|\^/| Maple 18 (X86 64 WINDOWS) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. #BEGIN OUTFILE1 # before write maple top matter # before write_ats library and user def block #BEGIN ATS LIBRARY BLOCK # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc # End Function number 2 # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc # End Function number 3 # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc # End Function number 4 # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 5 # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 6 # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc # End Function number 7 # Begin Function number 8 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := sec_temp mod int_trunc(glob_sec_in_minute); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," 0.0 Seconds"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " 0.0 Seconds") end if; fprintf(fd, "\n") end proc # End Function number 8 # Begin Function number 9 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year)); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour)); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod int_trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" 0.0 Seconds\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" 0.0 Seconds\n") end if end proc # End Function number 9 # Begin Function number 10 > zero_ats_ar := proc(arr_a) > global ATS_MAX_TERMS; > local iii; > iii := 1; > while (iii <= ATS_MAX_TERMS) do # do number 1 > arr_a [iii] := glob__0; > iii := iii + 1; > od;# end do number 1 > end; zero_ats_ar := proc(arr_a) local iii; global ATS_MAX_TERMS; iii := 1; while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1 end do end proc # End Function number 10 # Begin Function number 11 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > global ATS_MAX_TERMS; > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := glob__0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 7 > ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]); > fi;# end if 7; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; global ATS_MAX_TERMS; ret_ats := glob__0; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]) end if; iii_ats := iii_ats + 1 end do end if; ret_ats end proc # End Function number 11 # Begin Function number 12 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global ATS_MAX_TERMS; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := glob__0; > if (jjj_att < mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 7 > ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / c(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global ATS_MAX_TERMS; ret_att := glob__0; if jjj_att < mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/c(mmm_att) end if; ret_att end proc # End Function number 12 # Begin Function number 13 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc # End Function number 13 # Begin Function number 14 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc # End Function number 14 # Begin Function number 15 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc # End Function number 15 # Begin Function number 16 > logitem_good_digits := proc(file,rel_error) > global glob_small_float,glob_prec; > local good_digits; > fprintf(file,""); > fprintf(file,"%d",glob_min_good_digits); > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float, glob_prec; fprintf(file, ""); fprintf(file, "%d", glob_min_good_digits); fprintf(file, "") end proc # End Function number 16 # Begin Function number 17 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc # End Function number 17 # Begin Function number 18 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc # End Function number 18 # Begin Function number 19 > logitem_h_reason := proc(file) > global glob_h_reason; > fprintf(file,""); > if (glob_h_reason = 1) then # if number 6 > fprintf(file,"Max H"); > elif > (glob_h_reason = 2) then # if number 7 > fprintf(file,"Display Interval"); > elif > (glob_h_reason = 3) then # if number 8 > fprintf(file,"Optimal"); > elif > (glob_h_reason = 4) then # if number 9 > fprintf(file,"Pole Accuracy"); > elif > (glob_h_reason = 5) then # if number 10 > fprintf(file,"Min H (Pole)"); > elif > (glob_h_reason = 6) then # if number 11 > fprintf(file,"Pole"); > elif > (glob_h_reason = 7) then # if number 12 > fprintf(file,"Opt Iter"); > else > fprintf(file,"Impossible"); > fi;# end if 12 > fprintf(file,""); > end; logitem_h_reason := proc(file) global glob_h_reason; fprintf(file, ""); if glob_h_reason = 1 then fprintf(file, "Max H") elif glob_h_reason = 2 then fprintf(file, "Display Interval") elif glob_h_reason = 3 then fprintf(file, "Optimal") elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy") elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)") elif glob_h_reason = 6 then fprintf(file, "Pole") elif glob_h_reason = 7 then fprintf(file, "Opt Iter") else fprintf(file, "Impossible") end if; fprintf(file, "") end proc # End Function number 19 # Begin Function number 20 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc # End Function number 20 # Begin Function number 21 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc # End Function number 21 # Begin Function number 22 > chk_data := proc() > global glob_max_iter,ALWAYS, ATS_MAX_TERMS; > local errflag; > errflag := false; > if (glob_max_iter < 2) then # if number 12 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 12; > if (errflag) then # if number 12 > quit; > fi;# end if 12 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, ATS_MAX_TERMS; errflag := false; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc # End Function number 22 # Begin Function number 23 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := c(clock_sec2); > sub1 := c(t_end2-t_start2); > sub2 := c(t2-t_start2); > if (sub1 = glob__0) then # if number 12 > sec_left := glob__0; > else > if (sub2 > glob__0) then # if number 13 > rrr := (sub1/sub2); > sec_left := rrr * c(ms2) - c(ms2); > else > sec_left := glob__0; > fi;# end if 13 > fi;# end if 12; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := c(clock_sec2); sub1 := c(t_end2 - t_start2); sub2 := c(t2 - t_start2); if sub1 = glob__0 then sec_left := glob__0 else if glob__0 < sub2 then rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2) else sec_left := glob__0 end if end if; sec_left end proc # End Function number 23 # Begin Function number 24 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 12 > rrr := (glob__100*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 12; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := glob__100*sub2/sub1 else rrr := 0. end if; rrr end proc # End Function number 24 # Begin Function number 25 > comp_rad_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 12 > ret := float_abs(term1 * glob_h / term2); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM TWO TERM RADIUS ANALYSIS > end; comp_rad_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2) else ret := glob_larger_float end if; ret end proc # End Function number 25 # Begin Function number 26 > comp_ord_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM ORDER ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 12 > ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no)); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM TWO TERM ORDER ANALYSIS > end; comp_ord_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)* c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no)) else ret := glob_larger_float end if; ret end proc # End Function number 26 # Begin Function number 27 > c := proc(in_val) > #To Force Conversion when needed > local ret; > ret := evalf(in_val); > ret; > #End Conversion > end; c := proc(in_val) local ret; ret := evalf(in_val); ret end proc # End Function number 27 # Begin Function number 28 > comp_rad_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret,temp; > temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3); > if (float_abs(temp) > glob__0) then # if number 12 > ret := float_abs((term2*glob_h*term1)/(temp)); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM THREE TERM RADIUS ANALYSIS > end; comp_rad_from_three_terms := proc(term1, term2, term3, last_no) local ret, temp; global glob_h, glob_larger_float; temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2 - term1*term3*c(last_no) + term1*term3); if glob__0 < float_abs(temp) then ret := float_abs(term2*glob_h*term1/temp) else ret := glob_larger_float end if; ret end proc # End Function number 28 # Begin Function number 29 > comp_ord_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM ORDER ANALYSIS > local ret; > ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3)); > ret; > #TOP THREE TERM ORDER ANALYSIS > end; comp_ord_from_three_terms := proc(term1, term2, term3, last_no) local ret; ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3 - glob__4*term2*term2*c(last_no) + glob__4*term2*term2 + term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no)) /(term2*term2*c(last_no) - glob__2*term2*term2 - term1*term3*c(last_no) + term1*term3)); ret end proc # End Function number 29 # Begin Function number 30 > comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > #TOP SIX TERM RADIUS ANALYSIS > global glob_h,glob_larger_float,glob_six_term_ord_save; > local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs; > if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 12 > rm0 := term6/term5; > rm1 := term5/term4; > rm2 := term4/term3; > rm3 := term3/term2; > rm4 := term2/term1; > nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2; > nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3; > dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; > dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; > ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; > ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; > if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 13 > rad_c := glob_larger_float; > ord_no := glob_larger_float; > else > if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2; > if (float_abs(rcs) <> glob__0) then # if number 15 > if (rcs > glob__0) then # if number 16 > rad_c := sqrt(rcs) * float_abs(glob_h); > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 16 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 15 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 14 > fi;# end if 13 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 12; > glob_six_term_ord_save := ord_no; > rad_c; > #BOTTOM SIX TERM RADIUS ANALYSIS > end; comp_rad_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no, ds1, rcs; global glob_h, glob_larger_float, glob_six_term_ord_save; if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and term2 <> glob__0 and term1 <> glob__0 then rm0 := term6/term5; rm1 := term5/term4; rm2 := term4/term3; rm3 := term3/term2; rm4 := term2/term1; nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1 + c(last_no - 3)*rm2; nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2 + c(last_no - 4)*rm3; dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; if float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0 then rad_c := glob_larger_float; ord_no := glob_larger_float else if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2; if float_abs(rcs) <> glob__0 then if glob__0 < rcs then rad_c := sqrt(rcs)*float_abs(glob_h) else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if; glob_six_term_ord_save := ord_no; rad_c end proc # End Function number 30 # Begin Function number 31 > comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > global glob_six_term_ord_save; > #TOP SIX TERM ORDER ANALYSIS > #TOP SAVED FROM SIX TERM RADIUS ANALYSIS > glob_six_term_ord_save; > #BOTTOM SIX TERM ORDER ANALYSIS > end; comp_ord_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) global glob_six_term_ord_save; glob_six_term_ord_save end proc # End Function number 31 # Begin Function number 32 > factorial_2 := proc(nnn) > ret := nnn!; > ret;; > end; Warning, `ret` is implicitly declared local to procedure `factorial_2` factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc # End Function number 32 # Begin Function number 33 > factorial_1 := proc(nnn) > global ATS_MAX_TERMS,array_fact_1; > local ret; > if (nnn <= ATS_MAX_TERMS) then # if number 12 > if (array_fact_1[nnn] = 0) then # if number 13 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 13; > else > ret := factorial_2(nnn); > fi;# end if 12; > ret; > end; factorial_1 := proc(nnn) local ret; global ATS_MAX_TERMS, array_fact_1; if nnn <= ATS_MAX_TERMS then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc # End Function number 33 # Begin Function number 34 > factorial_3 := proc(mmm,nnn) > global ATS_MAX_TERMS,array_fact_2; > local ret; > if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 12 > if (array_fact_2[mmm,nnn] = 0) then # if number 13 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 13; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 12; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global ATS_MAX_TERMS, array_fact_2; if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc # End Function number 34 # Begin Function number 35 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc # End Function number 35 # Begin Function number 36 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc # End Function number 36 # Begin Function number 37 > float_abs := proc(x) > abs(x); > end; float_abs := proc(x) abs(x) end proc # End Function number 37 # Begin Function number 38 > expt := proc(x,y) > x^y; > end; expt := proc(x, y) x^y end proc # End Function number 38 # Begin Function number 39 > neg := proc(x) > -x; > end; neg := proc(x) -x end proc # End Function number 39 # Begin Function number 40 > int_trunc := proc(x) > trunc(x); > end; int_trunc := proc(x) trunc(x) end proc # End Function number 40 # Begin Function number 41 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer))); > omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,""); > omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,""); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS))); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(glob__10, c(-glob_desired_digits_correct))* c(float_abs(c(estimated_answer))); omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, ""); omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "") ; omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := c(float_abs(desired_abs_gbl_error)/( sqrt(c(estimated_steps))*c(ATS_MAX_TERMS))); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc # End Function number 41 #END ATS LIBRARY BLOCK #BEGIN USER FUNCTION BLOCK #BEGIN BLOCK 3 #BEGIN USER DEF BLOCK > exact_soln_y1 := proc(x) > return(c(1.0) + cos(c(x))); > end; exact_soln_y1 := proc(x) return c(1.0) + cos(c(x)) end proc > exact_soln_y2 := proc(x) > return(c(1.0) + sin(c(x))); > end; exact_soln_y2 := 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 > ; > if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 3 > rad_given := sqrt((array_x[1] - array_given_rad_poles[2,1]) * (array_x[1] - array_given_rad_poles[2,1]) + array_given_rad_poles[2,2] * array_given_rad_poles[2,2]); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 2 ",4,rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[2,1],4," "); > if (rad_given < glob_least_given_sing) then # if number 4 > glob_least_given_sing := rad_given; > fi;# end if 4; > elif > (glob_type_given_pole = 3) then # if number 4 > omniout_str(ALWAYS,"NO POLE (given) for Equation 2"); > elif > (glob_type_given_pole = 5) then # if number 5 > omniout_str(ALWAYS,"SOME POLE (given) for Equation 2"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 2"); > fi;# end if 5; > if (array_rad_test_poles[2,1] < glob_large_float) then # if number 5 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 2 ",4,array_rad_test_poles[2,1],4," "); > if (array_rad_test_poles[2,1]< glob_least_ratio_sing) then # if number 6 > glob_least_ratio_sing := array_rad_test_poles[2,1]; > fi;# end if 6; > omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[2,1],4," "); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 2"); > fi;# end if 5; > if ((array_rad_test_poles[2,2] > glob__small) and (array_rad_test_poles[2,2] < glob_large_float)) then # if number 5 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 2 ",4,array_rad_test_poles[2,2],4," "); > if (array_rad_test_poles[2,2]< glob_least_3_sing) then # if number 6 > glob_least_3_sing := array_rad_test_poles[2,2]; > fi;# end if 6; > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[2,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 2"); > fi;# end if 5; > if ((array_rad_test_poles[2,3] > glob__small) and (array_rad_test_poles[2,3] < glob_large_float)) then # if number 5 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 2 ",4,array_rad_test_poles[2,3],4," "); > if (array_rad_test_poles[2,3]< glob_least_6_sing) then # if number 6 > glob_least_6_sing := array_rad_test_poles[2,3]; > fi;# end if 6; > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[2,3],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 2"); > fi;# end if 5 > ; > 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; if glob_type_given_pole = 1 or glob_type_given_pole = 2 then rad_given := sqrt((array_x[1] - array_given_rad_poles[2, 1])* (array_x[1] - array_given_rad_poles[2, 1]) + array_given_rad_poles[2, 2]*array_given_rad_poles[2, 2]); omniout_float(ALWAYS, "Radius of convergence (given) for eq 2 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[2, 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 2") elif glob_type_given_pole = 5 then omniout_str(ALWAYS, "SOME POLE (given) for Equation 2") else omniout_str(ALWAYS, "NO INFO (given) for Equation 2") end if; if array_rad_test_poles[2, 1] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 2 ", 4, array_rad_test_poles[2, 1], 4, " "); if array_rad_test_poles[2, 1] < glob_least_ratio_sing then glob_least_ratio_sing := array_rad_test_poles[2, 1] end if; omniout_float(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[2, 1], 4, " ") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 2") end if; if glob__small < array_rad_test_poles[2, 2] and array_rad_test_poles[2, 2] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 2 ", 4, array_rad_test_poles[2, 2], 4, " "); if array_rad_test_poles[2, 2] < glob_least_3_sing then glob_least_3_sing := array_rad_test_poles[2, 2] end if; omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[2, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 2") end if; if glob__small < array_rad_test_poles[2, 3] and array_rad_test_poles[2, 3] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 2 ", 4, array_rad_test_poles[2, 3], 4, " "); if array_rad_test_poles[2, 3] < glob_least_6_sing then glob_least_6_sing := array_rad_test_poles[2, 3] end if; omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[2, 3], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 2") 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 5 > ret := glob__1; > else > ret := glob__m1; > fi;# end if 5; > ret;; > end; my_check_sign := proc(x0, xf) local ret; if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret end proc # End Function number 3 # Begin Function number 4 > est_size_answer := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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_y1[1]) < min_size) then # if number 5 > min_size := float_abs(array_y1[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 5; > if (float_abs(array_y2[1]) < min_size) then # if number 5 > min_size := float_abs(array_y2[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 5; > if (min_size < glob__1) then # if number 5 > min_size := glob__1; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 5; > min_size; > end; est_size_answer := proc() local min_size; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_y1[1]) < min_size then min_size := float_abs(array_y1[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if float_abs(array_y2[1]) < min_size then min_size := float_abs(array_y2[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < glob__1 then min_size := glob__1; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc # End Function number 4 # Begin Function number 5 > test_suggested_h := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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_y1[no_terms-3] + array_y1[no_terms - 2] * hn_div_ho + array_y1[no_terms - 1] * hn_div_ho_2 + array_y1[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 5 > max_estimated_step_error := est_tmp; > fi;# end if 5; > est_tmp := float_abs(array_y2[no_terms-3] + array_y2[no_terms - 2] * hn_div_ho + array_y2[no_terms - 1] * hn_div_ho_2 + array_y2[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 5 > max_estimated_step_error := est_tmp; > fi;# end if 5; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_y1[no_terms - 3] + array_y1[no_terms - 2]*hn_div_ho + array_y1[no_terms - 