolute error = 5.61e-29
relative error = 2.8610262962605956153528908475556e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2663
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
memory used=5548.6MB, alloc=44.3MB, time=56.41
memory used=5589.6MB, alloc=44.3MB, time=56.83
TOP MAIN SOLVE Loop
x[1] = 1.2999991340001731999835047629423
y[1] (closed_form) = 1.963557953762892393653588398444
y[1] (numeric) = 1.963557953762892393653588398387
absolute error = 5.70e-29
relative error = 2.9028936930925432593813157816550e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2578
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
memory used=5630.8MB, alloc=44.3MB, time=57.25
TOP MAIN SOLVE Loop
x[1] = 1.3099991273335078666500444454923
y[1] (closed_form) = 1.9661847265952827449106280599253
y[1] (numeric) = 1.9661847265952827449106280598678
absolute error = 5.75e-29
relative error = 2.9244454614175087831426664968604e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2491
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
memory used=5671.9MB, alloc=44.3MB, time=57.66
TOP MAIN SOLVE Loop
x[1] = 1.3199991206668425333165841280423
y[1] (closed_form) = 1.9687148818889872373233049278869
y[1] (numeric) = 1.9687148818889872373233049278285
absolute error = 5.84e-29
relative error = 2.9664021203499534954955729546078e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2404
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
memory used=5713.0MB, alloc=44.3MB, time=58.08
TOP MAIN SOLVE Loop
x[1] = 1.3299991140001771999831238105923
y[1] (closed_form) = 1.971148166630922304395640916125
y[1] (numeric) = 1.971148166630922304395640916066
absolute error = 5.90e-29
relative error = 2.9931793560117065209169231209950e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2316
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
memory used=5754.1MB, alloc=44.3MB, time=58.50
TOP MAIN SOLVE Loop
x[1] = 1.3399991073335118666496634931423
y[1] (closed_form) = 1.9734843374949659155320543756466
y[1] (numeric) = 1.9734843374949659155320543755871
absolute error = 5.95e-29
relative error = 3.0149719898727990911483531194475e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2227
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
memory used=5795.3MB, alloc=44.3MB, time=58.92
TOP MAIN SOLVE Loop
x[1] = 1.3499991006668465333162031756923
y[1] (closed_form) = 1.9757231608662899530264022858283
y[1] (numeric) = 1.9757231608662899530264022857676
absolute error = 6.07e-29
relative error = 3.0722927787810634527290744479362e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2137
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
memory used=5836.5MB, alloc=44.3MB, time=59.34
TOP MAIN SOLVE Loop
x[1] = 1.3599990940001811999827428582423
y[1] (closed_form) = 1.9778644128647214690472683706373
y[1] (numeric) = 1.977864412864721469047268370576
absolute error = 6.13e-29
relative error = 3.0993024396052314638657755939484e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2046
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
memory used=5877.6MB, alloc=44.3MB, time=59.75
TOP MAIN SOLVE Loop
x[1] = 1.3699990873335158666492825407923
y[1] (closed_form) = 1.9799078793671304865163810410555
y[1] (numeric) = 1.9799078793671304865163810409936
absolute error = 6.19e-29
relative error = 3.1264080841875372318792023351709e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1954
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
memory used=5918.8MB, alloc=44.3MB, time=60.17
TOP MAIN SOLVE Loop
x[1] = 1.3799990806668505333158222233423
y[1] (closed_form) = 1.9818533560288421051217147492293
y[1] (numeric) = 1.9818533560288421051217147491667
absolute error = 6.26e-29
relative error = 3.1586595350039095474063473605559e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1862
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
memory used=5960.0MB, alloc=44.3MB, time=60.59
TOP MAIN SOLVE Loop
x[1] = 1.3899990740001851999823619058923
y[1] (closed_form) = 1.9837006483040707712753717047744
y[1] (numeric) = 1.9837006483040707712753717047111
absolute error = 6.33e-29
relative error = 3.1910056617724654023910812119153e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1769
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
memory used=6001.1MB, alloc=44.3MB, time=61.02
TOP MAIN SOLVE Loop
x[1] = 1.3999990673335198666489015884423
y[1] (closed_form) = 1.9854495714653746686090011890652
y[1] (numeric) = 1.9854495714653746686090011890012
absolute error = 6.40e-29
relative error = 3.2234512988795963833657366597531e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1675
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
memory used=6042.3MB, alloc=44.3MB, time=61.44
TOP MAIN SOLVE Loop
x[1] = 1.4099990606668545333154412709923
y[1] (closed_form) = 1.987099950622128283586512737735
y[1] (numeric) = 1.9870999506221282835865127376709
absolute error = 6.41e-29
relative error = 3.2258065317716577463588265893929e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.158
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
memory used=6083.5MB, alloc=44.3MB, time=61.84
TOP MAIN SOLVE Loop
x[1] = 1.4199990540001891999819809535423
y[1] (closed_form) = 1.9886516207380112989953786398176
y[1] (numeric) = 1.9886516207380112989953786397526
absolute error = 6.50e-29
relative error = 3.2685463518179095949788624406268e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1485
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
memory used=6124.6MB, alloc=44.3MB, time=62.27
TOP MAIN SOLVE Loop
x[1] = 1.4299990473335238666485206360923
y[1] (closed_form) = 1.9901044266475120664440824649681
y[1] (numeric) = 1.9901044266475120664440824649028
absolute error = 6.53e-29