1]*hn_div_ho_2 + array_y1[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; est_tmp := float_abs(array_y2[no_terms - 3] + array_y2[no_terms - 2]*hn_div_ho + array_y2[no_terms - 1]*hn_div_ho_2 + array_y2[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc # End Function number 5 # Begin Function number 6 > track_estimated_error := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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_y1[no_terms-3])) + c(float_abs(array_y1[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y1[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y1[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y1[1])) > c(est_tmp)) then # if number 5 > est_tmp := c(glob_prec) * c(float_abs(array_y1[1])); > fi;# end if 5; > if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 5 > array_max_est_error[1] := c(est_tmp); > fi;# end if 5 > ; > est_tmp := c(float_abs(array_y2[no_terms-3])) + c(float_abs(array_y2[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y2[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y2[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y2[1])) > c(est_tmp)) then # if number 5 > est_tmp := c(glob_prec) * c(float_abs(array_y2[1])); > fi;# end if 5; > if (c(est_tmp) >= c(array_max_est_error[2])) then # if number 5 > array_max_est_error[2] := c(est_tmp); > fi;# end if 5 > ; > end; track_estimated_error := proc() local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_y1[no_terms - 3])) + c(float_abs(array_y1[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y1[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y1[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y1[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y1[1])) end if; if c(array_max_est_error[1]) <= c(est_tmp) then array_max_est_error[1] := c(est_tmp) end if; est_tmp := c(float_abs(array_y2[no_terms - 3])) + c(float_abs(array_y2[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y2[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y2[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y2[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y2[1])) end if; if c(array_max_est_error[2]) <= c(est_tmp) then array_max_est_error[2] := c(est_tmp) end if end proc # End Function number 6 # Begin Function number 7 > reached_interval := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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 5 > ret := true; > else > ret := false; > fi;# end if 5; > return(ret); > end; reached_interval := proc() local ret; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if glob_check_sign*glob_next_display - glob_h/glob__10 <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc # End Function number 7 # Begin Function number 8 > display_alot := proc(iter) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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 5 > if (iter >= 0) then # if number 6 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > closed_form_val_y := evalf(exact_soln_y1(ind_var)); > omniout_float(ALWAYS,"y1[1] (closed_form) ",33,closed_form_val_y,20," "); > term_no := 1; > numeric_val := array_y1[term_no]; > abserr := float_abs(numeric_val - closed_form_val_y); > omniout_float(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," "); > if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 7 > relerr := abserr*glob__100/float_abs(closed_form_val_y); > if (c(relerr) > c(glob_prec)) then # if number 8 > glob_good_digits := -int_trunc(log10(c(relerr))) + 3; > else > glob_good_digits := Digits; > fi;# end if 8; > else > relerr := glob__m1 ; > glob_good_digits := -16; > fi;# end if 7; > if (glob_good_digits < glob_min_good_digits) then # if number 7 > glob_min_good_digits := glob_good_digits; > fi;# end if 7; > if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 7 > glob_min_apfp_est_good_digits := glob_apfp_est_good_digits; > fi;# end if 7; > if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 7 > est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*33*ATS_MAX_TERMS/float_abs(numeric_val)); > if (evalf(est_rel_err) > glob_prec) then # if number 8 > glob_est_digits := -int_trunc(log10(est_rel_err)) + 3; > else > glob_est_digits := Digits; > fi;# end if 8; > else > relerr := glob__m1 ; > glob_est_digits := -16; > fi;# end if 7; > array_est_digits[1] := glob_est_digits; > if (glob_iter = 1) then # if number 7 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 7; > 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," "); > ; > closed_form_val_y := evalf(exact_soln_y2(ind_var)); > omniout_float(ALWAYS,"y2[1] (closed_form) ",33,closed_form_val_y,20," "); > term_no := 1; > numeric_val := array_y2[term_no]; > abserr := float_abs(numeric_val - closed_form_val_y); > omniout_float(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," "); > if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 7 > relerr := abserr*glob__100/float_abs(closed_form_val_y); > if (c(relerr) > c(glob_prec)) then # if number 8 > glob_good_digits := -int_trunc(log10(c(relerr))) + 3; > else > glob_good_digits := Digits; > fi;# end if 8; > else > relerr := glob__m1 ; > glob_good_digits := -16; > fi;# end if 7; > if (glob_good_digits < glob_min_good_digits) then # if number 7 > glob_min_good_digits := glob_good_digits; > fi;# end if 7; > if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 7 > glob_min_apfp_est_good_digits := glob_apfp_est_good_digits; > fi;# end if 7; > if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 7 > est_rel_err := evalf(array_max_est_error[2]*100.0 * sqrt(glob_iter)*33*ATS_MAX_TERMS/float_abs(numeric_val)); > if (evalf(est_rel_err) > glob_prec) then # if number 8 > glob_est_digits := -int_trunc(log10(est_rel_err)) + 3; > else > glob_est_digits := Digits; > fi;# end if 8; > else > relerr := glob__m1 ; > glob_est_digits := -16; > fi;# end if 7; > array_est_digits[2] := glob_est_digits; > if (glob_iter = 1) then # if number 7 > array_1st_rel_error[2] := relerr; > else > array_last_rel_error[2] := relerr; > fi;# end if 7; > array_est_rel_error[2] := 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 6; > #BOTTOM DISPLAY ALOT > fi;# end if 5; > end; display_alot := proc(iter) local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_y1(ind_var)); omniout_float(ALWAYS, "y1[1] (closed_form) ", 33, closed_form_val_y, 20, " "); term_no := 1; numeric_val := array_y1[term_no]; abserr := float_abs(numeric_val - closed_form_val_y); omniout_float(ALWAYS, "y1[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)*33*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, " "); closed_form_val_y := evalf(exact_soln_y2(ind_var)); omniout_float(ALWAYS, "y2[1] (closed_form) ", 33, closed_form_val_y, 20, " "); term_no := 1; numeric_val := array_y2[term_no]; abserr := float_abs(numeric_val - closed_form_val_y); omniout_float(ALWAYS, "y2[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[2]*100.0* sqrt(glob_iter)*33*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[2] := glob_est_digits; if glob_iter = 1 then array_1st_rel_error[2] := relerr else array_last_rel_error[2] := relerr end if; array_est_rel_error[2] := est_rel_err; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Desired digits ", 32, glob_desired_digits_correct, 4, " "); omniout_int(INFO, "Estimated correct digits ", 32, glob_est_digits, 4, " "); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc # End Function number 8 # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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 5 > 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 5; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr((left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := clock_sec1 - glob_orig_start_sec; glob_clock_sec := clock_sec1 - glob_clock_start_sec; left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1; expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, clock_sec1 - glob_orig_start_sec); opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec; glob_optimal_expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec) ; glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(total_clock_sec); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(glob_clock_sec); if c(percent_done) < glob__100 then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(expect_sec); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(glob_optimal_expect_sec); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(glob_total_exp_sec) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(left_sec); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc # End Function number 9 # Begin Function number 10 > check_for_pole := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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_y1_higher[1,last_no-1],array_y1_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[1,1]) then # if number 8 > array_rad_test_poles[1,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y1_higher[1,last_no-1],array_y1_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 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[2,1] := glob_larger_float; > array_ord_test_poles[2,1] := 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_y2_higher[1,last_no-1],array_y2_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[2,1]) then # if number 10 > array_rad_test_poles[2,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no); > array_rad_test_poles[2,1] := rad_c; > array_ord_test_poles[2,1] := tmp_ord; > fi;# end if 10; > fi;# end if 9; > #BOTTOM general radius test2 > 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_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 9 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 9; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 9 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 10 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 11 > found_sing := 0; > fi;# end if 11; > 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 11 > if (rad_c < array_rad_test_poles[1,2]) then # if number 12 > array_rad_test_poles[1,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no); > array_rad_test_poles[1,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 13 > glob_min_pole_est := rad_c; > fi;# end if 13; > array_ord_test_poles[1,2] := tmp_ord; > fi;# end if 12; > fi;# end if 11; > #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[2,2] := glob_larger_float; > array_ord_test_poles[2,2] := 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_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 11 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 11; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 11 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 12 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 13 > found_sing := 0; > fi;# end if 13; > 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 13 > if (rad_c < array_rad_test_poles[2,2]) then # if number 14 > array_rad_test_poles[2,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no); > array_rad_test_poles[2,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 15 > glob_min_pole_est := rad_c; > fi;# end if 15; > array_ord_test_poles[2,2] := tmp_ord; > fi;# end if 14; > fi;# end if 13; > #BOTTOM general radius test2 > 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_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 13 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 13; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 13 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 14 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 15 > found_sing := 0; > fi;# end if 15; > 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 15 > if (rad_c < array_rad_test_poles[1,3]) then # if number 16 > array_rad_test_poles[1,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no); > array_rad_test_poles[1,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 17 > glob_min_pole_est := rad_c; > fi;# end if 17; > array_ord_test_poles[1,3] := tmp_ord; > fi;# end if 16; > fi;# end if 15; > #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[2,3] := glob_larger_float; > array_ord_test_poles[2,3] := 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_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 15 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 15; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 15 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 16 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 17 > found_sing := 0; > fi;# end if 17; > 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 17 > if (rad_c < array_rad_test_poles[2,3]) then # if number 18 > array_rad_test_poles[2,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no); > array_rad_test_poles[2,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 19 > glob_min_pole_est := rad_c; > fi;# end if 19; > array_ord_test_poles[2,3] := tmp_ord; > fi;# end if 18; > fi;# end if 17; > #BOTTOM general radius test2 > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 17 > 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 18 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 18; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y1[term] := array_y1[term]* ratio; > array_y1_higher[1,term] := array_y1_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > array_y2[term] := array_y2[term]* ratio; > array_y2_higher[1,term] := array_y2_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 17; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 17 > display_poles(); > fi;# end if 17 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad, last_no; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_y1_higher[1, last_no - 1], array_y1_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_y1_higher[1, last_no - 1], array_y1_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[2, 1] := glob_larger_float; array_ord_test_poles[2, 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_y2_higher[1, last_no - 1], array_y2_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[2, 1] then array_rad_test_poles[2, 1] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_ratio(array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no], last_no); array_rad_test_poles[2, 1] := rad_c; array_ord_test_poles[2, 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_y1_higher[1, last_no - 2], array_y1_higher[1, last_no - 1], array_y1_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_y1_higher[1, last_no - 2], array_y1_higher[1, last_no - 1], array_y1_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[2, 2] := glob_larger_float; array_ord_test_poles[2, 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_y2_higher[1, last_no - 2], array_y2_higher[1, last_no - 1], array_y2_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[2, 2] then array_rad_test_poles[2, 2] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_three_terms( array_y2_higher[1, last_no - 2], array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no], last_no); array_rad_test_poles[2, 2] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[2, 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_y1_higher[1, last_no - 5], array_y1_higher[1, last_no - 4], array_y1_higher[1, last_no - 3], array_y1_higher[1, last_no - 2], array_y1_higher[1, last_no - 1], array_y1_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_y1_higher[1, last_no - 5], array_y1_higher[1, last_no - 4], array_y1_higher[1, last_no - 3], array_y1_higher[1, last_no - 2], array_y1_higher[1, last_no - 1], array_y1_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; 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[2, 3] := glob_larger_float; array_ord_test_poles[2, 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_y2_higher[1, last_no - 5], array_y2_higher[1, last_no - 4], array_y2_higher[1, last_no - 3], array_y2_higher[1, last_no - 2], array_y2_higher[1, last_no - 1], array_y2_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[2, 3] then array_rad_test_poles[2, 3] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_six_terms( array_y2_higher[1, last_no - 5], array_y2_higher[1, last_no - 4], array_y2_higher[1, last_no - 3], array_y2_higher[1, last_no - 2], array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no], last_no); array_rad_test_poles[2, 3] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[2, 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_y1[term] := array_y1[term]*ratio; array_y1_higher[1, term] := array_y1_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; array_y2[term] := array_y2[term]*ratio; array_y2_higher[1, term] := array_y2_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc # End Function number 10 # Begin Function number 11 > atomall := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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 neg FULL $eq_no = 1 > array_tmp1[1] := neg(array_y2[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre add FULL - CONST $eq_no = 1 i = 1 > array_tmp3[1] := array_tmp2[1] + array_const_1D0[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y1_set_initial[1,2]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1)); > if (2 <= ATS_MAX_TERMS) then # if number 3 > array_y1[2] := temporary; > array_y1_higher[1,2] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(1); > array_y1_higher[2,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #emit pre sub FULL - CONST $eq_no = 2 i = 1 > array_tmp5[1] := array_y1[1] - array_const_1D0[1]; > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if ( not array_y2_set_initial[2,2]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1)); > if (2 <= ATS_MAX_TERMS) then # if number 3 > array_y2[2] := temporary; > array_y2_higher[1,2] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(1); > array_y2_higher[2,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre neg FULL $eq_no = 1 > array_tmp1[2] := neg(array_y2[2]); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre add FULL CONST $eq_no = 1 i = 2 > array_tmp3[2] := array_tmp2[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y1_set_initial[1,3]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_y1[3] := temporary; > array_y1_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y1_higher[2,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #emit pre sub FULL CONST $eq_no = 2 i = 2 > array_tmp5[2] := array_y1[2]; > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if ( not array_y2_set_initial[2,3]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_y2[3] := temporary; > array_y2_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y2_higher[2,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre neg FULL $eq_no = 1 > array_tmp1[3] := neg(array_y2[3]); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre add FULL CONST $eq_no = 1 i = 3 > array_tmp3[3] := array_tmp2[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y1_set_initial[1,4]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y1[4] := temporary; > array_y1_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y1_higher[2,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #emit pre sub FULL CONST $eq_no = 2 i = 3 > array_tmp5[3] := array_y1[3]; > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if ( not array_y2_set_initial[2,4]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y2[4] := temporary; > array_y2_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y2_higher[2,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre neg FULL $eq_no = 1 > array_tmp1[4] := neg(array_y2[4]); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre add FULL CONST $eq_no = 1 i = 4 > array_tmp3[4] := array_tmp2[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y1_set_initial[1,5]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y1[5] := temporary; > array_y1_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y1_higher[2,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #emit pre sub FULL CONST $eq_no = 2 i = 4 > array_tmp5[4] := array_y1[4]; > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if ( not array_y2_set_initial[2,5]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y2[5] := temporary; > array_y2_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y2_higher[2,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre neg FULL $eq_no = 1 > array_tmp1[5] := neg(array_y2[5]); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre add FULL CONST $eq_no = 1 i = 5 > array_tmp3[5] := array_tmp2[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y1_set_initial[1,6]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_y1[6] := temporary; > array_y1_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y1_higher[2,5] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #emit pre sub FULL CONST $eq_no = 2 i = 5 > array_tmp5[5] := array_y1[5]; > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if ( not array_y2_set_initial[2,6]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y2_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 neg FULL $eq_no = 1 > array_tmp1[kkk] := neg(array_y2[kkk]); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit FULL - NOT FULL add $eq_no = 1 > array_tmp3[kkk] := array_tmp2[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_y1_set_initial[1,kkk + order_d]) then # if number 2 > temporary := c(array_tmp3[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_y1[kkk + order_d] := c(temporary); > array_y1_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_y1_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; > #emit FULL - NOT FULL sub $eq_no = 2 > array_tmp5[kkk] := array_y1[kkk]; > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_y2_set_initial[2,kkk + order_d]) then # if number 2 > temporary := c(array_tmp5[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_y2[kkk + order_d] := c(temporary); > array_y2_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_y2_higher[adj3,term] := c(temporary); > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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] := neg(array_y2[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; array_tmp3[1] := array_tmp2[1] + array_const_1D0[1]; if not array_y1_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp3[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_y1[2] := temporary; array_y1_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_y1_higher[2, 1] := c(temporary) end if end if; kkk := 2; array_tmp5[1] := array_y1[1] - array_const_1D0[1]; if not array_y2_set_initial[2, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp5[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_y2[2] := temporary; array_y2_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_y2_higher[2, 1] := c(temporary) end if end if; kkk := 2; array_tmp1[2] := neg(array_y2[2]); array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]; if not array_y1_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp3[2])*expt(glob_h, c(1))*c(factorial_3(1, 2)); if 3 <= ATS_MAX_TERMS then array_y1[3] := temporary; array_y1_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y1_higher[2, 2] := c(temporary) end if end if; kkk := 3; array_tmp5[2] := array_y1[2]; if not array_y2_set_initial[2, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2)); if 3 <= ATS_MAX_TERMS then array_y2[3] := temporary; array_y2_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y2_higher[2, 2] := c(temporary) end if end if; kkk := 3; array_tmp1[3] := neg(array_y2[3]); array_tmp2[3] := array_tmp1[3]; array_tmp3[3] := array_tmp2[3]; if not array_y1_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp3[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_y1[4] := temporary; array_y1_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y1_higher[2, 3] := c(temporary) end if end if; kkk := 4; array_tmp5[3] := array_y1[3]; if not array_y2_set_initial[2, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_y2[4] := temporary; array_y2_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y2_higher[2, 3] := c(temporary) end if end if; kkk := 4; array_tmp1[4] := neg(array_y2[4]); array_tmp2[4] := array_tmp1[4]; array_tmp3[4] := array_tmp2[4]; if not array_y1_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp3[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_y1[5] := temporary; array_y1_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y1_higher[2, 4] := c(temporary) end if end if; kkk := 5; array_tmp5[4] := array_y1[4]; if not array_y2_set_initial[2, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_y2[5] := temporary; array_y2_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y2_higher[2, 4] := c(temporary) end if end if; kkk := 5; array_tmp1[5] := neg(array_y2[5]); array_tmp2[5] := array_tmp1[5]; array_tmp3[5] := array_tmp2[5]; if not array_y1_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp3[5])*expt(glob_h, c(1))*c(factorial_3(4, 5)); if 6 <= ATS_MAX_TERMS then array_y1[6] := temporary; array_y1_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y1_higher[2, 5] := c(temporary) end if end if; kkk := 6; array_tmp5[5] := array_y1[5]; if not array_y2_set_initial[2, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5)); if 6 <= ATS_MAX_TERMS then array_y2[6] := temporary; array_y2_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y2_higher[2, 5] := c(temporary) end if end if; kkk := 6; while kkk <= ATS_MAX_TERMS do array_tmp1[kkk] := neg(array_y2[kkk]); array_tmp2[kkk] := array_tmp1[kkk]; array_tmp3[kkk] := array_tmp2[kkk]; order_d := 1; if kkk + order_d <= ATS_MAX_TERMS then if not array_y1_set_initial[1, kkk + order_d] then temporary := c(array_tmp3[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_y1[kkk + order_d] := c(temporary); array_y1_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_y1_higher[adj3, term] := c(temporary) end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; array_tmp5[kkk] := array_y1[kkk]; order_d := 1; if kkk + order_d <= ATS_MAX_TERMS then if not array_y2_set_initial[2, kkk + order_d] then temporary := c(array_tmp5[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_y2[kkk + order_d] := c(temporary); array_y2_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_y2_higher[adj3, term] := c(temporary) end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc # End Function number 12 #END OUTFILE5 # Begin Function number 12 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it; > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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_y1_init:= Array(0..(40),[]); > array_y2_init:= Array(0..(40),[]); > array_norms:= Array(0..(40),[]); > array_fact_1:= Array(0..(40),[]); > array_1st_rel_error:= Array(0..(3),[]); > array_last_rel_error:= Array(0..(3),[]); > array_est_rel_error:= Array(0..(3),[]); > array_max_est_error:= Array(0..(3),[]); > array_type_pole:= Array(0..(3),[]); > array_type_real_pole:= Array(0..(3),[]); > array_type_complex_pole:= Array(0..(3),[]); > array_est_digits:= Array(0..(3),[]); > array_y1:= Array(0..(40),[]); > array_x:= Array(0..(40),[]); > array_y2:= Array(0..(40),[]); > array_tmp0:= Array(0..(40),[]); > array_tmp1:= Array(0..(40),[]); > array_tmp2:= Array(0..(40),[]); > array_tmp3:= Array(0..(40),[]); > array_tmp4:= Array(0..(40),[]); > array_tmp5:= Array(0..(40),[]); > array_m1:= Array(0..(40),[]); > array_y1_higher := Array(0..(2) ,(0..40+ 1),[]); > array_y1_higher_work := Array(0..(2) ,(0..40+ 1),[]); > array_y1_higher_work2 := Array(0..(2) ,(0..40+ 1),[]); > array_y1_set_initial := Array(0..(3) ,(0..40+ 1),[]); > array_y2_higher := Array(0..(2) ,(0..40+ 1),[]); > array_y2_higher_work := Array(0..(2) ,(0..40+ 1),[]); > array_y2_higher_work2 := Array(0..(2) ,(0..40+ 1),[]); > array_y2_set_initial := Array(0..(3) ,(0..40+ 1),[]); > array_given_rad_poles := Array(0..(3) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(3) ,(0..3+ 1),[]); > array_rad_test_poles := Array(0..(3) ,(0..4+ 1),[]); > array_ord_test_poles := Array(0..(3) ,(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_y1_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_y2_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 <= 3) do # do number 1 > array_1st_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_last_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_est_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_max_est_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_type_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_type_real_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_type_complex_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) 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_y1[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_y2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp5[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y1_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_y1_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_y1_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 <=3) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y1_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 <= 40) do # do number 2 > array_y2_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_y2_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_y2_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 <=3) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y2_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 <=3) 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 <=3) 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 <=3) 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 <=3) 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_y1); > zero_ats_ar(array_x); > zero_ats_ar(array_y2); > zero_ats_ar(array_tmp0); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_tmp3); > zero_ats_ar(array_tmp4); > zero_ats_ar(array_tmp5); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_const_1D0); > array_const_1D0[1] := c(1.0); > 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_y1_set_initial[1,1] := true; > array_y1_set_initial[1,2] := false; > array_y1_set_initial[1,3] := false; > array_y1_set_initial[1,4] := false; > array_y1_set_initial[1,5] := false; > array_y1_set_initial[1,6] := false; > array_y1_set_initial[1,7] := false; > array_y1_set_initial[1,8] := false; > array_y1_set_initial[1,9] := false; > array_y1_set_initial[1,10] := false; > array_y1_set_initial[1,11] := false; > array_y1_set_initial[1,12] := false; > array_y1_set_initial[1,13] := false; > array_y1_set_initial[1,14] := false; > array_y1_set_initial[1,15] := false; > array_y1_set_initial[1,16] := false; > array_y1_set_initial[1,17] := false; > array_y1_set_initial[1,18] := false; > array_y1_set_initial[1,19] := false; > array_y1_set_initial[1,20] := false; > array_y1_set_initial[1,21] := false; > array_y1_set_initial[1,22] := false; > array_y1_set_initial[1,23] := false; > array_y1_set_initial[1,24] := false; > array_y1_set_initial[1,25] := false; > array_y1_set_initial[1,26] := false; > array_y1_set_initial[1,27] := false; > array_y1_set_initial[1,28] := false; > array_y1_set_initial[1,29] := false; > array_y1_set_initial[1,30] := false; > array_y1_set_initial[1,31] := false; > array_y1_set_initial[1,32] := false; > array_y1_set_initial[1,33] := false; > array_y1_set_initial[1,34] := false; > array_y1_set_initial[1,35] := false; > array_y1_set_initial[1,36] := false; > array_y1_set_initial[1,37] := false; > array_y1_set_initial[1,38] := false; > array_y1_set_initial[1,39] := false; > array_y1_set_initial[1,40] := false; > array_y2_set_initial[2,1] := true; > array_y2_set_initial[2,2] := false; > array_y2_set_initial[2,3] := false; > array_y2_set_initial[2,4] := false; > array_y2_set_initial[2,5] := false; > array_y2_set_initial[2,6] := false; > array_y2_set_initial[2,7] := false; > array_y2_set_initial[2,8] := false; > array_y2_set_initial[2,9] := false; > array_y2_set_initial[2,10] := false; > array_y2_set_initial[2,11] := false; > array_y2_set_initial[2,12] := false; > array_y2_set_initial[2,13] := false; > array_y2_set_initial[2,14] := false; > array_y2_set_initial[2,15] := false; > array_y2_set_initial[2,16] := false; > array_y2_set_initial[2,17] := false; > array_y2_set_initial[2,18] := false; > array_y2_set_initial[2,19] := false; > array_y2_set_initial[2,20] := false; > array_y2_set_initial[2,21] := false; > array_y2_set_initial[2,22] := false; > array_y2_set_initial[2,23] := false; > array_y2_set_initial[2,24] := false; > array_y2_set_initial[2,25] := false; > array_y2_set_initial[2,26] := false; > array_y2_set_initial[2,27] := false; > array_y2_set_initial[2,28] := false; > array_y2_set_initial[2,29] := false; > array_y2_set_initial[2,30] := false; > array_y2_set_initial[2,31] := false; > array_y2_set_initial[2,32] := false; > array_y2_set_initial[2,33] := false; > array_y2_set_initial[2,34] := false; > array_y2_set_initial[2,35] := false; > array_y2_set_initial[2,36] := false; > array_y2_set_initial[2,37] := false; > array_y2_set_initial[2,38] := false; > array_y2_set_initial[2,39] := false; > array_y2_set_initial[2,40] := 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 := 2; > 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/mtest1postode.ode#################"); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = neg ( y2 ) + 1.0 ; "); > omniout_str(ALWAYS,"diff ( y2 , x , 1 ) = y1 - 1.0 ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=40;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := c(0.1);"); > omniout_str(ALWAYS,"x_end := c(10.0);"); > omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);"); > omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_type_given_pole := 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_y1 := proc(x)"); > omniout_str(ALWAYS,"return(c(1.0) + cos(c(x)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x)"); > omniout_str(ALWAYS,"return(c(1.0) + sin(c(x)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := glob__0; > glob_smallish_float := glob__0; > glob_large_float := c(1.0e100); > glob_larger_float := c( 1.1e100); > glob_almost_1 := c( 0.99); > # before second block > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN BLOCK 2 > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := c(0.1); > x_end := c(10.0); > array_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > glob_look_poles := true; > 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 17 > #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 18 > glob_display_interval := c(display_max); > fi;# end if 18; > 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_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y1[term_no] := array_y1_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 18 > array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 18; > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > order_diff := 1; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y2[term_no] := array_y2_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 18 > array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 18; > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > if (glob_subiter_method = 1 ) then # if number 18 > atomall(); > elif > (glob_subiter_method = 2 ) then # if number 19 > subiter := 1; > while (subiter <= 2) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > else > subiter := 1; > while (subiter <= 2 + ATS_MAX_TERMS) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > fi;# end if 19; > if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 19 > 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 19; > if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 19 > omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL"); > glob_h_reason := 2; > glob_h := glob_display_interval; > found_h := true; > fi;# end if 19; > if (glob_look_poles) then # if number 19 > check_for_pole(); > fi;# end if 19; > if ( not found_h) then # if number 19 > 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 20 > 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 20; > fi;# end if 19; > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 19 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 19; > if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 19 > 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 19; > else > found_h := true; > glob_h := glob_h * glob_check_sign; > fi;# end if 18; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 18 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 18; > #BEGIN SOLUTION CODE > if (found_h) then # if number 18 > 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_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y1[term_no] := array_y1_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 19 > array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 19; > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > order_diff := 1; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y2[term_no] := array_y2_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 19 > array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 19; > 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 19 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 19; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > track_estimated_error(); > if (glob_subiter_method = 1 ) then # if number 19 > atomall(); > elif > (glob_subiter_method = 2 ) then # if number 20 > subiter := 1; > while (subiter <= 2) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > else > subiter := 1; > while (subiter <= 2 + ATS_MAX_TERMS) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > fi;# end if 20; > track_estimated_error(); > display_alot(current_iter); > if (glob_look_poles) then # if number 20 > check_for_pole(); > fi;# end if 20; > if (reached_interval()) then # if number 20 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 20; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y1; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y1_higher_work[2,iii] := array_y1_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_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y1_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_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y1_higher_work[1,iii] := array_y1_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_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y1_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_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y1_higher_work[1,iii] := array_y1_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_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y1_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_y1[term_no] := array_y1_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y1_higher[ord,term_no] := array_y1_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 > #Jump Series array_y2; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[2,iii] := array_y2_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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := glob__0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[1,iii] := array_y2_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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := glob__0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[1,iii] := array_y2_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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := glob__0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #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_y2[term_no] := array_y2_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y2_higher[ord,term_no] := array_y2_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 20 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 20; > if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 20 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 20; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y1 , x , 1 ) = neg ( y2 ) + 1.0 ; "); > omniout_str(INFO,"diff ( y2 , x , 1 ) = y1 - 1.0 ; "); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 20 > logstart(html_log_file); > logitem_str(html_log_file,"2015-05-02T17:53:20-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest1") > ; > logitem_str(html_log_file,"diff ( y1 , x , 1 ) = neg ( y2 ) + 1.0 ; ") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_h_reason(html_log_file) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_float(html_log_file,glob_desired_digits_correct) > ; > if (array_est_digits[1] <> -16) then # if number 21 > logitem_integer(html_log_file,array_est_digits[1]) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 21; > if (glob_min_good_digits <> -16) then # if number 21 > logitem_integer(html_log_file,glob_min_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 21; > if (glob_good_digits <> -16) then # if number 21 > logitem_integer(html_log_file,glob_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 21; > 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 21 > logitem_str(html_log_file,"Not Given") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 4) then # if number 22 > logitem_str(html_log_file,"No Solution") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 5) then # if number 23 > logitem_str(html_log_file,"Some Pole") > ; > logitem_str(html_log_file,"????") > ; > elif > (glob_type_given_pole = 3) then # if number 24 > logitem_str(html_log_file,"No Pole") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 1) then # if number 25 > 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 26 > logitem_str(html_log_file,"Complex Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > fi;# end if 26; > if (glob_least_ratio_sing < glob_large_float) then # if number 26 > logitem_float(html_log_file,glob_least_ratio_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 26; > if (glob_least_3_sing < glob_large_float) then # if number 26 > logitem_float(html_log_file,glob_least_3_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 26; > if (glob_least_6_sing < glob_large_float) then # if number 26 > logitem_float(html_log_file,glob_least_6_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 26; > 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 26 > logitem_time(html_log_file,(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 26; > log_revs(html_log_file," 308.maple.seems.ok ") > ; > logitem_str(html_log_file,"mtest1 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest1 maple results") > ; > logitem_str(html_log_file,"OK") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff ( y2 , x , 1 ) = y1 - 1.0 ; ") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > logditto(html_log_file) > ; > if (array_est_digits[2] <> -16) then # if number 26 > logitem_integer(html_log_file,array_est_digits[2]) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 26; > if (glob_min_good_digits <> -16) then # if number 26 > logitem_integer(html_log_file,glob_min_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 26; > if (glob_good_digits <> -16) then # if number 26 > logitem_integer(html_log_file,glob_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 26; > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > logditto(html_log_file) > ; > if (glob_type_given_pole = 0) then # if number 26 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > elif > (glob_type_given_pole = 4) then # if number 27 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > elif > (glob_type_given_pole = 5) then # if number 28 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > elif > (glob_type_given_pole = 3) then # if number 29 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > elif > (glob_type_given_pole = 1) then # if number 30 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > elif > (glob_type_given_pole = 2) then # if number 31 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > fi;# end if 31; > if (glob_least_ratio_sing < glob_large_float) then # if number 31 > logditto(html_log_file) > ; > else > logditto(html_log_file) > ; > fi;# end if 31; > if (glob_least_3_sing < glob_large_float) then # if number 31 > logditto(html_log_file) > ; > else > logditto(html_log_file) > ; > fi;# end if 31; > if (glob_least_6_sing < glob_large_float) then # if number 31 > logditto(html_log_file) > ; > else > logditto(html_log_file) > ; > fi;# end if 31; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > if (c(glob_percent_done) < glob__100) then # if number 31 > logditto(html_log_file) > ; > 0; > else > logditto(html_log_file) > ; > 0; > fi;# end if 31; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 30; > if (glob_html_log) then # if number 30 > fclose(html_log_file); > fi;# end if 30 > ; > ;; > fi;# end if 29 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, found_h, repeat_it; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_y1_init := Array(0 .. 