relative error = 3.2812348500728176571278128135937e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1389
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
memory used=6165.8MB, alloc=44.3MB, time=62.69
TOP MAIN SOLVE Loop
x[1] = 1.4399990406668585333150603186423
y[1] (closed_form) = 1.9914582230714440075344171469674
y[1] (numeric) = 1.9914582230714440075344171469012
absolute error = 6.62e-29
relative error = 3.3241972757981908339444914880263e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1293
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
memory used=6206.9MB, alloc=44.3MB, time=63.11
TOP MAIN SOLVE Loop
x[1] = 1.4499990340001931999816000011923
y[1] (closed_form) = 1.9927128746314733920835145028156
y[1] (numeric) = 1.9927128746314733920835145027493
absolute error = 6.63e-29
relative error = 3.3271225796772820060244833236657e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1196
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
memory used=6248.1MB, alloc=44.3MB, time=63.52
memory used=6289.1MB, alloc=44.3MB, time=63.94
TOP MAIN SOLVE Loop
x[1] = 1.4599990273335278666481396837423
y[1] (closed_form) = 1.9938682558636570406318274297399
y[1] (numeric) = 1.9938682558636570406318274296732
absolute error = 6.67e-29
relative error = 3.3452561273216348955422378683731e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1099
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
memory used=6330.3MB, alloc=44.3MB, time=64.34
TOP MAIN SOLVE Loop
x[1] = 1.4699990206668625333146793662923
y[1] (closed_form) = 1.9949242512309885974799003590034
y[1] (numeric) = 1.9949242512309885974799003589366
absolute error = 6.68e-29
relative error = 3.3484980674720040423883167405379e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1001
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
memory used=6371.5MB, alloc=44.3MB, time=64.77
TOP MAIN SOLVE Loop
x[1] = 1.4799990140001971999812190488423
y[1] (closed_form) = 1.995880755134952119638752289782
y[1] (numeric) = 1.9958807551349521196387522897145
absolute error = 6.75e-29
relative error = 3.3819655721584411877812473344841e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0903
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
memory used=6412.6MB, alloc=44.3MB, time=65.19
TOP MAIN SOLVE Loop
x[1] = 1.4899990073335318666477587313923
y[1] (closed_form) = 1.9967376719260818263461457755348
y[1] (numeric) = 1.9967376719260818263461457754672
absolute error = 6.76e-29
relative error = 3.3855223422910666796927515317157e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08045
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
memory used=6453.8MB, alloc=44.3MB, time=65.59
TOP MAIN SOLVE Loop
x[1] = 1.4999990006668665333142984139423
y[1] (closed_form) = 1.9974949159135269531839979402871
y[1] (numeric) = 1.9974949159135269531839979402189
absolute error = 6.82e-29
relative error = 3.4142765248946660617082608285608e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07056
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
memory used=6494.9MB, alloc=44.3MB, time=66.02
TOP MAIN SOLVE Loop
x[1] = 1.5099989940002011999808380964923
y[1] (closed_form) = 1.9981524113736207543207677608644
y[1] (numeric) = 1.9981524113736207543207677607957
absolute error = 6.87e-29
relative error = 3.4381761675913649946179344655036e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06065
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
memory used=6536.1MB, alloc=44.3MB, time=66.44
TOP MAIN SOLVE Loop
x[1] = 1.5199989873335358666473777790423
y[1] (closed_form) = 1.9987100925574527959868787017319
y[1] (numeric) = 1.9987100925574527959868787016632
absolute error = 6.87e-29
relative error = 3.4372168457955201333411224927364e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05071
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
memory used=6577.3MB, alloc=44.3MB, time=66.86
TOP MAIN SOLVE Loop
x[1] = 1.5299989806668705333139174615923
y[1] (closed_form) = 1.9991679036974437839611490054679
y[1] (numeric) = 1.9991679036974437839611490053991
absolute error = 6.88e-29
relative error = 3.4414318013386966538498423402345e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04075
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
memory used=6618.5MB, alloc=44.3MB, time=67.28
TOP MAIN SOLVE Loop
x[1] = 1.5399989740002051999804571441423
y[1] (closed_form) = 1.9995257990129222675918366290704
y[1] (numeric) = 1.9995257990129222675918366290015
absolute error = 6.89e-29
relative error = 3.4458170049125093737237743545873e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03078
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
memory used=6659.8MB, alloc=44.3MB, time=67.69
TOP MAIN SOLVE Loop
x[1] = 1.5499989673335398666469968266923
y[1] (closed_form) = 1.9997837427147026626872875072108
y[1] (numeric) = 1.9997837427147026626872875071423
absolute error = 6.85e-29
relative error = 3.4253703806498286194484923088478e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02079
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
memory used=6700.9MB, alloc=44.3MB, time=68.11
TOP MAIN SOLVE Loop
x[1] = 1.5599989606668745333135365092423
y[1] (closed_form) = 1.9999417090086641354783234765211
y[1] (numeric) = 1.9999417090086641354783234764526
absolute error = 6.85e-29
relative error = 3.4250998262321476845997127383304e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 9.9999933333346666665396825467373e-05
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0108
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
memory used=6742.1MB, alloc=44.3MB, time=68.53
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
TOP MAIN SOLVE Loop
x[1] = 1.5700692419926469577202759246453