40, []); array_y2_init := Array(0 .. 40, []); array_norms := Array(0 .. 40, []); array_fact_1 := Array(0 .. 40, []); array_1st_rel_error := Array(0 .. 3, []); array_last_rel_error := Array(0 .. 3, []); array_est_rel_error := Array(0 .. 3, []); array_max_est_error := Array(0 .. 3, []); array_type_pole := Array(0 .. 3, []); array_type_real_pole := Array(0 .. 3, []); array_type_complex_pole := Array(0 .. 3, []); array_est_digits := Array(0 .. 3, []); array_y1 := Array(0 .. 40, []); array_x := Array(0 .. 40, []); array_y2 := Array(0 .. 40, []); array_tmp0 := Array(0 .. 40, []); array_tmp1 := Array(0 .. 40, []); array_tmp2 := Array(0 .. 40, []); array_tmp3 := Array(0 .. 40, []); array_tmp4 := Array(0 .. 40, []); array_tmp5 := Array(0 .. 40, []); array_m1 := Array(0 .. 40, []); array_y1_higher := Array(0 .. 2, 0 .. 41, []); array_y1_higher_work := Array(0 .. 2, 0 .. 41, []); array_y1_higher_work2 := Array(0 .. 2, 0 .. 41, []); array_y1_set_initial := Array(0 .. 3, 0 .. 41, []); array_y2_higher := Array(0 .. 2, 0 .. 41, []); array_y2_higher_work := Array(0 .. 2, 0 .. 41, []); array_y2_higher_work2 := Array(0 .. 2, 0 .. 41, []); array_y2_set_initial := Array(0 .. 3, 0 .. 41, []); array_given_rad_poles := Array(0 .. 3, 0 .. 4, []); array_given_ord_poles := Array(0 .. 3, 0 .. 4, []); array_rad_test_poles := Array(0 .. 3, 0 .. 5, []); array_ord_test_poles := Array(0 .. 3, 0 .. 5, []); array_fact_2 := Array(0 .. 40, 0 .. 41, []); term := 1; while term <= 40 do array_y1_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_y2_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 <= 3 do array_1st_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 3 do array_last_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 3 do array_est_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 3 do array_max_est_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 3 do array_type_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 3 do array_type_real_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 3 do array_type_complex_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 3 do array_est_digits[term] := 0; term := term + 1 end do ; term := 1; while term <= 40 do array_y1[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_y2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y1_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_y1_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_y1_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 40 do array_y1_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 <= 40 do array_y2_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_y2_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_y2_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 40 do array_y2_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 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 <= 3 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 <= 3 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 <= 3 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_y1); zero_ats_ar(array_x); zero_ats_ar(array_y2); zero_ats_ar(array_tmp0); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2); zero_ats_ar(array_tmp3); zero_ats_ar(array_tmp4); zero_ats_ar(array_tmp5); zero_ats_ar(array_m1); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_const_1D0); array_const_1D0[1] := c(1.0); 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_y1_set_initial[1, 1] := true; array_y1_set_initial[1, 2] := false; array_y1_set_initial[1, 3] := false; array_y1_set_initial[1, 4] := false; array_y1_set_initial[1, 5] := false; array_y1_set_initial[1, 6] := false; array_y1_set_initial[1, 7] := false; array_y1_set_initial[1, 8] := false; array_y1_set_initial[1, 9] := false; array_y1_set_initial[1, 10] := false; array_y1_set_initial[1, 11] := false; array_y1_set_initial[1, 12] := false; array_y1_set_initial[1, 13] := false; array_y1_set_initial[1, 14] := false; array_y1_set_initial[1, 15] := false; array_y1_set_initial[1, 16] := false; array_y1_set_initial[1, 17] := false; array_y1_set_initial[1, 18] := false; array_y1_set_initial[1, 19] := false; array_y1_set_initial[1, 20] := false; array_y1_set_initial[1, 21] := false; array_y1_set_initial[1, 22] := false; array_y1_set_initial[1, 23] := false; array_y1_set_initial[1, 24] := false; array_y1_set_initial[1, 25] := false; array_y1_set_initial[1, 26] := false; array_y1_set_initial[1, 27] := false; array_y1_set_initial[1, 28] := false; array_y1_set_initial[1, 29] := false; array_y1_set_initial[1, 30] := false; array_y1_set_initial[1, 31] := false; array_y1_set_initial[1, 32] := false; array_y1_set_initial[1, 33] := false; array_y1_set_initial[1, 34] := false; array_y1_set_initial[1, 35] := false; array_y1_set_initial[1, 36] := false; array_y1_set_initial[1, 37] := false; array_y1_set_initial[1, 38] := false; array_y1_set_initial[1, 39] := false; array_y1_set_initial[1, 40] := false; array_y2_set_initial[2, 1] := true; array_y2_set_initial[2, 2] := false; array_y2_set_initial[2, 3] := false; array_y2_set_initial[2, 4] := false; array_y2_set_initial[2, 5] := false; array_y2_set_initial[2, 6] := false; array_y2_set_initial[2, 7] := false; array_y2_set_initial[2, 8] := false; array_y2_set_initial[2, 9] := false; array_y2_set_initial[2, 10] := false; array_y2_set_initial[2, 11] := false; array_y2_set_initial[2, 12] := false; array_y2_set_initial[2, 13] := false; array_y2_set_initial[2, 14] := false; array_y2_set_initial[2, 15] := false; array_y2_set_initial[2, 16] := false; array_y2_set_initial[2, 17] := false; array_y2_set_initial[2, 18] := false; array_y2_set_initial[2, 19] := false; array_y2_set_initial[2, 20] := false; array_y2_set_initial[2, 21] := false; array_y2_set_initial[2, 22] := false; array_y2_set_initial[2, 23] := false; array_y2_set_initial[2, 24] := false; array_y2_set_initial[2, 25] := false; array_y2_set_initial[2, 26] := false; array_y2_set_initial[2, 27] := false; array_y2_set_initial[2, 28] := false; array_y2_set_initial[2, 29] := false; array_y2_set_initial[2, 30] := false; array_y2_set_initial[2, 31] := false; array_y2_set_initial[2, 32] := false; array_y2_set_initial[2, 33] := false; array_y2_set_initial[2, 34] := false; array_y2_set_initial[2, 35] := false; array_y2_set_initial[2, 36] := false; array_y2_set_initial[2, 37] := false; array_y2_set_initial[2, 38] := false; array_y2_set_initial[2, 39] := false; array_y2_set_initial[2, 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 := 2; 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/mtest1postode.ode#################"); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = neg ( y2 ) + 1.0 ; "); omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = y1 - 1.0 ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=40;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := c(0.1);"); omniout_str(ALWAYS, "x_end := c(10.0);"); omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);"); omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_type_given_pole := 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_y1 := proc(x)"); omniout_str(ALWAYS, "return(c(1.0) + cos(c(x)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x)"); omniout_str(ALWAYS, "return(c(1.0) + sin(c(x)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := glob__0; glob_smallish_float := glob__0; glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := c(0.1); x_end := c(10.0); array_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); glob_look_poles := true; 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_y1[term_no] := array_y1_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_y1_higher[r_order, term_no] := array_y1_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; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_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_y2_higher[r_order, term_no] := array_y2_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; if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 2 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 2 + ATS_MAX_TERMS do atomall(); subiter := subiter + 1 end do end if; 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_y1[term_no] := array_y1_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_y1_higher[r_order, term_no] := array_y1_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; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_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_y2_higher[r_order, term_no] := array_y2_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(); if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 2 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 2 + ATS_MAX_TERMS do atomall(); subiter := subiter + 1 end do end if; 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_y1_higher_work[2, iii] := array_y1_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_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_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_y1[term_no] := array_y1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y1_higher[ord, term_no] := array_y1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 2; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_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_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_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_y2[term_no] := array_y2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y2_higher[ord, term_no] := array_y2_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 ( y1 , x , 1 ) = neg ( y2 ) + 1.0 ; "); omniout_str(INFO, "diff ( y2 , x , 1 ) = y1 - 1.0 ; "); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2015-05-02T17:53:20-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest1"); logitem_str(html_log_file, "diff ( y1 , x , 1 ) = neg ( y2 ) + 1.0 ; "); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_h_reason(html_log_file); logitem_integer(html_log_file, Digits); logitem_float(html_log_file, glob_desired_digits_correct); if array_est_digits[1] <> -16 then logitem_integer(html_log_file, array_est_digits[1]) else logitem_str(html_log_file, "Unknown") end if; if glob_min_good_digits <> -16 then logitem_integer(html_log_file, glob_min_good_digits) else logitem_str(html_log_file, "Unknown") end if; if glob_good_digits <> -16 then logitem_integer(html_log_file, glob_good_digits) else logitem_str(html_log_file, "Unknown") end if; logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); logitem_integer(html_log_file, ATS_MAX_TERMS); if glob_type_given_pole = 0 then logitem_str(html_log_file, "Not Given"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 4 then logitem_str(html_log_file, "No Solution"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 5 then logitem_str(html_log_file, "Some Pole"); logitem_str(html_log_file, "????") elif glob_type_given_pole = 3 then logitem_str(html_log_file, "No Pole"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 1 then logitem_str(html_log_file, "Real Sing"); logitem_float(html_log_file, glob_least_given_sing) elif glob_type_given_pole = 2 then logitem_str(html_log_file, "Complex Sing"); logitem_float(html_log_file, glob_least_given_sing) end if; if glob_least_ratio_sing < glob_large_float then logitem_float(html_log_file, glob_least_ratio_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_3_sing < glob_large_float then logitem_float(html_log_file, glob_least_3_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_6_sing < glob_large_float then logitem_float(html_log_file, glob_least_6_sing) else logitem_str(html_log_file, "NONE") end if; logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, glob_clock_sec); if c(glob_percent_done) < glob__100 then logitem_time(html_log_file, glob_total_exp_sec); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 308.maple.seems.ok "); logitem_str(html_log_file, "mtest1 diffeq.mxt"); logitem_str(html_log_file, "mtest1 maple results"); logitem_str(html_log_file, "OK"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff ( y2 , x , 1 ) = y1 - 1.0 ; "); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); if array_est_digits[2] <> -16 then logitem_integer(html_log_file, array_est_digits[2]) 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"); logditto(html_log_file); if glob_type_given_pole = 0 then logditto(html_log_file); logditto(html_log_file) elif glob_type_given_pole = 4 then logditto(html_log_file); logditto(html_log_file) elif glob_type_given_pole = 5 then logditto(html_log_file); logditto(html_log_file) elif glob_type_given_pole = 3 then logditto(html_log_file); logditto(html_log_file) elif glob_type_given_pole = 1 then logditto(html_log_file); logditto(html_log_file) elif glob_type_given_pole = 2 then logditto(html_log_file); logditto(html_log_file) end if; if glob_least_ratio_sing < glob_large_float then logditto(html_log_file) else logditto(html_log_file) end if; if glob_least_3_sing < glob_large_float then logditto(html_log_file) else logditto(html_log_file) end if; if glob_least_6_sing < glob_large_float then logditto(html_log_file) else logditto(html_log_file) end if; logditto(html_log_file); logditto(html_log_file); if c(glob_percent_done) < glob__100 then logditto(html_log_file); 0 else logditto(html_log_file); 0 end if; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); 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/mtest1postode.ode################# diff ( y1 , x , 1 ) = neg ( y2 ) + 1.0 ; diff ( y2 , x , 1 ) = y1 - 1.0 ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=40; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := c(0.1); x_end := c(10.0); array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); glob_look_poles := true; 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_y1 := proc(x) return(c(1.0) + cos(c(x))); end; exact_soln_y2 := proc(x) return(c(1.0) + sin(c(x))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion memory used=3.6MB, alloc=40.3MB, time=0.14 TOP MAIN SOLVE Loop x[1] = 0.1 y1[1] (closed_form) = 1.9950041652780257660955619878039 y1[1] (numeric) = 1.9950041652780257660955619878039 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.0998334166468281523068141984106 y2[1] (numeric) = 1.0998334166468281523068141984106 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 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) = 32.01 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09933 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 2 memory used=45.5MB, alloc=40.3MB, time=0.63 TOP MAIN SOLVE Loop x[1] = 0.11 y1[1] (closed_form) = 1.9939560979566968503578396114198 y1[1] (numeric) = 1.9939560979566968503578396114199 absolute error = 1e-31 relative error = 5.0151555544515163299513758223921e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.1097783008371748086649494900834 y2[1] (numeric) = 1.1097783008371748086649494900834 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 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) = 32.01 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1091 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 2 memory used=87.3MB, alloc=40.3MB, time=1.08 memory used=128.8MB, alloc=40.3MB, time=1.55 TOP MAIN SOLVE Loop x[1] = 0.12 y1[1] (closed_form) = 1.9928086358538662522480981678576 y1[1] (numeric) = 1.9928086358538662522480981678577 absolute error = 1e-31 relative error = 5.0180432882935908112451694551819e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.119712207288919359967350614271 y2[1] (numeric) = 1.1197122072889193599673506142709 absolute error = 1e-31 relative error = 8.9308662841251848826513335689902e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 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) = 32.01 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1189 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 2 memory used=170.6MB, alloc=40.3MB, time=2.00 memory used=212.2MB, alloc=40.3MB, time=2.47 TOP MAIN SOLVE Loop x[1] = 0.13 y1[1] (closed_form) = 1.9915618937147880395945121711518 y1[1] (numeric) = 1.991561893714788039594512171152 absolute error = 2e-31 relative error = 1.0042369289710964831422071099758e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.1296341426196948595412058107083 y2[1] (numeric) = 1.1296341426196948595412058107081 absolute error = 2e-31 relative error = 1.7704847300045926851243791841683e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 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) = 32.02 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1285 Order of pole (three term test) = 32.98 NO COMPLEX POLE (six term test) for Equation 2 memory used=254.0MB, alloc=40.3MB, time=2.94 TOP MAIN SOLVE Loop memory used=295.7MB, alloc=40.3MB, time=3.41 x[1] = 0.14 y1[1] (closed_form) = 1.9902159962126371718989482270114 y1[1] (numeric) = 1.9902159962126371718989482270116 absolute error = 2e-31 relative error = 1.0049160512255864176420440742915e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.1395431146442364817179883517054 y2[1] (numeric) = 1.139543114644236481717988351705 absolute error = 4e-31 relative error = 3.5101787274181315499106401304621e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 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) = 32.02 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1382 Order of pole (three term test) = 32.98 NO COMPLEX POLE (six term test) for Equation 2 memory used=337.5MB, alloc=40.3MB, time=3.88 TOP MAIN SOLVE Loop x[1] = 0.15 y1[1] (closed_form) = 1.9887710779360422867349809986543 y1[1] (numeric) = 1.9887710779360422867349809986545 absolute error = 2e-31 relative error = 1.0056461611839262823506671282776e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.1494381324735992214977254386876 y2[1] (numeric) = 1.1494381324735992214977254386874 absolute error = 2e-31 relative error = 1.7399805552787651589749040948674e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 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) = 32.02 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1478 Order of pole (three term test) = 32.98 NO COMPLEX POLE (six