y[1] (closed_form) = 1.9999997356738568135044570853918
y[1] (numeric) = 1.9999997356738568135044570853235
absolute error = 6.83e-29
relative error = 3.4150004513369491410186615291711e-27 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 8.0787161193420794939568999024857e-05
SETTING H FOR POLE
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0007271
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
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memory used=6783.4MB, alloc=44.3MB, time=68.94
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memory used=6824.4MB, alloc=44.3MB, time=69.38
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memory used=6865.3MB, alloc=44.3MB, time=69.80
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memory used=6906.2MB, alloc=44.3MB, time=70.22
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memory used=6947.1MB, alloc=44.3MB, time=70.64
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memory used=6988.0MB, alloc=44.3MB, time=71.06
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memory used=7028.9MB, alloc=44.3MB, time=71.48
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memory used=7069.9MB, alloc=44.3MB, time=71.92
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memory used=7110.7MB, alloc=44.3MB, time=72.34
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memory used=7151.6MB, alloc=44.3MB, time=72.77
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memory used=7192.5MB, alloc=44.3MB, time=73.19
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memory used=7233.3MB, alloc=44.3MB, time=73.61
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memory used=7274.2MB, alloc=44.3MB, time=74.05
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memory used=7315.1MB, alloc=44.3MB, time=74.47
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memory used=7356.1MB, alloc=44.3MB, time=74.89
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memory used=7397.0MB, alloc=44.3MB, time=75.31
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memory used=7438.0MB, alloc=44.3MB, time=75.73
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memory used=7478.9MB, alloc=44.3MB, time=76.16
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memory used=7519.8MB, alloc=44.3MB, time=76.58
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memory used=7560.8MB, alloc=44.3MB, time=77.02
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memory used=7601.7MB, alloc=44.3MB, time=77.44
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memory used=7642.7MB, alloc=44.3MB, time=77.86
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memory used=7683.5MB, alloc=44.3MB, time=78.28
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memory used=7724.5MB, alloc=44.3MB, time=78.70
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memory used=7765.4MB, alloc=44.3MB, time=79.14
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memory used=7806.4MB, alloc=44.3MB, time=79.56
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memory used=7847.3MB, alloc=44.3MB, time=79.98
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memory used=7888.1MB, alloc=44.3MB, time=80.41
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memory used=7929.0MB, alloc=44.3MB, time=80.83
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memory used=7970.0MB, alloc=44.3MB, time=81.25
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memory used=8010.9MB, alloc=44.3MB, time=81.69
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memory used=8051.8MB, alloc=44.3MB, time=82.11
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memory used=8092.7MB, alloc=44.3MB, time=82.55
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memory used=8133.5MB, alloc=44.3MB, time=82.97
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memory used=8174.4MB, alloc=44.3MB, time=83.39
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memory used=8215.3MB, alloc=44.3MB, time=83.81
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memory used=8256.2MB, alloc=44.3MB, time=84.23
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memory used=8297.1MB, alloc=44.3MB, time=84.67
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memory used=8338.1MB, alloc=44.3MB, time=85.09
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memory used=8379.0MB, alloc=44.3MB, time=85.52
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memory used=8419.9MB, alloc=44.3MB, time=85.94
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memory used=8460.8MB, alloc=44.3MB, time=86.38
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memory used=8501.6MB, alloc=44.3MB, time=86.80
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memory used=8542.5MB, alloc=44.3MB, time=87.22
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memory used=8583.3MB, alloc=44.3MB, time=87.64
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memory used=8624.2MB, alloc=44.3MB, time=88.06
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memory used=8665.2MB, alloc=44.3MB, time=88.48
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memory used=8706.1MB, alloc=44.3MB, time=88.91
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memory used=8746.9MB, alloc=44.3MB, time=89.34
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memory used=8787.9MB, alloc=44.3MB, time=89.76
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memory used=8828.8MB, alloc=44.3MB, time=90.19
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memory used=8869.7MB, alloc=44.3MB, time=90.61
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memory used=8910.6MB, alloc=44.3MB, time=91.03