term test) for Equation 2 memory used=379.3MB, alloc=40.3MB, time=4.34 memory used=420.9MB, alloc=40.3MB, time=4.80 TOP MAIN SOLVE Loop x[1] = 0.16 y1[1] (closed_form) = 1.9872272833756269490409525240183 y1[1] (numeric) = 1.9872272833756269490409525240185 absolute error = 2e-31 relative error = 1.0064274060301127337338940958891e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.159318206614245963311463159686 y2[1] (numeric) = 1.1593182066142459633114631596857 absolute error = 3e-31 relative error = 2.5877278411432957513901436913893e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.03 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1573 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 2 memory used=462.6MB, alloc=40.3MB, time=5.27 memory used=504.2MB, alloc=40.3MB, time=5.72 TOP MAIN SOLVE Loop x[1] = 0.17 y1[1] (closed_form) = 1.9855847669095607091719299902125 y1[1] (numeric) = 1.9855847669095607091719299902126 absolute error = 1e-31 relative error = 5.0362997171681461508806471945451e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.1691823490669960101576243766708 y2[1] (numeric) = 1.1691823490669960101576243766706 absolute error = 2e-31 relative error = 1.7105971550083645811415309402222e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.03 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1667 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 2 memory used=546.0MB, alloc=40.3MB, time=6.19 TOP MAIN SOLVE Loop memory used=587.6MB, alloc=40.3MB, time=6.64 x[1] = 0.18 y1[1] (closed_form) = 1.9838436927881214145927160246115 y1[1] (numeric) = 1.9838436927881214145927160246116 absolute error = 1e-31 relative error = 5.0407197080864074714095761345369e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.1790295734258241783418027396992 y2[1] (numeric) = 1.1790295734258241783418027396989 absolute error = 3e-31 relative error = 2.5444654380323207512376551905900e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.03 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1761 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 2 memory used=629.5MB, alloc=40.3MB, time=7.11 TOP MAIN SOLVE Loop x[1] = 0.19 y1[1] (closed_form) = 1.9820042351172703189678775041899 y1[1] (numeric) = 1.9820042351172703189678775041901 absolute error = 2e-31 relative error = 1.0090795794296902276075654013421e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.1888588949765005779928511529813 y2[1] (numeric) = 1.188858894976500577992851152981 absolute error = 3e-31 relative error = 2.5234281483500185301324555349713e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.04 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1855 Order of pole (three term test) = 32.96 NO COMPLEX POLE (six term test) for Equation 2 memory used=671.2MB, alloc=40.3MB, time=7.58 memory used=712.9MB, alloc=40.3MB, time=8.03 TOP MAIN SOLVE Loop x[1] = 0.2 y1[1] (closed_form) = 1.9800665778412416311241965167482 y1[1] (numeric) = 1.9800665778412416311241965167485 absolute error = 3e-31 relative error = 1.5151005696337423332428237405056e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.1986693307950612154594126271184 y2[1] (numeric) = 1.1986693307950612154594126271181 absolute error = 3e-31 relative error = 2.5027753050210606656367468154235e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.04 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1947 Order of pole (three term test) = 32.96 NO COMPLEX POLE (six term test) for Equation 2 memory used=754.8MB, alloc=40.3MB, time=8.50 memory used=796.5MB, alloc=40.3MB, time=8.97 TOP MAIN SOLVE Loop x[1] = 0.21 y1[1] (closed_form) = 1.9780309147241482449161385680994 y1[1] (numeric) = 1.9780309147241482449161385680997 absolute error = 3e-31 relative error = 1.5166598143984889496365564690110e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.2084598998460995706087124262276 y2[1] (numeric) = 1.2084598998460995706087124262274 absolute error = 2e-31 relative error = 1.6549990614125508560057056837875e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.04 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2039 Order of pole (three term test) = 32.96 NO COMPLEX POLE (six term test) for Equation 2 memory used=838.2MB, alloc=40.3MB, time=9.42 TOP MAIN SOLVE Loop memory used=880.0MB, alloc=40.3MB, time=9.89 x[1] = 0.22 y1[1] (closed_form) = 1.9758974493306054894060229810447 y1[1] (numeric) = 1.9758974493306054894060229810452 absolute error = 5e-31 relative error = 2.5304957004190171564532112113104e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.218229623080869319951791005457 y2[1] (numeric) = 1.2182296230808693199517910054567 absolute error = 3e-31 relative error = 2.4625899281722293393850446163784e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.05 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.213 Order of pole (three term test) = 32.95 NO COMPLEX POLE (six term test) for Equation 2 memory used=921.8MB, alloc=40.3MB, time=10.34 TOP MAIN SOLVE Loop x[1] = 0.23 y1[1] (closed_form) = 1.9736663950053748369677306480716 y1[1] (numeric) = 1.9736663950053748369677306480722 absolute error = 6e-31 relative error = 3.0400274409007507817083398467313e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.2279775235351883954046172123601 y2[1] (numeric) = 1.2279775235351883954046172123598 absolute error = 3e-31 relative error = 2.4430414584164278404004273601661e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.05 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.222 Order of pole (three term test) = 32.95 NO COMPLEX POLE (six term test) for Equation 2 memory used=963.7MB, alloc=40.3MB, time=10.83 memory used=1005.4MB, alloc=40.3MB, time=11.30 TOP MAIN SOLVE Loop x[1] = 0.24 y1[1] (closed_form) = 1.9713379748520296049261752469634 y1[1] (numeric) = 1.9713379748520296049261752469641 absolute error = 7e-31 relative error = 3.5508878179681118724898367705815e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.2377026264271345883607920844898 y2[1] (numeric) = 1.2377026264271345883607920844896 absolute error = 2e-31 relative error = 1.6158970315619209864958087473642e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.06 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2309 Order of pole (three term test) = 32.94 NO COMPLEX POLE (six term test) for Equation 2 memory used=1047.2MB, alloc=40.3MB, time=11.77 memory used=1088.9MB, alloc=40.3MB, time=12.22 TOP MAIN SOLVE Loop x[1] = 0.25 y1[1] (closed_form) = 1.9689124217106447841445954494942 y1[1] (numeric) = 1.968912421710644784144595449495 absolute error = 8e-31 relative error = 4.0631568533908592651295073313858e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.2474039592545229295968487048494 y2[1] (numeric) = 1.2474039592545229295968487048492 absolute error = 2e-31 relative error = 1.6033298476904351319729627552716e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.06 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2397 Order of pole (three term test) = 32.94 NO COMPLEX POLE (six term test) for Equation 2 memory used=1130.7MB, alloc=40.3MB, time=12.69 TOP MAIN SOLVE Loop x[1] = 0.26 y1[1] (closed_form) = 1.9663899781345132255582176464501 y1[1] (numeric) = 1.966389978134513225558217646451 absolute error = 9e-31 relative error = 4.5769151084354969112124928792545e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.2570805518921550973533884643652 y2[1] (numeric) = 1.2570805518921550973533884643649 absolute error = 3e-31 relative error = 2.3864819127814888902615199723276e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.07 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2484 Order of pole (three term test) = 32.93 NO COMPLEX POLE (six term test) for Equation 2 memory used=1172.5MB, alloc=40.3MB, time=13.16 memory used=1214.3MB, alloc=40.3MB, time=13.61 TOP MAIN SOLVE Loop x[1] = 0.27 y1[1] (closed_form) = 1.9637708963658905130162327094922 y1[1] (numeric) = 1.9637708963658905130162327094933 absolute error = 1.1e-30 relative error = 5.6014680838565987023130090620512e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.2667314366888311287322865210205 y2[1] (numeric) = 1.2667314366888311287322865210202 absolute error = 3e-31 relative error = 2.3682999514418313301192155511596e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.07 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2571 Order of pole (three term test) = 32.93 NO COMPLEX POLE (six term test) for Equation 2 memory used=1256.1MB, alloc=40.3MB, time=14.08 memory used=1297.6MB, alloc=40.3MB, time=14.55 TOP MAIN SOLVE Loop x[1] = 0.28 y1[1] (closed_form) = 1.9610554383107709479245900535965 y1[1] (numeric) = 1.9610554383107709479245900535975 absolute error = 1.0e-30 relative error = 5.0992949024500179833358581186582e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.2763556485641137333196695584578 y2[1] (numeric) = 1.2763556485641137333196695584576 absolute error = 2e-31 relative error = 1.5669613733836476662755628934786e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.08 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2656 Order of pole (three term test) = 32.92 NO COMPLEX POLE (six term test) for Equation 2 memory used=1339.4MB, alloc=40.3MB, time=15.00 memory used=1381.2MB, alloc=40.3MB, time=15.47 TOP MAIN SOLVE Loop x[1] = 0.29 y1[1] (closed_form) = 1.9582438755126971680701247779319 y1[1] (numeric) = 1.9582438755126971680701247779329 absolute error = 1.0e-30 relative error = 5.1066162519629238259191461445522e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.2859522251048355326839402055044 y2[1] (numeric) = 1.2859522251048355326839402055042 absolute error = 2e-31 relative error = 1.5552677315340798752445732797177e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.08 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.274 Order of pole (three term test) = 32.92 NO COMPLEX POLE (six term test) for Equation 2 memory used=1423.0MB, alloc=40.3MB, time=15.94 TOP MAIN SOLVE Loop x[1] = 0.3 y1[1] (closed_form) = 1.955336489125606019642310227568 y1[1] (numeric) = 1.9553364891256060196423102275691 absolute error = 1.1e-30 relative error = 5.6256301977564062033316022634293e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.295520206661339575105320745685 y2[1] (numeric) = 1.2955202066613395751053207456848 absolute error = 2e-31 relative error = 1.5437814012597780076888756295055e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.09 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2823 Order of pole (three term test) = 32.91 NO COMPLEX POLE (six term test) for Equation 2 memory used=1464.8MB, alloc=40.3MB, time=16.39 memory used=1506.5MB, alloc=40.3MB, time=16.86 TOP MAIN SOLVE Loop x[1] = 0.31 y1[1] (closed_form) = 1.9523335698857133978428054362022 y1[1] (numeric) = 1.9523335698857133978428054362033 absolute error = 1.1e-30 relative error = 5.6342830803467273621917995925121e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.305058636443443501565643323959 y2[1] (numeric) = 1.3050586364434435015656433239587 absolute error = 3e-31 relative error = 2.2987472870764064686855305439498e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.09 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2905 Order of pole (three term test) = 32.91 NO COMPLEX POLE (six term test) for Equation 2 memory used=1548.3MB, alloc=40.3MB, time=17.31 memory used=1590.0MB, alloc=40.3MB, time=17.78 TOP MAIN SOLVE Loop x[1] = 0.32 y1[1] (closed_form) = 1.9492354180824408675753072737661 y1[1] (numeric) = 1.9492354180824408675753072737672 absolute error = 1.1e-30 relative error = 5.6432383169095312104675503259976e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.3145665606161177666617575434172 y2[1] (numeric) = 1.3145665606161177666617575434169 absolute error = 3e-31 relative error = 2.2821210350839478866800472968371e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2986 Order of pole (three term test) = 32.9 NO COMPLEX POLE (six term test) for Equation 2 memory used=1631.9MB, alloc=40.3MB, time=18.25 TOP MAIN SOLVE Loop memory used=1673.5MB, alloc=40.3MB, time=18.70 x[1] = 0.33 y1[1] (closed_form) = 1.9460423435283869715294105783662 y1[1] (numeric) = 1.9460423435283869715294105783672 absolute error = 1.0e-30 relative error = 5.1386343330376406753083627226715e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.3240430283948683467001956961702 y2[1] (numeric) = 1.32404302839486834670019569617 absolute error = 2e-31 relative error = 1.5105249278979939004455728596918e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.11 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3066 Order of pole (three term test) = 32.89 NO COMPLEX POLE (six term test) for Equation 2 memory used=1715.3MB, alloc=40.3MB, time=19.17 TOP MAIN SOLVE Loop x[1] = 0.34 y1[1] (closed_form) = 1.9427546655283462285026440600266 y1[1] (numeric) = 1.9427546655283462285026440600276 absolute error = 1.0e-30 relative error = 5.1473303229877599789431571449149e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.3334870921408143967817714870308 y2[1] (numeric) = 1.3334870921408143967817714870307 absolute error = 1e-31 relative error = 7.4991352064351394557937651507292e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.11 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3144 Order of pole (three term test) = 32.89 NO COMPLEX POLE (six term test) for Equation 2 memory used=1757.0MB, alloc=40.3MB, time=19.64 memory used=1798.7MB, alloc=40.3MB, time=20.09 TOP MAIN SOLVE Loop x[1] = 0.35 y1[1] (closed_form) = 1.9393727128473789200350323573037 y1[1] (numeric) = 1.9393727128473789200350323573046 absolute error = 9e-31 relative error = 4.6406757919091465277971328208936e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.3428978074554513491896349069176 y2[1] (numeric) = 1.3428978074554513491896349069176 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.12 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3221 Order of pole (three term test) = 32.88 NO COMPLEX POLE (six term test) for Equation 2 memory used=1840.4MB, alloc=40.3MB, time=20.56 memory used=1882.1MB, alloc=40.3MB, time=21.02 TOP MAIN SOLVE Loop x[1] = 0.36 y1[1] (closed_form) = 1.9358968236779348583509123681247 y1[1] (numeric) = 1.9358968236779348583509123681256 absolute error = 9e-31 relative error = 4.6490080927460023819523534627274e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.3522742332750899768499134359207 y2[1] (numeric) = 1.3522742332750899768499134359207 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.12 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3297 Order of pole (three term test) = 32.88 NO COMPLEX POLE (six term test) for Equation 2 memory used=1924.0MB, alloc=40.3MB, time=21.48 TOP MAIN SOLVE Loop memory used=1965.8MB, alloc=40.3MB, time=21.98 x[1] = 0.37 y1[1] (closed_form) = 1.9323273456060344232038129044909 y1[1] (numeric) = 1.9323273456060344232038129044917 absolute error = 8e-31 relative error = 4.1400852801630076839914592661823e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.3616154319649619780372924691272 y2[1] (numeric) = 1.3616154319649619780372924691272 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.13 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3371 Order of pole (three term test) = 32.87 NO COMPLEX POLE (six term test) for Equation 2 memory used=2007.6MB, alloc=40.3MB, time=22.45 TOP MAIN SOLVE Loop x[1] = 0.38 y1[1] (closed_form) = 1.9286646355765102494925308077246 y1[1] (numeric) = 1.9286646355765102494925308077252 absolute error = 6e-31 relative error = 3.1109607597520443134137085159000e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.3709204694129826718454854663492 y2[1] (numeric) = 1.3709204694129826718454854663494 absolute error = 2e-31 relative error = 1.4588738330359778051773601637369e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.14 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3445 Order of pole (three term test) = 32.86 NO COMPLEX POLE (six term test) for Equation 2 memory used=2049.5MB, alloc=40.3MB, time=22.92 memory used=2091.1MB, alloc=40.3MB, time=23.37 TOP MAIN SOLVE Loop x[1] = 0.39 y1[1] (closed_form) = 1.9249090598573130414506767528811 y1[1] (numeric) = 1.9249090598573130414506767528817 absolute error = 6e-31 relative error = 3.1170303704865722764433345347010e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.3801884151231614282311820978472 y2[1] (numeric) = 1.3801884151231614282311820978474 absolute error = 2e-31 relative error = 1.4490775158560721171750110187086e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.14 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3516 Order of pole (three term test) = 32.86 NO COMPLEX POLE (six term test) for Equation 2 memory used=2133.0MB, alloc=40.3MB, time=23.84 memory used=2174.7MB, alloc=40.3MB, time=24.31 TOP MAIN SOLVE Loop x[1] = 0.4 y1[1] (closed_form) = 1.9210609940028850827985267320518 y1[1] (numeric) = 1.9210609940028850827985267320523 absolute error = 5e-31 relative error = 2.6027283962398181476349164956869e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.3894183423086504916663117567957 y2[1] (numeric) = 1.389418342308650491666311756796 absolute error = 3e-31 relative error = 2.1591769078096487269562799734596e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.15 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3587 Order of pole (three term test) = 32.85 NO COMPLEX POLE (six term test) for Equation 2 memory used=2216.4MB, alloc=40.3MB, time=24.78 TOP MAIN SOLVE Loop memory used=2258.1MB, alloc=40.3MB, time=25.25 x[1] = 0.41 y1[1] (closed_form) = 1.917120822816605105475642058277 y1[1] (numeric) = 1.9171208228166051054756420582777 absolute error = 7e-31 relative error = 3.6513087316613176131147236089912e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.3986093279844228935937976400511 y2[1] (numeric) = 1.3986093279844228935937976400515 absolute error = 4e-31 relative error = 2.8599837852965830296132404161208e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.16 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3656 Order of pole (three term test) = 32.84 NO COMPLEX POLE (six term test) for Equation 2 memory used=2300.0MB, alloc=40.3MB, time=25.70 TOP MAIN SOLVE Loop x[1] = 0.42 y1[1] (closed_form) = 1.9130889403123082724360887896657 y1[1] (numeric) = 1.9130889403123082724360887896664 absolute error = 7e-31 relative error = 3.6590039555909318025708625671599e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.4077604530595701859727871580863 y2[1] (numeric) = 1.4077604530595701859727871580868 absolute error = 5e-31 relative error = 3.5517406311089363653815726493951e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.17 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3723 Order of pole (three term test) = 32.83 NO COMPLEX POLE (six term test) for Equation 2 memory used=2341.8MB, alloc=40.3MB, time=26.17 memory used=2383.5MB, alloc=40.3MB, time=26.63 TOP MAIN SOLVE Loop x[1] = 0.43 y1[1] (closed_form) = 1.9089657496748851224759104776634 y1[1] (numeric) = 1.9089657496748851224759104776642 absolute error = 8e-31 relative error = 4.1907509348255595873890222898837e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.4168708024292107662169186726246 y2[1] (numeric) = 1.416870802429210766216918672625 absolute error = 4e-31 relative error = 2.8231226115620705555107735438864e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.17 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3789 Order of pole (three term test) = 32.83 NO COMPLEX POLE (six term test) for Equation 2 memory used=2425.3MB, alloc=40.3MB, time=27.09 memory used=2467.1MB, alloc=40.3MB, time=27.56 TOP MAIN SOLVE Loop x[1] = 0.44 y1[1] (closed_form) = 1.9047516632199634171655373889984 y1[1] (numeric) = 1.9047516632199634171655373889991 absolute error = 7e-31 relative error = 3.6750197598812281994924040423398e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.4259394650659996027697207507799 y2[1] (numeric) = 1.4259394650659996027697207507804 absolute error = 5e-31 relative error = 3.5064602127191809077482146374345e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.18 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3854 Order of pole (three term test) = 32.82 NO COMPLEX POLE (six term test) for Equation 2 memory used=2508.9MB, alloc=40.3MB, time=28.01 TOP MAIN SOLVE Loop x[1] = 0.45 y1[1] (closed_form) = 1.9004471023526769216688406114864 y1[1] (numeric) = 1.9004471023526769216688406114873 absolute error = 9e-31 relative error = 4.7357277078948225995494293730509e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.4349655341112302104208442462319 y2[1] (numeric) = 1.4349655341112302104208442462325 absolute error = 6e-31 relative error = 4.1812850952662078217022876062265e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.19 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3917 Order of pole (three term test) = 32.81 NO COMPLEX POLE (six term test) for Equation 2 memory used=2550.7MB, alloc=40.3MB, time=28.48 memory used=2592.4MB, alloc=40.3MB, time=28.94 TOP