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memory used=8951.5MB, alloc=44.3MB, time=91.45
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memory used=8992.4MB, alloc=44.3MB, time=91.89
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memory used=9033.3MB, alloc=44.3MB, time=92.31
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memory used=9074.1MB, alloc=44.3MB, time=92.73
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memory used=9115.0MB, alloc=44.3MB, time=93.16
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memory used=9155.9MB, alloc=44.3MB, time=93.58
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memory used=9196.8MB, alloc=44.3MB, time=94.02
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memory used=9237.6MB, alloc=44.3MB, time=94.44
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memory used=9278.4MB, alloc=44.3MB, time=94.86
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memory used=9319.4MB, alloc=44.3MB, time=95.28
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memory used=9360.2MB, alloc=44.3MB, time=95.70
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memory used=9401.1MB, alloc=44.3MB, time=96.13
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memory used=9441.9MB, alloc=44.3MB, time=96.55
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memory used=9482.9MB, alloc=44.3MB, time=96.98
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memory used=9523.8MB, alloc=44.3MB, time=97.41
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memory used=9564.6MB, alloc=44.3MB, time=97.83
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memory used=9605.6MB, alloc=44.3MB, time=98.25
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memory used=9646.6MB, alloc=44.3MB, time=98.67
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memory used=9687.5MB, alloc=44.3MB, time=99.09
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memory used=9728.3MB, alloc=44.3MB, time=99.53
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memory used=9769.2MB, alloc=44.3MB, time=99.95
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memory used=9810.0MB, alloc=44.3MB, time=100.38
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memory used=9850.9MB, alloc=44.3MB, time=100.80
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memory used=9891.8MB, alloc=44.3MB, time=101.23
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memory used=9932.7MB, alloc=44.3MB, time=101.66
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memory used=9973.6MB, alloc=44.3MB, time=102.08
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memory used=10014.4MB, alloc=44.3MB, time=102.50
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memory used=10055.3MB, alloc=44.3MB, time=102.92
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memory used=10096.2MB, alloc=44.3MB, time=103.36
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memory used=10137.1MB, alloc=44.3MB, time=103.78
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memory used=10178.0MB, alloc=44.3MB, time=104.20
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memory used=10218.9MB, alloc=44.3MB, time=104.63
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memory used=10259.8MB, alloc=44.3MB, time=105.06
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memory used=10300.7MB, alloc=44.3MB, time=105.48
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memory used=10341.6MB, alloc=44.3MB, time=105.91
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memory used=10382.5MB, alloc=44.3MB, time=106.34
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memory used=10423.3MB, alloc=44.3MB, time=106.77
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memory used=10464.2MB, alloc=44.3MB, time=107.19
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memory used=10505.1MB, alloc=44.3MB, time=107.61
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memory used=10546.0MB, alloc=44.3MB, time=108.03
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memory used=10586.9MB, alloc=44.3MB, time=108.47
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memory used=10627.9MB, alloc=44.3MB, time=108.89
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memory used=10668.7MB, alloc=44.3MB, time=109.31
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memory used=10709.6MB, alloc=44.3MB, time=109.73
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memory used=10750.5MB, alloc=44.3MB, time=110.16
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memory used=10791.3MB, alloc=44.3MB, time=110.59
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memory used=10832.3MB, alloc=44.3MB, time=111.02
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memory used=10873.1MB, alloc=44.3MB, time=111.44
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memory used=10914.1MB, alloc=44.3MB, time=111.86
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TOP MAIN SOLVE Loop
x[1] = 1.5800006545330880033857654165932
y[1] (closed_form) = 1.9999576404745022585371372596482
y[1] (numeric) = 1.9999576404745022585371372595813
absolute error = 6.69e-29
relative error = 3.3450708478069347147516949115340e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 1e-06
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NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.009204
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
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memory used=10955.1MB, alloc=44.3MB, time=112.30
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memory used=10996.0MB, alloc=44.3MB, time=112.72
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memory used=11036.9MB, alloc=44.3MB, time=113.14
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memory used=11077.7MB, alloc=44.3MB, time=113.58
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memory used=11118.6MB, alloc=44.3MB, time=114.00
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memory used=11159.5MB, alloc=44.3MB, time=114.42
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memory used=11200.4MB, alloc=44.3MB, time=114.84
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memory used=11241.5MB, alloc=44.3MB, time=115.28
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memory used=11282.4MB, alloc=44.3MB, time=115.70
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memory used=11323.3MB, alloc=44.3MB, time=116.12
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memory used=11364.1MB, alloc=44.3MB, time=116.55
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memory used=11405.0MB, alloc=44.3MB, time=116.97
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memory used=11445.8MB, alloc=44.3MB, time=117.39
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memory used=11486.7MB, alloc=44.3MB, time=117.81
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memory used=11527.6MB, alloc=44.3MB, time=118.25
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memory used=11568.6MB, alloc=44.3MB, time=118.67
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memory used=11609.4MB, alloc=44.3MB, time=119.09
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memory used=11650.2MB, alloc=44.3MB, time=119.52
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memory used=11691.1MB, alloc=44.3MB, time=119.94
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memory used=11731.9MB, alloc=44.3MB, time=120.37
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memory used=11772.8MB, alloc=44.3MB, time=120.80
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memory used=11813.7MB, alloc=44.3MB, time=121.22
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memory used=11854.7MB, alloc=44.3MB, time=121.64
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memory used=11895.6MB, alloc=44.3MB, time=122.06
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memory used=11936.5MB, alloc=44.3MB, time=122.50
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memory used=11977.3MB, alloc=44.3MB, time=122.92
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memory used=12018.3MB, alloc=44.3MB, time=123.34
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memory used=12059.2MB, alloc=44.3MB, time=123.77
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memory used=12100.1MB, alloc=44.3MB, time=124.19
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memory used=12141.0MB, alloc=44.3MB, time=124.61
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memory used=12181.9MB, alloc=44.3MB, time=125.03
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memory used=12222.8MB, alloc=44.3MB, time=125.45
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memory used=12263.8MB, alloc=44.3MB, time=125.87
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memory used=12304.7MB, alloc=44.3MB, time=126.31
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memory used=12345.5MB, alloc=44.3MB, time=126.73
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memory used=12386.4MB, alloc=44.3MB, time=127.16
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memory used=12427.3MB, alloc=44.3MB, time=127.58
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memory used=12468.2MB, alloc=44.3MB, time=128.00
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memory used=12509.1MB, alloc=44.3MB, time=128.42
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memory used=12550.0MB, alloc=44.3MB, time=128.84
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memory used=12591.0MB, alloc=44.3MB, time=129.27
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memory used=12631.9MB, alloc=44.3MB, time=129.69
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memory used=12672.8MB, alloc=44.3MB, time=130.13
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memory used=12713.7MB, alloc=44.3MB, time=130.55
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memory used=12754.6MB, alloc=44.3MB, time=130.97
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memory used=12795.4MB, alloc=44.3MB, time=131.39
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memory used=12836.3MB, alloc=44.3MB, time=131.81
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memory used=12877.2MB, alloc=44.3MB, time=132.23
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memory used=12918.2MB, alloc=44.3MB, time=132.66
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memory used=12959.0MB, alloc=44.3MB, time=133.08
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memory used=13000.0MB, alloc=44.3MB, time=133.52
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memory used=13040.9MB, alloc=44.3MB, time=133.94
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memory used=13081.9MB, alloc=44.3MB, time=134.36
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memory used=13122.8MB, alloc=44.3MB, time=134.78
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memory used=13163.7MB, alloc=44.3MB, time=135.20
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memory used=13204.7MB, alloc=44.3MB, time=135.64
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memory used=13245.7MB, alloc=44.3MB, time=136.06
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memory used=13286.6MB, alloc=44.3MB, time=136.48