MAIN SOLVE Loop x[1] = 0.46 y1[1] (closed_form) = 1.8960524975255252425363899035004 y1[1] (numeric) = 1.8960524975255252425363899035012 absolute error = 8e-31 relative error = 4.2192924565329982571935800869880e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.4439481069655197652415136439289 y2[1] (numeric) = 1.4439481069655197652415136439295 absolute error = 6e-31 relative error = 4.1552739818393451603310637481914e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.2 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3978 Order of pole (three term test) = 32.8 NO COMPLEX POLE (six term test) for Equation 2 memory used=2634.3MB, alloc=40.3MB, time=29.41 memory used=2676.0MB, alloc=40.3MB, time=29.87 TOP MAIN SOLVE Loop x[1] = 0.47 y1[1] (closed_form) = 1.8915682881953289364540192765334 y1[1] (numeric) = 1.8915682881953289364540192765343 absolute error = 9e-31 relative error = 4.7579566945407753522039746130520e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.4528862853790682907032748003964 y2[1] (numeric) = 1.452886285379068290703274800397 absolute error = 6e-31 relative error = 4.1297106734231148956894654287902e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.21 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4038 Order of pole (three term test) = 32.79 NO COMPLEX POLE (six term test) for Equation 2 memory used=2717.8MB, alloc=40.3MB, time=30.33 memory used=2759.6MB, alloc=40.3MB, time=30.80 TOP MAIN SOLVE Loop x[1] = 0.48 y1[1] (closed_form) = 1.8869949227792841943999548311587 y1[1] (numeric) = 1.8869949227792841943999548311596 absolute error = 9e-31 relative error = 4.7694881906434792396618320604904e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.4617791755414828891366429425886 y2[1] (numeric) = 1.4617791755414828891366429425893 absolute error = 7e-31 relative error = 4.7886849923190409489817796102860e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.21 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4096 Order of pole (three term test) = 32.79 NO COMPLEX POLE (six term test) for Equation 2 memory used=2801.5MB, alloc=40.3MB, time=31.26 TOP MAIN SOLVE Loop x[1] = 0.49 y1[1] (closed_form) = 1.8823328586101214957054681591367 y1[1] (numeric) = 1.8823328586101214957054681591375 absolute error = 8e-31 relative error = 4.2500453431530949657466873062150e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.470625888171158036181358337188 y2[1] (numeric) = 1.4706258881711580361813583371885 absolute error = 5e-31 relative error = 3.3999129487771383339742580691484e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.22 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4152 Order of pole (three term test) = 32.78 NO COMPLEX POLE (six term test) for Equation 2 memory used=2843.3MB, alloc=40.3MB, time=31.72 memory used=2885.1MB, alloc=40.3MB, time=32.19 TOP MAIN SOLVE Loop x[1] = 0.5 y1[1] (closed_form) = 1.8775825618903727161162815826038 y1[1] (numeric) = 1.8775825618903727161162815826046 absolute error = 8e-31 relative error = 4.2607979869313995633948077194479e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.4794255386042030002732879352156 y2[1] (numeric) = 1.4794255386042030002732879352161 absolute error = 5e-31 relative error = 3.3796902037512218738644431408307e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.23 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4207 Order of pole (three term test) = 32.77 NO COMPLEX POLE (six term test) for Equation 2 memory used=2927.0MB, alloc=40.3MB, time=32.66 memory used=2968.6MB, alloc=40.3MB, time=33.11 TOP MAIN SOLVE Loop x[1] = 0.51 y1[1] (closed_form) = 1.8727445076457512631058084735755 y1[1] (numeric) = 1.8727445076457512631058084735763 absolute error = 8e-31 relative error = 4.2718053462919468607950533130625e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.4881772468829074945001302376746 y2[1] (numeric) = 1.4881772468829074945001302376751 absolute error = 5e-31 relative error = 3.3598148409222447531071760797816e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.24 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4261 Order of pole (three term test) = 32.76 NO COMPLEX POLE (six term test) for Equation 2 memory used=3010.5MB, alloc=40.3MB, time=33.58 TOP MAIN SOLVE Loop memory used=3052.2MB, alloc=40.3MB, time=34.03 x[1] = 0.52 y1[1] (closed_form) = 1.8678191796776499003878475719885 y1[1] (numeric) = 1.8678191796776499003878475719893 absolute error = 8e-31 relative error = 4.2830698426496766086447025780276e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.4968801378437367143344589425478 y2[1] (numeric) = 1.4968801378437367143344589425483 absolute error = 5e-31 relative error = 3.3402808104612336398629058143727e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.25 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4312 Order of pole (three term test) = 32.75 NO COMPLEX POLE (six term test) for Equation 2 memory used=3094.0MB, alloc=40.3MB, time=34.50 TOP MAIN SOLVE Loop x[1] = 0.53 y1[1] (closed_form) = 1.8628070705147610118066950185642 y1[1] (numeric) = 1.8628070705147610118066950185648 absolute error = 6e-31 relative error = 3.2209454725453575015572376807506e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.5055333412048469618136610224661 y2[1] (numeric) = 1.5055333412048469618136610224666 absolute error = 5e-31 relative error = 3.3210822126321056338591721703018e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.26 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4362 Order of pole (three term test) = 32.74 NO COMPLEX POLE (six term test) for Equation 2 memory used=3135.8MB, alloc=40.3MB, time=34.97 memory used=3177.6MB, alloc=40.3MB, time=35.42 TOP MAIN SOLVE Loop x[1] = 0.54 y1[1] (closed_form) = 1.8577086813638241425379687789178 y1[1] (numeric) = 1.8577086813638241425379687789183 absolute error = 5e-31 relative error = 2.6914876644325547016896916446517e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.5141359916531131046772806829582 y2[1] (numeric) = 1.5141359916531131046772806829588 absolute error = 6e-31 relative error = 3.9626559523555618777898480986526e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.26 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.441 Order of pole (three term test) = 32.74 NO COMPLEX POLE (six term test) for Equation 2 memory used=3219.4MB, alloc=40.3MB, time=35.89 memory used=3261.1MB, alloc=40.3MB, time=36.36 TOP MAIN SOLVE Loop x[1] = 0.55 y1[1] (closed_form) = 1.8525245220595057428049817976178 y1[1] (numeric) = 1.8525245220595057428049817976183 absolute error = 5e-31 relative error = 2.6990196029585366177845095383462e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.5226872289306591677883781077573 y2[1] (numeric) = 1.522687228930659167788378107758 absolute error = 7e-31 relative error = 4.5971358181784351351004520689163e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.27 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4456 Order of pole (three term test) = 32.73 NO COMPLEX POLE (six term test) for Equation 2 memory used=3303.0MB, alloc=40.3MB, time=36.81 TOP MAIN SOLVE Loop memory used=3344.7MB, alloc=40.3MB, time=37.28 x[1] = 0.56 y1[1] (closed_form) = 1.8472551110134161260945255038663 y1[1] (numeric) = 1.8472551110134161260945255038668 absolute error = 5e-31 relative error = 2.7067187256323072748962087373348e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.531186197920883403851869441112 y2[1] (numeric) = 1.5311861979208834038518694411127 absolute error = 7e-31 relative error = 4.5716190555432964649544973449706e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.28 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4501 Order of pole (three term test) = 32.72 NO COMPLEX POLE (six term test) for Equation 2 memory used=3386.5MB, alloc=40.3MB, time=37.75 TOP MAIN SOLVE Loop x[1] = 0.57 y1[1] (closed_form) = 1.841900975162268740133756363916 y1[1] (numeric) = 1.8419009751622687401337563639166 absolute error = 6e-31 relative error = 3.2575041117351104674930814373731e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.5396320487339692409944634930788 y2[1] (numeric) = 1.5396320487339692409944634930796 absolute error = 8e-31 relative error = 5.1960466830879202118571122483276e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.29 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4543 Order of pole (three term test) = 32.71 NO COMPLEX POLE (six term test) for Equation 2 memory used=3428.3MB, alloc=40.3MB, time=38.22 memory used=3470.1MB, alloc=40.3MB, time=38.67 TOP MAIN SOLVE Loop x[1] = 0.58 y1[1] (closed_form) = 1.83646264991518693465788732805 y1[1] (numeric) = 1.8364626499151869346578873280506 absolute error = 6e-31 relative error = 3.2671505735643995019872788096361e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.5480239367918735561826960595765 y2[1] (numeric) = 1.5480239367918735561826960595773 absolute error = 8e-31 relative error = 5.1678787451951217633635930628633e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.3 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4584 Order of pole (three term test) = 32.7 NO COMPLEX POLE (six term test) for Equation 2 memory used=3511.9MB, alloc=40.3MB, time=39.14 memory used=3553.6MB, alloc=40.3MB, time=39.59 TOP MAIN SOLVE Loop x[1] = 0.59 y1[1] (closed_form) = 1.8309406791001634952479965224907 y1[1] (numeric) = 1.8309406791001634952479965224912 absolute error = 5e-31 relative error = 2.7308366989023951066447606287685e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.5563610229127837757225433788758 y2[1] (numeric) = 1.5563610229127837757225433788765 absolute error = 7e-31 relative error = 4.4976711039057355599970448083517e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.31 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4623 Order of pole (three term test) = 32.69 NO COMPLEX POLE (six term test) for Equation 2 memory used=3595.4MB, alloc=40.3MB, time=40.06 TOP MAIN SOLVE Loop memory used=3637.2MB, alloc=40.3MB, time=40.53 x[1] = 0.6 y1[1] (closed_form) = 1.8253356149096782972409524989554 y1[1] (numeric) = 1.8253356149096782972409524989559 absolute error = 5e-31 relative error = 2.7392222883063678244810698399098e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.5646424733950353572009454456587 y2[1] (numeric) = 1.5646424733950353572009454456595 absolute error = 8e-31 relative error = 5.1129891563286154652821857122691e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.32 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.466 Order of pole (three term test) = 32.68 NO COMPLEX POLE (six term test) for Equation 2 memory used=3679.0MB, alloc=40.3MB, time=41.00 TOP MAIN SOLVE Loop x[1] = 0.61 y1[1] (closed_form) = 1.8196480178454795179007465786548 y1[1] (numeric) = 1.8196480178454795179007465786554 absolute error = 6e-31 relative error = 3.2973409918607163947175790284959e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.5728674601004812611909760321627 y2[1] (numeric) = 1.5728674601004812611909760321635 absolute error = 8e-31 relative error = 5.0862518317270846211117817492476e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.33 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4695 Order of pole (three term test) = 32.67 NO COMPLEX POLE (six term test) for Equation 2 memory used=3720.9MB, alloc=40.3MB, time=41.47 memory used=3762.7MB, alloc=40.3MB, time=41.92 TOP MAIN SOLVE Loop x[1] = 0.62 y1[1] (closed_form) = 1.8138784566625339286839996543607 y1[1] (numeric) = 1.8138784566625339286839996543612 absolute error = 5e-31 relative error = 2.7565242762736188216392931606199e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.5810351605373050758429632275822 y2[1] (numeric) = 1.581035160537305075842963227583 absolute error = 8e-31 relative error = 5.0599760205720214346801590183153e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.34 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4729 Order of pole (three term test) = 32.66 NO COMPLEX POLE (six term test) for Equation 2 memory used=3804.5MB, alloc=40.3MB, time=42.39 memory used=3846.2MB, alloc=40.3MB, time=42.84 TOP MAIN SOLVE Loop x[1] = 0.63 y1[1] (closed_form) = 1.8080275083121518725237089657771 y1[1] (numeric) = 1.8080275083121518725237089657774 absolute error = 3e-31 relative error = 1.6592667900283167397894795205249e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.5891447579422695131181120907946 y2[1] (numeric) = 1.5891447579422695131181120907955 absolute error = 9e-31 relative error = 5.6634236465995706380680710139379e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.35 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.476 Order of pole (three term test) = 32.65 NO COMPLEX POLE (six term test) for Equation 2 memory used=3888.1MB, alloc=40.3MB, time=43.31 TOP MAIN SOLVE Loop x[1] = 0.64 y1[1] (closed_form) = 1.8020957578842926135861107792603 y1[1] (numeric) = 1.8020957578842926135861107792607 absolute error = 4e-31 relative error = 2.2196378757897439639791373119786e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.5971954413623920518835462392079 y2[1] (numeric) = 1.5971954413623920518835462392089 absolute error = 1.0e-30 relative error = 6.2609745438980830325611501935312e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.36 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.479 Order of pole (three term test) = 32.64 NO COMPLEX POLE (six term test) for Equation 2 memory used=3929.9MB, alloc=40.3MB, time=43.78 memory used=3971.7MB, alloc=40.3MB, time=44.23 TOP MAIN SOLVE Loop x[1] = 0.65 y1[1] (closed_form) = 1.7960837985490558289176045706799 y1[1] (numeric) = 1.7960837985490558289176045706801 absolute error = 2e-31 relative error = 1.1135337903585987259748653798338e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.6051864057360395603725216786059 y2[1] (numeric) = 1.605186405736039560372521678607 absolute error = 1.1e-30 relative error = 6.8527866674500510200641691409838e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.37 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4818 Order of pole (three term test) = 32.63 NO COMPLEX POLE (six term test) for Equation 2 memory used=4013.5MB, alloc=40.3MB, time=44.70 memory used=4055.3MB, alloc=40.3MB, time=45.17 TOP MAIN SOLVE Loop x[1] = 0.66 y1[1] (closed_form) = 1.7899922314973650927838170912302 y1[1] (numeric) = 1.7899922314973650927838170912305 absolute error = 3e-31 relative error = 1.6759849273147060944544637298514e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.6131168519734337886151454793963 y2[1] (numeric) = 1.6131168519734337886151454793974 absolute error = 1.1e-30 relative error = 6.8190968227397562192516814649674e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.38 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4844 Order of pole (three term test) = 32.62 NO COMPLEX POLE (six term test) for Equation 2 memory used=4097.2MB, alloc=40.3MB, time=45.63 TOP MAIN SOLVE Loop memory used=4138.9MB, alloc=40.3MB, time=46.09 x[1] = 0.67 y1[1] (closed_form) = 1.7838216658808492853029421448381 y1[1] (numeric) = 1.7838216658808492853029421448385 absolute error = 4e-31 relative error = 2.2423766212217207014451307891782e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.6209859870365596803574439141266 y2[1] (numeric) = 1.6209859870365596803574439141276 absolute error = 1.0e-30 relative error = 6.1690847915852219097077708295877e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.39 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4867 Order of pole (three term test) = 32.61 NO COMPLEX POLE (six term test) for Equation 2 memory used=4180.8MB, alloc=40.3MB, time=46.55 TOP MAIN SOLVE Loop x[1] = 0.68 y1[1] (closed_form) = 1.7775727187509279371823940840443 y1[1] (numeric) = 1.7775727187509279371823940840447 absolute error = 4e-31 relative error = 2.2502595577697301451039766634115e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.6287930240184685137041781874202 y2[1] (numeric) = 1.6287930240184685137041781874211 absolute error = 9e-31 relative error = 5.5255639404666010201687723786083e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.4 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4889 Order of pole (three term test) = 32.6 NO COMPLEX POLE (six term test) for Equation 2 memory used=4222.6MB, alloc=40.3MB, time=47.02 memory used=4264.3MB, alloc=40.3MB, time=47.47 TOP MAIN SOLVE Loop x[1] = 0.69 y1[1] (closed_form) = 1.7712460149971066019735393154978 y1[1] (numeric) = 1.771246014997106601973539315498 absolute error = 2e-31 relative error = 1.1291486236615567354709239226839e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.6365371822219679402374292070087 y2[1] (numeric) = 1.6365371822219679402374292070096 absolute error = 9e-31 relative error = 5.4994167549437968042439004288060e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.41 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4909 Order of pole (three term test) = 32.59 NO COMPLEX POLE (six term test) for Equation 2 memory used=4306.1MB, alloc=40.3MB, time=47.94 memory used=4347.8MB, alloc=40.3MB, time=48.41 TOP MAIN SOLVE Loop x[1] = 0.7 y1[1] (closed_form) = 1.7648421872844884262558599901919 y1[1] (numeric) = 1.764842187284488426255859990192 absolute error = 1e-31 relative error = 5.6662290101908264424809517128610e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.6442176872376910536726143513987 y2[1] (numeric) = 1.6442176872376910536726143513997 absolute error = 1.0e-30 relative error = 6.0819197346065175188260274521277e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.42 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4927 Order of pole (three term test) = 32.58 NO COMPLEX POLE (six term test) for Equation 2 memory used=4389.6MB, alloc=40.3MB, time=48.86 TOP MAIN SOLVE Loop memory used=4431.3MB, alloc=40.3MB, time=49.33 x[1] = 0.71 y1[1] (closed_form) = 1.7583618759905081665414579441396 y1[1] (numeric) = 1.7583618759905081665414579441396 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.6518337710215366812101279728528 y2[1] (numeric) = 1.6518337710215366812101279728538 absolute error = 1.0e-30 relative error = 6.0538779236943083185531773730902e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.42 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4943 Order of pole (three term test) = 32.58 NO COMPLEX POLE (six term test) for Equation 2 memory used=4473.1MB, alloc=40.3MB, time=49.78 TOP MAIN SOLVE Loop x[1] = 0.72 y1[1] (closed_form) = 1.751805729140894979445486962252 y1[1] (numeric) = 1.7518057291408949794454869622519 absolute error = 1e-31 relative error = 5.7083955336212487798204503837466e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.6593846719714731536180038326482 y2[1] (numeric) = 1.6593846719714731536180038326492 absolute error = 1.0e-30 relative error = 6.0263302228284727680754475327508e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.43 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4957 Order of pole (three term test) = 32.57 NO COMPLEX POLE (six term test) for Equation 2 memory used=4515.0MB, alloc=40.3MB, time=50.25 memory used=4556.8MB, alloc=40.3MB, time=50.72 TOP MAIN SOLVE Loop x[1] = 0.73 y1[1] (closed_form) = 1.7451744023448703887901321585503 y1[1] (numeric) = 1.7451744023448703887901321585502 absolute error = 1e-31 relative error = 5.7300863378260019292174571738854e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.6668696350036978737325941307615 y2[1] (numeric) = 1.6668696350036978737325941307625 absolute error = 1.0e-30 relative error = 5.9992694029595274613422544528161e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.44 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4969 Order of pole (three term test) = 32.56 NO COMPLEX POLE (six term test) for Equation 2 memory used=4598.6MB, alloc=40.3MB, time=51.17 memory used=4640.3MB, alloc=40.3MB, time=51.64 TOP MAIN SOLVE Loop x[1] = 0.74 y1[1] (closed_form) = 1.7384685587295879097914245606988 y1[1] (numeric) = 1.7384685587295879097914245606986 absolute error = 2e-31 relative error = 1.1504378321696712944993922812682e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.6742879116281450674838811576082 y2[1] (numeric) = 1.6742879116281450674838811576093 absolute error = 1.1e-30 relative error = 6.5699572478565866926210579484038e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.45 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4979 Order of pole (three term test) = 32.55 NO COMPLEX POLE (six term test) for Equation 2 memory used=4682.1MB, alloc=40.3MB, time=52.11 TOP MAIN SOLVE Loop memory used=4723.9MB, alloc=40.3MB, time=52.56 x[1] = 0.75 y1[1] (closed_form) = 1.7316888688738208863118387530001 y1[1] (numeric) = 1.7316888688738208863118387529997 absolute error = 4e-31 relative error = 2.3098837625498758610321808593125e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.6816387600233341667332419527799 y2[1] (numeric) = 1.6816387600233341667332419527809 absolute error = 1.0e-30 relative error = 5.9465803463409950795293630973964e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.46 