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memory used=13327.5MB, alloc=44.3MB, time=136.91
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memory used=13368.3MB, alloc=44.3MB, time=137.33
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memory used=13409.2MB, alloc=44.3MB, time=137.75
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memory used=13450.1MB, alloc=44.3MB, time=138.17
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memory used=13491.0MB, alloc=44.3MB, time=138.59
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memory used=13532.0MB, alloc=44.3MB, time=139.02
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memory used=13572.9MB, alloc=44.3MB, time=139.44
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memory used=13613.9MB, alloc=44.3MB, time=139.88
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memory used=13654.8MB, alloc=44.3MB, time=140.30
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memory used=13695.8MB, alloc=44.3MB, time=140.72
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memory used=13736.7MB, alloc=44.3MB, time=141.14
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memory used=13777.6MB, alloc=44.3MB, time=141.56
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memory used=13818.6MB, alloc=44.3MB, time=142.00
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memory used=13859.5MB, alloc=44.3MB, time=142.42
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memory used=13900.4MB, alloc=44.3MB, time=142.84
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memory used=13941.3MB, alloc=44.3MB, time=143.26
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memory used=13982.3MB, alloc=44.3MB, time=143.69
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memory used=14023.2MB, alloc=44.3MB, time=144.11
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memory used=14064.1MB, alloc=44.3MB, time=144.55
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memory used=14105.0MB, alloc=44.3MB, time=144.97
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memory used=14146.0MB, alloc=44.3MB, time=145.39
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memory used=14187.0MB, alloc=44.3MB, time=145.81
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memory used=14227.9MB, alloc=44.3MB, time=146.23
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memory used=14268.8MB, alloc=44.3MB, time=146.66
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memory used=14309.7MB, alloc=44.3MB, time=147.08
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memory used=14350.6MB, alloc=44.3MB, time=147.50
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memory used=14391.5MB, alloc=44.3MB, time=147.92
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memory used=14432.4MB, alloc=44.3MB, time=148.36
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memory used=14473.3MB, alloc=44.3MB, time=148.78
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memory used=14514.2MB, alloc=44.3MB, time=149.20
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memory used=14555.1MB, alloc=44.3MB, time=149.63
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memory used=14596.1MB, alloc=44.3MB, time=150.05
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memory used=14636.9MB, alloc=44.3MB, time=150.47
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memory used=14677.9MB, alloc=44.3MB, time=150.94
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memory used=14718.8MB, alloc=44.3MB, time=151.36
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memory used=14759.7MB, alloc=44.3MB, time=151.78
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memory used=14800.6MB, alloc=44.3MB, time=152.20
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memory used=14841.5MB, alloc=44.3MB, time=152.64
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memory used=14882.5MB, alloc=44.3MB, time=153.06
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memory used=14923.5MB, alloc=44.3MB, time=153.48
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memory used=14964.4MB, alloc=44.3MB, time=153.91
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memory used=15005.3MB, alloc=44.3MB, time=154.33
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memory used=15046.1MB, alloc=44.3MB, time=154.75
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memory used=15087.1MB, alloc=44.3MB, time=155.17
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memory used=15128.0MB, alloc=44.3MB, time=155.59
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memory used=15168.9MB, alloc=44.3MB, time=156.01
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memory used=15209.9MB, alloc=44.3MB, time=156.45
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memory used=15250.7MB, alloc=44.3MB, time=156.88
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memory used=15291.6MB, alloc=44.3MB, time=157.30
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memory used=15332.5MB, alloc=44.3MB, time=157.72
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memory used=15373.5MB, alloc=44.3MB, time=158.14
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memory used=15414.3MB, alloc=44.3MB, time=158.56
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TOP MAIN SOLVE Loop
x[1] = 1.5900006545330880033857654165932
y[1] (closed_form) = 1.9998156025654097283893926681036
y[1] (numeric) = 1.9998156025654097283893926680376
absolute error = 6.60e-29
relative error = 3.3003042838216519981336012461981e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 1e-06
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NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0192
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
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memory used=15455.3MB, alloc=44.3MB, time=158.98
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memory used=15496.2MB, alloc=44.3MB, time=159.42
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memory used=15537.1MB, alloc=44.3MB, time=159.84
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memory used=15578.0MB, alloc=44.3MB, time=160.27
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memory used=15619.0MB, alloc=44.3MB, time=160.69
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memory used=15659.9MB, alloc=44.3MB, time=161.11
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memory used=15700.9MB, alloc=44.3MB, time=161.55
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memory used=15741.7MB, alloc=44.3MB, time=161.97
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memory used=15782.7MB, alloc=44.3MB, time=162.39
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memory used=15823.7MB, alloc=44.3MB, time=162.84
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memory used=15864.7MB, alloc=44.3MB, time=163.26
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memory used=15905.5MB, alloc=44.3MB, time=163.69
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memory used=15946.4MB, alloc=44.3MB, time=164.11
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memory used=15987.4MB, alloc=44.3MB, time=164.53
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memory used=16028.3MB, alloc=44.3MB, time=164.95
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memory used=16069.2MB, alloc=44.3MB, time=165.38
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memory used=16110.1MB, alloc=44.3MB, time=165.81
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memory used=16150.9MB, alloc=44.3MB, time=166.23
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memory used=16191.8MB, alloc=44.3MB, time=166.66
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memory used=16232.8MB, alloc=44.3MB, time=167.08
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memory used=16273.7MB, alloc=44.3MB, time=167.50
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memory used=16314.5MB, alloc=44.3MB, time=167.94
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memory used=16355.4MB, alloc=44.3MB, time=168.36
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memory used=16396.3MB, alloc=44.3MB, time=168.78
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memory used=16437.3MB, alloc=44.3MB, time=169.20
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memory used=16478.2MB, alloc=44.3MB, time=169.63
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memory used=16519.1MB, alloc=44.3MB, time=170.05
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memory used=16560.1MB, alloc=44.3MB, time=170.48
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memory used=16600.9MB, alloc=44.3MB, time=170.91
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memory used=16641.9MB, alloc=44.3MB, time=171.33
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memory used=16682.8MB, alloc=44.3MB, time=171.75
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memory used=16723.8MB, alloc=44.3MB, time=172.17
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memory used=16764.7MB, alloc=44.3MB, time=172.59
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memory used=16805.7MB, alloc=44.3MB, time=173.03
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memory used=16846.6MB, alloc=44.3MB, time=173.45
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memory used=16887.5MB, alloc=44.3MB, time=173.88
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memory used=16928.5MB, alloc=44.3MB, time=174.30
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memory used=16969.5MB, alloc=44.3MB, time=174.73
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memory used=17010.3MB, alloc=44.3MB, time=175.16
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memory used=17051.2MB, alloc=44.3MB, time=175.58
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memory used=17092.2MB, alloc=44.3MB, time=176.00
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memory used=17133.2MB, alloc=44.3MB, time=176.42
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memory used=17174.0MB, alloc=44.3MB, time=176.84
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memory used=17215.0MB, alloc=44.3MB, time=177.28
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memory used=17256.0MB, alloc=44.3MB, time=177.70
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memory used=17296.9MB, alloc=44.3MB, time=178.14
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memory used=17337.8MB, alloc=44.3MB, time=178.56
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memory used=17378.7MB, alloc=44.3MB, time=178.98
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memory used=17419.6MB, alloc=44.3MB, time=179.42
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memory used=17460.5MB, alloc=44.3MB, time=179.84
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Finished!
Maximum Time Reached before Solution Completed!
diff ( y , x , 1 ) = cos ( x ) ;
Iterations = 39553
Total Elapsed Time = 3 Minutes 0 Seconds
Elapsed Time(since restart) = 2 Minutes 59 Seconds
Expected Time Remaining = 6 Minutes 24 Seconds
Optimized Time Remaining = 6 Minutes 24 Seconds
Expected Total Time = 9 Minutes 24 Seconds
Time to Timeout = 0 Seconds
Percent Done = 31.89 %
> quit
memory used=17485.7MB, alloc=44.3MB, time=180.09