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4987 Order of pole (three term test) = 32.54 NO COMPLEX POLE (six term test) for Equation 2 memory used=4765.8MB, alloc=40.3MB, time=53.03 TOP MAIN SOLVE Loop x[1] = 0.76 y1[1] (closed_form) = 1.724836010740905172339688366667 y1[1] (numeric) = 1.7248360107409051723396883666667 absolute error = 3e-31 relative error = 1.7392957830880089047314622841127e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.6889214451105513391477556387697 y2[1] (numeric) = 1.6889214451105513391477556387707 absolute error = 1.0e-30 relative error = 5.9209384953634905857483909054948e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.47 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4994 Order of pole (three term test) = 32.53 NO COMPLEX POLE (six term test) for Equation 2 memory used=4807.5MB, alloc=40.3MB, time=53.50 memory used=4849.3MB, alloc=40.3MB, time=53.95 TOP MAIN SOLVE Loop x[1] = 0.77 y1[1] (closed_form) = 1.7179106696109433633712905653243 y1[1] (numeric) = 1.717910669610943363371290565324 absolute error = 3e-31 relative error = 1.7463073331277536436436098781629e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.6961352386273567470198837344522 y2[1] (numeric) = 1.6961352386273567470198837344531 absolute error = 9e-31 relative error = 5.3061806600300888047605693798603e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.48 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4998 Order of pole (three term test) = 32.52 NO COMPLEX POLE (six term test) for Equation 2 memory used=4891.1MB, alloc=40.3MB, time=54.42 memory used=4932.8MB, alloc=40.3MB, time=54.87 TOP MAIN SOLVE Loop x[1] = 0.78 y1[1] (closed_form) = 1.7109135380122773572162650237646 y1[1] (numeric) = 1.7109135380122773572162650237642 absolute error = 4e-31 relative error = 2.3379322865415869835560852635835e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.7032794192004101843678973251179 y2[1] (numeric) = 1.7032794192004101843678973251188 absolute error = 9e-31 relative error = 5.2839245860347283979756198357756e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.49 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5 Order of pole (three term test) = 32.51 NO COMPLEX POLE (six term test) for Equation 2 memory used=4974.5MB, alloc=40.3MB, time=55.34 TOP MAIN SOLVE Loop x[1] = 0.79 y1[1] (closed_form) = 1.703845315652236096912780861085 y1[1] (numeric) = 1.7038453156522360969127808610844 absolute error = 6e-31 relative error = 3.5214464276078873548269116380575e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.7103532724176078098140288749692 y2[1] (numeric) = 1.7103532724176078098140288749701 absolute error = 9e-31 relative error = 5.2620707927072730160340494674210e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5 Order of pole (three term test) = 32.5 NO COMPLEX POLE (six term test) for Equation 2 memory used=5016.4MB, alloc=40.3MB, time=55.81 memory used=5058.1MB, alloc=40.3MB, time=56.28 TOP MAIN SOLVE Loop x[1] = 0.8 y1[1] (closed_form) = 1.6967067093471654209207499816423 y1[1] (numeric) = 1.6967067093471654209207499816416 absolute error = 7e-31 relative error = 4.1256393703384128431764496480596e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.7173560908995227616271746105814 y2[1] (numeric) = 1.7173560908995227616271746105825 absolute error = 1.1e-30 relative error = 6.4051946234623837643034099777316e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.51 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4998 Order of pole (three term test) = 32.49 NO COMPLEX POLE (six term test) for Equation 2 memory used=5099.9MB, alloc=40.3MB, time=56.75 memory used=5141.7MB, alloc=40.3MB, time=57.20 TOP MAIN SOLVE Loop x[1] = 0.81 y1[1] (closed_form) = 1.6894984329517470175496392406801 y1[1] (numeric) = 1.6894984329517470175496392406795 absolute error = 6e-31 relative error = 3.5513498461891519385642759755239e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.7242871743701425109281768525145 y2[1] (numeric) = 1.7242871743701425109281768525156 absolute error = 1.1e-30 relative error = 6.3794477877608426596711428358684e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.52 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4994 Order of pole (three term test) = 32.48 NO COMPLEX POLE (six term test) for Equation 2 memory used=5183.5MB, alloc=40.3MB, time=57.67 memory used=5225.2MB, alloc=40.3MB, time=58.12 TOP MAIN SOLVE Loop x[1] = 0.82 y1[1] (closed_form) = 1.6822212072876135516665579784369 y1[1] (numeric) = 1.6822212072876135516665579784365 absolute error = 4e-31 relative error = 2.3778085680239020031373752737322e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.7311458297268958793813133646877 y2[1] (numeric) = 1.7311458297268958793813133646888 absolute error = 1.1e-30 relative error = 6.3541729478303689846719965308294e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.53 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4988 Order of pole (three term test) = 32.47 NO COMPLEX POLE (six term test) for Equation 2 memory used=5267.1MB, alloc=40.3MB, time=58.59 TOP MAIN SOLVE Loop x[1] = 0.83 y1[1] (closed_form) = 1.6748757600712671021124629178644 y1[1] (numeric) = 1.6748757600712671021124629178641 absolute error = 3e-31 relative error = 1.7911776333023937015518563885435e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.7379313711099627187285802261381 y2[1] (numeric) = 1.7379313711099627187285802261391 absolute error = 1.0e-30 relative error = 5.7539671394580506308555960959128e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.54 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.498 Order of pole (three term test) = 32.46 NO COMPLEX POLE (six term test) for Equation 2 memory used=5308.9MB, alloc=40.3MB, time=59.06 memory used=5350.6MB, alloc=40.3MB, time=59.52 TOP MAIN SOLVE Loop x[1] = 0.84 y1[1] (closed_form) = 1.6674628258413081179226710368709 y1[1] (numeric) = 1.6674628258413081179226710368706 absolute error = 3e-31 relative error = 1.7991405586426602600450780880416e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.7446431199708593212565726706296 y2[1] (numeric) = 1.7446431199708593212565726706307 absolute error = 1.1e-30 relative error = 6.3050144032802149239545741058735e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.55 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.497 Order of pole (three term test) = 32.45 NO COMPLEX POLE (six term test) for Equation 2 memory used=5392.5MB, alloc=40.3MB, time=59.98 memory used=5434.2MB, alloc=40.3MB, time=60.45 TOP MAIN SOLVE Loop x[1] = 0.85 y1[1] (closed_form) = 1.6599831458849821703954160294615 y1[1] (numeric) = 1.6599831458849821703954160294613 absolute error = 2e-31 relative error = 1.2048315098607495773354058660782e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.7512804051402927027120715242355 y2[1] (numeric) = 1.7512804051402927027120715242365 absolute error = 1.0e-30 relative error = 5.7101078563138000370993153595601e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.56 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4958 Order of pole (three term test) = 32.44 NO COMPLEX POLE (six term test) for Equation 2 memory used=5476.0MB, alloc=40.3MB, time=60.92 TOP MAIN SOLVE Loop memory used=5517.7MB, alloc=40.3MB, time=61.39 x[1] = 0.86 y1[1] (closed_form) = 1.6524374681640518462720306642239 y1[1] (numeric) = 1.6524374681640518462720306642237 absolute error = 2e-31 relative error = 1.2103332431829381617794594347584e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.7578425628952769722945887295286 y2[1] (numeric) = 1.7578425628952769722945887295296 absolute error = 1.0e-30 relative error = 5.6887915966315963416482375164598e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.57 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4944 Order of pole (three term test) = 32.43 NO COMPLEX POLE (six term test) for Equation 2 memory used=5559.6MB, alloc=40.3MB, time=61.84 TOP MAIN SOLVE Loop x[1] = 0.87 y1[1] (closed_form) = 1.6448265472400011947776638054828 y1[1] (numeric) = 1.6448265472400011947776638054827 absolute error = 1e-31 relative error = 6.0796684104958529208545021706576e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.7643289370255050781448028237228 y2[1] (numeric) = 1.7643289370255050781448028237238 absolute error = 1.0e-30 relative error = 5.6678773385982504834720026856375e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.58 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4929 Order of pole (three term test) = 32.42 NO COMPLEX POLE (six term test) for Equation 2 memory used=5601.4MB, alloc=40.3MB, time=62.31 memory used=5643.1MB, alloc=40.3MB, time=62.78 TOP MAIN SOLVE Loop x[1] = 0.88 y1[1] (closed_form) = 1.6371511441985802080154986057221 y1[1] (numeric) = 1.6371511441985802080154986057219 absolute error = 2e-31 relative error = 1.2216343048637955235862318432519e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.770738878898969291209645130756 y2[1] (numeric) = 1.7707388788989692912096451307569 absolute error = 9e-31 relative error = 5.0826240431317152491304712522212e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.59 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4911 Order of pole (three term test) = 32.41 NO COMPLEX POLE (six term test) for Equation 2 memory used=5685.0MB, alloc=40.3MB, time=63.23 memory used=5726.7MB, alloc=40.3MB, time=63.70 TOP MAIN SOLVE Loop x[1] = 0.89 y1[1] (closed_form) = 1.6294120265736968802035530573802 y1[1] (numeric) = 1.6294120265736968802035530573801 absolute error = 1e-31 relative error = 6.1371831291977448468527348948596e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.7770717475268238654903337129732 y2[1] (numeric) = 1.7770717475268238654903337129742 absolute error = 1.0e-30 relative error = 5.6272348113784054238570141075072e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.6 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4891 Order of pole (three term test) = 32.4 NO COMPLEX POLE (six term test) for Equation 2 memory used=5768.5MB, alloc=40.3MB, time=64.16 TOP MAIN SOLVE Loop memory used=5810.2MB, alloc=40.3MB, time=64.62 x[1] = 0.9 y1[1] (closed_form) = 1.6216099682706644564847161514071 y1[1] (numeric) = 1.6216099682706644564847161514072 absolute error = 1e-31 relative error = 6.1667109820891841753494332291975e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.7833269096274833884613823157136 y2[1] (numeric) = 1.7833269096274833884613823157146 absolute error = 1.0e-30 relative error = 5.6074968341552619311245879096031e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.61 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4869 Order of pole (three term test) = 32.39 NO COMPLEX POLE (six term test) for Equation 2 memory used=5852.1MB, alloc=40.3MB, time=65.09 TOP MAIN SOLVE Loop x[1] = 0.91 y1[1] (closed_form) = 1.6137457494888115465211782261747 y1[1] (numeric) = 1.6137457494888115465211782261748 absolute error = 1e-31 relative error = 6.1967630298438980922494390229635e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.7895037396899504118789575178716 y2[1] (numeric) = 1.7895037396899504118789575178727 absolute error = 1.1e-30 relative error = 6.1469555810516836618086184536913e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.62 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4846 Order of pole (three term test) = 32.38 NO COMPLEX POLE (six term test) for Equation 2 memory used=5894.0MB, alloc=40.3MB, time=65.56 memory used=5935.6MB, alloc=40.3MB, time=66.02 TOP MAIN SOLVE Loop x[1] = 0.92 y1[1] (closed_form) = 1.6058201566434628417974047066744 y1[1] (numeric) = 1.6058201566434628417974047066743 absolute error = 1e-31 relative error = 6.2273474141103839376996914003978e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.7956016200363660302682761024816 y2[1] (numeric) = 1.7956016200363660302682761024827 absolute error = 1.1e-30 relative error = 6.1260804608637069354695367328441e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.63 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.482 Order of pole (three term test) = 32.37 NO COMPLEX POLE (six term test) for Equation 2 memory used=5977.5MB, alloc=40.3MB, time=66.48 memory used=6019.3MB, alloc=40.3MB, time=66.95 TOP MAIN SOLVE Loop x[1] = 0.93 y1[1] (closed_form) = 1.597833982287298238494907084433 y1[1] (numeric) = 1.5978339822872982384949070844329 absolute error = 1e-31 relative error = 6.2584724763989603782639539155790e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.8016199408837771520843192159106 y2[1] (numeric) = 1.8016199408837771520843192159118 absolute error = 1.2e-30 relative error = 6.6606722803664406717716384081577e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.64 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4792 Order of pole (three term test) = 32.36 NO COMPLEX POLE (six term test) for Equation 2 memory used=6061.1MB, alloc=40.3MB, time=67.41 TOP MAIN SOLVE Loop x[1] = 0.94 y1[1] (closed_form) = 1.589788025031098229960989815224 y1[1] (numeric) = 1.5897880250310982299609898152238 absolute error = 2e-31 relative error = 1.2580293526622063428193425676008e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.8075581004051142868702197986342 y2[1] (numeric) = 1.8075581004051142868702197986354 absolute error = 1.2e-30 relative error = 6.6387907516281391004657365866966e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=6102.9MB, alloc=40.3MB, time=67.87 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) = 32.65 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4763 Order of pole (three term test) = 32.35 NO COMPLEX POLE (six term test) for Equation 2 memory used=6144.6MB, alloc=40.3MB, time=68.34 TOP MAIN SOLVE Loop x[1] = 0.95 y1[1] (closed_form) = 1.5816830894638834941661809737605 y1[1] (numeric) = 1.58168308946388349416618097376 absolute error = 5e-31 relative error = 3.1611895159698305161625311336748e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.8134155047893737506854221021026 y2[1] (numeric) = 1.8134155047893737506854221021038 absolute error = 1.2e-30 relative error = 6.6173471928011264134592541873134e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.66 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4732 Order of pole (three term test) = 32.34 NO COMPLEX POLE (six term test) for Equation 2 memory used=6186.5MB, alloc=40.3MB, time=68.80 memory used=6228.2MB, alloc=40.3MB, time=69.27 TOP MAIN SOLVE Loop x[1] = 0.96 y1[1] (closed_form) = 1.5735199860724566621250508003519 y1[1] (numeric) = 1.5735199860724566621250508003513 absolute error = 6e-31 relative error = 3.8131069532686030959891061427726e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.8191915683009982716332221464304 y2[1] (numeric) = 1.8191915683009982716332221464316 absolute error = 1.2e-30 relative error = 6.5963366415595183056497609050378e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.67 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4698 Order of pole (three term test) = 32.33 NO COMPLEX POLE (six term test) for Equation 2 memory used=6270.1MB, alloc=40.3MB, time=69.75 memory used=6311.9MB, alloc=40.3MB, time=70.28 TOP MAIN SOLVE Loop x[1] = 0.97 y1[1] (closed_form) = 1.5652995311603543130365277548499 y1[1] (numeric) = 1.5652995311603543130365277548493 absolute error = 6e-31 relative error = 3.8331321772978546448763949764241e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.8248857133384500574766200378563 y2[1] (numeric) = 1.8248857133384500574766200378575 absolute error = 1.2e-30 relative error = 6.5757542580829200636082281336399e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.68 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4663 Order of pole (three term test) = 32.32 NO COMPLEX POLE (six term test) for Equation 2 memory used=6353.7MB, alloc=40.3MB, time=70.80 TOP MAIN SOLVE Loop x[1] = 0.98 y1[1] (closed_form) = 1.5570225467662173008766582673599 y1[1] (numeric) = 1.5570225467662173008766582673593 absolute error = 6e-31 relative error = 3.8535087449192112922450918099611e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.8304973704919704680845332877192 y2[1] (numeric) = 1.8304973704919704680845332877203 absolute error = 1.1e-30 relative error = 6.0092957123689306232259040553489e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.69 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4626 Order of pole (three term test) = 32.31 NO COMPLEX POLE (six term test) for Equation 2 memory used=6395.5MB, alloc=40.3MB, time=71.27 memory used=6437.3MB, alloc=40.3MB, time=71.73 TOP MAIN SOLVE Loop x[1] = 0.99 y1[1] (closed_form) = 1.5486898605815875753431264086536 y1[1] (numeric) = 1.5486898605815875753431264086531 absolute error = 5e-31 relative error = 3.2285353751346469972147487334409e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.8360259786005205167892594115471 y2[1] (numeric) = 1.8360259786005205167892594115483 absolute error = 1.2e-30 relative error = 6.5358552329127691884278112370427e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.7 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4587 Order of pole (three term test) = 32.3 NO COMPLEX POLE (six term test) for Equation 2 memory used=6479.1MB, alloc=40.3MB, time=72.20 memory used=6520.8MB, alloc=40.3MB, time=72.66 TOP MAIN SOLVE Loop x[1] = 1 y1[1] (closed_form) = 1.540302305868139717400936607443 y1[1] (numeric) = 1.5403023058681397174009366074424 absolute error = 6e-31 relative error = 3.8953392312285745106512994965630e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.8414709848078965066525023216303 y2[1] (numeric) = 1.8414709848078965066525023216314 absolute error = 1.1e-30 relative error = 5.9734853770435744380681973998392e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.71 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4546 Order of pole (three term test) = 32.29 NO COMPLEX POLE (six term test) for Equation 2 memory used=6562.6MB, alloc=40.3MB, time=73.13 TOP MAIN SOLVE Loop memory used=6604.3MB, alloc=40.3MB, time=73.59 x[1] = 1.01 y1[1] (closed_form) = 1.5318607213743554662067313557792 y1[1] (numeric) = 1.5318607213743554662067313557784 absolute error = 8e-31 relative error = 5.2224068992529272055856311269539e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.846831844618015190123098784782 y2[1] (numeric) = 1.846831844618015190123098784783 absolute error = 1.0e-30 relative error = 5.4146781306277100697667690010343e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.72 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4504 Order of pole (three term test) = 32.28 NO COMPLEX POLE (six term test) for Equation 2 memory used=6646.1MB, alloc=40.3MB, time=74.05 TOP MAIN SOLVE Loop x[1] = 1.02 y1[1] (closed_form) = 1.5233659512516495698896138080338 y1[1] (numeric) = 1.5233659512516495698896138080331 absolute error = 7e-31 relative error = 4.5950876046878693697908454245795e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.8521080219493629236165499854554 y2[1] (numeric) = 1.8521080219493629236165499854565 absolute error = 1.1e-30 relative error = 5.9391784224455686912587188287402e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.73 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.446 Order of pole (three term test) = 32.27 NO COMPLEX POLE (six term test) for Equation 2 memory used=6687.9MB, alloc=40.3MB, time=74.52 memory used=6729.7MB, alloc=40.3MB, time=74.98 TOP MAIN SOLVE Loop x[1] = 1.03 y1[1] (closed_form) = 1.5148188449699553475335022998374 y1[1] (numeric) = 1.5148188449699553475335022998366 absolute error = 8e-31 relative error = 5.2811595436407913205679819553151e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.8572989891886033721462743852944 y2[1] (numeric) = 1.8572989891886033721462743852957 absolute error = 1.3e-30 relative error = 6.9994115517606020612001546146059e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.73 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4414 Order of pole (three term test) = 32.27 NO COMPLEX POLE (six term test) for Equation 2 memory used=6771.5MB, alloc=40.3MB, time=75.44 memory used=6813.3MB, alloc=40.3MB, time=75.91 TOP MAIN SOLVE Loop x[1] = 1.04 y1[1] (closed_form) = 1.5062202572327784037344734209922 y1[1] (numeric) = 1.5062202572327784037344734209915 absolute error = 7e-31 relative error = 4.6473946731139912470772395250600e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.8624042272433384032807916921162 y2[1] (numeric) = 1.8624042272433384032807916921174 absolute error = 1.2e-30 relative error = 6.4432843442166980626135497348783e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.74 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4366 Order of pole (three term test) = 32.26 NO COMPLEX POLE (six term test) for Equation 2 memory used=6855.1MB, alloc=40.3MB, time=76.38 TOP MAIN SOLVE Loop memory used=6896.8MB, alloc=40.3MB, time=76.83 x[1] = 1.05 y1[1] (closed_form) = 1.4975710478917269902908495728121 y1[1] (numeric) = 1.4975710478917269902908495728114 absolute error = 7e-31 relative error = 4.6742356630455462459820387855994e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.8674232255940168943814094850003 y2[1] (numeric) = 1.8674232255940168943814094850015 absolute error = 1.2e-30 relative error = 6.4259669878438333369681345826992e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.75 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4316 Order of pole (three term test) = 32.25 NO COMPLEX POLE (six term test) for Equation 2 memory used=6938.6MB, alloc=40.3MB, time=77.30 TOP MAIN SOLVE Loop x[1] = 1.06 y1[1] (closed_form) = 1.4888720818605275619186375399564 y1[1] (numeric) = 1.4888720818605275619186375399559 absolute error = 5e-31 relative error = 3.3582468641307916456851203742251e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.8723554823449862622829459219974 y2[1] (numeric) = 1.8723554823449862622829459219986 absolute error = 1.2e-30 relative error = 6.4090393694742681684315028837423e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.76 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4265 Order of pole (three term test) = 32.24 NO COMPLEX POLE (six term test) for Equation 2 memory used=6980.5MB, alloc=40.3MB, time=77.76 memory used=7022.2MB, alloc=40.3MB, time=78.23 TOP MAIN SOLVE Loop x[1] = 1.07 y1[1] (closed_form) = 1.4801242290285341243650930681759 y1[1] (numeric) = 1.4801242290285341243650930681755 absolute error = 4e-31 relative error = 2.7024758608440340703949211437902e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.8772005042746816103070632577768 y2[1] (numeric) = 1.8772005042746816103070632577781 absolute error = 1.3e-30 relative error = 6.9252058959056050268377083921943e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.77 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4212 Order of pole (three term test) = 32.23 NO COMPLEX POLE (six term test) for Equation 2 memory used=7064.0MB, alloc=40.3MB, time=78.69 memory used=7105.8MB, alloc=40.3MB, time=79.16 TOP MAIN SOLVE Loop x[1] = 1.08 y1[1] (closed_form) = 1.471328364173740023913524788526 y1[1] (numeric) = 1.4713283641737400239135247885256 absolute error = 4e-31 relative error = 2.7186317462494489472062900332304e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.8819578068849474737353349876248 y2[1] (numeric) = 1.881957806884947473735334987626 absolute error = 1.2e-30 relative error = 6.3763384896830547548809387809117e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.78 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4157 Order of pole (three term test) = 32.22 NO COMPLEX POLE (six term test) for Equation 2 memory used=7147.6MB, alloc=40.3MB, time=79.63 TOP MAIN SOLVE Loop memory used=7189.4MB, alloc=40.3MB, time=80.08 x[1] = 1.09 y1[1] (closed_form) = 1.4624853668753008770278970738751 y1[1] (numeric) = 1.4624853668753008770278970738747 absolute error = 4e-31 relative error = 2.7350701009380156368116273771998e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.886626914449487231608600628636 y2[1] (numeric) = 1.8866269144494872316086006286373 absolute error = 1.3e-30 relative error = 6.8906045495451684396543670149804e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.79 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4101 Order of pole (three term test) = 32.21 NO COMPLEX POLE (six term test) for Equation 2 memory used=7230.9MB, alloc=40.3MB, time=80.55 TOP MAIN SOLVE Loop x[1] = 1.1 y1[1] (closed_form) = 1.4535961214255773877713700517847 y1[1] (numeric) = 1.4535961214255773877713700517843 absolute error = 4e-31 relative error = 2.7517960051221805953487480031032e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.8912073600614353399518025778717 y2[1] (numeric) = 1.891207360061435339951802577873 absolute error = 1.3e-30 relative error = 6.8739157188864253632188556277634e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.79 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4042 Order of pole (three term test) = 32.21 NO COMPLEX POLE (six term test) for Equation 2 memory used=7272.4MB, alloc=40.3MB, time=81.00 memory used=7313.9MB, alloc=40.3MB, time=81.47 TOP MAIN SOLVE Loop x[1] = 1.11 y1[1] (closed_form) = 1.4446615167417068486437375119336 y1[1] (numeric) = 1.4446615167417068486437375119331 absolute error = 5e-31 relative error = 3.4610183368606733179351061534537e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.8956986856800476292406259593394 y2[1] (numeric) = 1.8956986856800476292406259593406 absolute error = 1.2e-30 relative error = 6.3301199133844506307150958466920e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.8 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3983 Order of pole (three term test) = 32.2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7355.4MB, alloc=40.3MB, time=81.92 memory used=7396.9MB, alloc=40.3MB, time=82.38 TOP MAIN SOLVE Loop x[1] = 1.12 y1[1] (closed_form) = 1.4356824462767121676139887939611 y1[1] (numeric) = 1.4356824462767121676139887939608 absolute error = 3e-31 relative error = 2.0895985792541915969706446406115e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9001004421765049971191032473392 y2[1] (numeric) = 1.9001004421765049971191032473404 absolute error = 1.2e-30 relative error = 6.3154556115225042011133830149338e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.81 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3922 Order of pole (three term test) = 32.19 NO COMPLEX POLE (six term test) for Equation 2 memory used=7438.4MB, alloc=40.3MB, time=82.84 TOP MAIN SOLVE Loop memory used=7479.9MB, alloc=40.3MB, time=83.30 x[1] = 1.13 y1[1] (closed_form) = 1.4266598079301573103712158356535 y1[1] (numeric) = 1.4266598079301573103712158356531 absolute error = 4e-31 relative error = 2.8037517968655226646327619856208e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9044121893788259160370815224114 y2[1] (numeric) = 1.9044121893788259160370815224125 absolute error = 1.1e-30 relative error = 5.7760604880332860516758634632680e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.82 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3859 Order of pole (three term test) = 32.18 NO COMPLEX POLE (six term test) for Equation 2 memory used=7521.4MB, alloc=40.3MB, time=83.75 TOP MAIN SOLVE Loop x[1] = 1.14 y1[1] (closed_form) = 1.4175945039583580921751867408226 y1[1] (numeric) = 1.4175945039583580921751867408222 absolute error = 4e-31 relative error = 2.8216813685653935037129581349355e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9086334961158832645942155781022 y2[1] (numeric) = 1.9086334961158832645942155781032 absolute error = 1.0e-30 relative error = 5.2393505722027037878934821367571e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.83 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3794 Order of pole (three term test) = 32.17 NO COMPLEX POLE (six term test) for Equation 2 memory used=7563.0MB, alloc=40.3MB, time=84.25 memory used=7604.5MB, alloc=40.3MB, time=84.70 TOP MAIN SOLVE Loop x[1] = 1.15 y1[1] (closed_form) = 1.4084874408841572981525767188099 y1[1] (numeric) = 1.4084874408841572981525767188095 absolute error = 4e-31 relative error = 2.8399259261332559459646770122429e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9127639402605210809440330497537 y2[1] (numeric) = 1.9127639402605210809440330497545 absolute error = 8e-31 relative error = 4.1824293273274427113429530660990e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.83 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3729 Order of pole (three term test) = 32.17 NO COMPLEX POLE (six term test) for Equation 2 memory used=7646.1MB, alloc=40.3MB, time=85.17 memory used=7687.6MB, alloc=40.3MB, time=85.62 TOP MAIN SOLVE Loop x[1] = 1.16 y1[1] (closed_form) = 1.399339529406273154451639623394 y1[1] (numeric) = 1.3993395294062731544516396233934 absolute error = 6e-31 relative error = 4.2877370887576831451683561801968e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9168031087717669266186616668743 y2[1] (numeric) = 1.916803108771766926618661666875 absolute error = 7e-31 relative error = 3.6519139435689884114565642582163e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.84 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3661 Order of pole (three term test) = 32.16 NO COMPLEX POLE (six term test) for Equation 2 memory used=7729.2MB, alloc=40.3MB, time=86.09 TOP MAIN SOLVE Loop memory used=7770.7MB, alloc=40.3MB, time=86.55 x[1] = 1.17 y1[1] (closed_form) = 1.3901516843082302153326619350505 y1[1] (numeric) = 1.3901516843082302153326619350499 absolute error = 6e-31 relative error = 4.3160757690882709719480063350905e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.920750597736135639573013008962 y2[1] (numeric) = 1.9207505977361356395730130089626 absolute error = 6e-31 relative error = 3.1237788014080596920625910853260e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.85 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3592 Order of pole (three term test) = 32.15 NO COMPLEX POLE (six term test) for Equation 2 memory used=7812.3MB, alloc=40.3MB, time=87.01 TOP MAIN SOLVE Loop x[1] = 1.18 y1[1] (closed_form) = 1.3809248243668817730295994667128 y1[1] (numeric) = 1.3809248243668817730295994667122 absolute error = 6e-31 relative error = 4.3449142879670111154211702769903e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9246060124080203461075380258748 y2[1] (numeric) = 1.9246060124080203461075380258755 absolute error = 7e-31 relative error = 3.6371080391886388428364436604748e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.85 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3522 Order of pole (three term test) = 32.15 NO COMPLEX POLE (six term test) for Equation 2 memory used=7853.9MB, alloc=40.3MB, time=87.47 memory used=7895.4MB, alloc=40.3MB, time=87.92 TOP MAIN SOLVE Loop x[1] = 1.19 y1[1] (closed_form) = 1.3716598722605329380656795583505 y1[1] (numeric) = 1.37165987226053293806567955835 absolute error = 5e-31 relative error = 3.6452185422322397015495260973051e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9283689672491666926020211116027 y2[1] (numeric) = 1.9283689672491666926020211116033 absolute error = 6e-31 relative error = 3.1114377496745587000916069602963e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.86 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.345 Order of pole (three term test) = 32.14 NO COMPLEX POLE (six term test) for Equation 2 memory used=7936.9MB, alloc=40.3MB, time=88.39 memory used=7978.4MB, alloc=40.3MB, time=88.84 TOP MAIN SOLVE Loop x[1] = 1.2 y1[1] (closed_form) = 1.3623577544766735776383733556231 y1[1] (numeric) = 1.3623577544766735776383733556226 absolute error = 5e-31 relative error = 3.6701079313198936158870182224103e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9320390859672263496701344354948 y2[1] (numeric) = 1.9320390859672263496701344354954 absolute error = 6e-31 relative error = 3.1055272347123620581247067478483e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.87 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3377 Order of pole (three term test) = 32.13 NO COMPLEX POLE (six term test) for Equation 2 memory used=8019.9MB, alloc=40.3MB, time=89.31 TOP MAIN SOLVE Loop x[1] = 1.21 y1[1] (closed_form) = 1.3530194012193303387030107136648 y1[1] (numeric) = 1.3530194012193303387030107136642 absolute error = 6e-31 relative error = 4.4345262119618149244432275901208e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9356160015533859334164648885436 y2[1] (numeric) = 1.9356160015533859334164648885443 absolute error = 7e-31 relative error = 3.6164197828403486951992418383993e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.88 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3303 Order of pole (three term test) = 32.12 NO COMPLEX POLE (six term test) for Equation 2 memory used=8061.6MB, alloc=40.3MB, time=89.78 memory used=8103.2MB, alloc=40.3MB, time=90.23 TOP MAIN SOLVE Loop x[1] = 1.22 y1[1] (closed_form) = 1.3436457463160470204755229744352 y1[1] (numeric) = 1.3436457463160470204755229744346 absolute error = 6e-31 relative error = 4.4654627281413681562211564779427e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9390993563190675809352452718884 y2[1] (numeric) = 1.9390993563190675809352452718889 absolute error = 5e-31 relative error = 2.5785166622360937580441889740517e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.88 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3227 Order of pole (three term test) = 32.12 NO COMPLEX POLE (six term test) for Equation 2 memory used=8144.8MB, alloc=40.3MB, time=90.69 memory used=8186.4MB, alloc=40.3MB, time=91.16 TOP MAIN SOLVE Loop x[1] = 1.23 y1[1] (closed_form) = 1.3342377271245025982395472454977 y1[1] (numeric) = 1.3342377271245025982395472454972 absolute error = 5e-31 relative error = 3.7474581166100032844358135653642e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9424888019316975100238235653892 y2[1] (numeric) = 1.9424888019316975100238235653897 absolute error = 5e-31 relative error = 2.5740174126243492231592685466759e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.89 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.315 Order of pole (three term test) = 32.11 NO COMPLEX POLE (six term test) for Equation 2 memory used=8227.9MB, alloc=40.3MB, time=91.61 memory used=8269.4MB, alloc=40.3MB, time=92.08 TOP MAIN SOLVE Loop x[1] = 1.24 y1[1] (closed_form) = 1.3247962844387762365776934156974 y1[1] (numeric) = 1.3247962844387762365776934156969 absolute error = 5e-31 relative error = 3.7741651744729576917519206818506e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9457839994495389862847059630818 y2[1] (numeric) = 1.9457839994495389862847059630824 absolute error = 6e-31 relative error = 3.0835899574142844497850570195552e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.89 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3072 Order of pole (three term test) = 32.11 NO COMPLEX POLE (six term test) for Equation 2 memory used=8311.0MB, alloc=40.3MB, time=92.55 TOP MAIN SOLVE Loop x[1] = 1.25 y1[1] (closed_form) = 1.315322362395268665447538552438 y1[1] (numeric) = 1.3153223623952686654475385524375 absolute error = 5e-31 relative error = 3.8013494964798946052030395033268e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.948984619355586214348490847036 y2[1] (numeric) = 1.9489846193555862143484908470366 absolute error = 6e-31 relative error = 3.0785260901565475934770177933065e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.9 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2992 Order of pole (three term test) = 32.1 NO COMPLEX POLE (six term test) for Equation 2 memory used=8352.5MB, alloc=40.3MB, time=93.00 memory used=8394.0MB, alloc=40.3MB, time=93.47 TOP MAIN SOLVE Loop x[1] = 1.26 y1[1] (closed_form) = 1.3058169083782893268863424891765 y1[1] (numeric) = 1.3058169083782893268863424891759 absolute error = 6e-31 relative error = 4.5948248651883949986250696369504e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9520903415905157638568162214254 y2[1] (numeric) = 1.952090341590515763856816221426 absolute error = 6e-31 relative error = 3.0736282395164897095969180833147e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.91 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2912 Order of pole (three term test) = 32.09 NO COMPLEX POLE (six term test) for Equation 2 memory used=8435.5MB, alloc=40.3MB, time=93.94 memory used=8477.0MB, alloc=40.3MB, time=94.39 TOP MAIN SOLVE Loop x[1] = 1.27 y1[1] (closed_form) = 1.296280872925318733551137016088 y1[1] (numeric) = 1.2962808729253187335511370160874 absolute error = 6e-31 relative error = 4.6286265001039413538785822801755e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9551008555846922350901817421829 y2[1] (numeric) = 1.9551008555846922350901817421836 absolute error = 7e-31 relative error = 3.5803779533954430253479725766800e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.91 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.283 Order of pole (three term test) = 32.09 NO COMPLEX POLE (six term test) for Equation 2 memory used=8518.6MB, alloc=40.3MB, time=94.86 memory used=8560.1MB, alloc=40.3MB, time=95.31 TOP MAIN SOLVE Loop x[1] = 1.28 y1[1] (closed_form) = 1.2867152096319555127793868935926 y1[1] (numeric) = 1.286715209631955512779386893592 absolute error = 6e-31 relative error = 4.6630365096222068293378630738269e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9580158602892249637007538591603 y2[1] (numeric) = 1.958015860289224963700753859161 absolute error = 7e-31 relative error = 3.5750476500052491777052134906350e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.92 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2747 Order of pole (three term test) = 32.08 NO COMPLEX POLE (six term test) for Equation 2 memory used=8601.6MB, alloc=40.3MB, time=95.78 TOP MAIN SOLVE Loop x[1] = 1.29 y1[1] (closed_form) = 1.2771208750565576413866060900612 y1[1] (numeric) = 1.2771208750565576413866060900606 absolute error = 6e-31 relative error = 4.6980674399627900425012581394146e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9608350642060726589055612912854 y2[1] (numeric) = 1.9608350642060726589055612912861 absolute error = 7e-31 relative error = 3.5699076009915434930311400530652e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.92 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2663 Order of pole (three term test) = 32.08 NO COMPLEX POLE (six term test) for Equation 2 memory used=8643.2MB, alloc=40.3MB, time=96.23 memory used=8684.7MB, alloc=40.3MB, time=96.70 TOP MAIN SOLVE Loop x[1] = 1.3 y1[1] (closed_form) = 1.2674988286245874069979841092929 y1[1] (numeric) = 1.2674988286245874069979841092924 absolute error = 5e-31 relative error = 3.9447768211554843931490763461198e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9635581854171929647013486300396 y2[1] (numeric) = 1.9635581854171929647013486300403 absolute error = 7e-31 relative error = 3.5649567463735357177349704320266e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.93 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2578 Order of pole (three term test) = 32.07 NO COMPLEX POLE (six term test) for Equation 2 memory used=8726.2MB, alloc=40.3MB, time=97.16 memory used=8767.7MB, alloc=40.3MB, time=97.62 TOP MAIN SOLVE Loop x[1] = 1.31 y1[1] (closed_form) = 1.2578500325326696613381769786162 y1[1] (numeric) = 1.2578500325326696613381769786158 absolute error = 4e-31 relative error = 3.1800293330247296540453150291050e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9661849516127340291692578059375 y2[1] (numeric) = 1.9661849516127340291692578059382 absolute error = 7e-31 relative error = 3.5601940673273660634899321296923e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.93 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2491 Order of pole (three term test) = 32.07 NO COMPLEX POLE (six term test) for Equation 2 memory used=8809.3MB, alloc=40.3MB, time=98.09 memory used=8850.8MB, alloc=40.3MB, time=98.55 TOP MAIN SOLVE Loop x[1] = 1.32 y1[1] (closed_form) = 1.2481754516523729595739827294274 y1[1] (numeric) = 1.2481754516523729595739827294268 absolute error = 6e-31 relative error = 4.8070165072202116355064903575976e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9687151001182652627358998459728 y2[1] (numeric) = 1.9687151001182652627358998459735 absolute error = 7e-31 relative error = 3.5556185857361960772126246903190e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.94 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2404 Order of pole (three term test) = 32.06 NO COMPLEX POLE (six term test) for Equation 2 memory used=8892.3MB, alloc=40.3MB, time=99.00 TOP MAIN SOLVE Loop x[1] = 1.33 y1[1] (closed_form) = 1.2384760534337232075157849860106 y1[1] (numeric) = 1.2384760534337232075157849860101 absolute error = 5e-31 relative error = 4.0372197638681061316968435110434e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9711483779210445623376830377638 y2[1] (numeric) = 1.9711483779210445623376830377646 absolute error = 8e-31 relative error = 4.0585478442965009614917397508622e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.94 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2316 Order of pole (three term test) = 32.06 NO COMPLEX POLE (six term test) for Equation 2 memory used=8933.7MB, alloc=40.3MB, time=99.47 memory used=8975.3MB, alloc=40.3MB, time=99.92 TOP MAIN SOLVE Loop x[1] = 1.34 y1[1] (closed_form) = 1.2287528078084594652326394923001 y1[1] (numeric) = 1.2287528078084594652326394922997 absolute error = 4e-31 relative error = 3.2553333547487024677583419710191e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9734845416953193747878703480896 y2[1] (numeric) = 1.9734845416953193747878703480906 absolute error = 1.0e-30 relative error = 5.0671792906011378093288912483107e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.95 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2227 Order of pole (three term test) = 32.05 NO COMPLEX POLE (six term test) for Equation 2 memory used=9016.8MB, alloc=40.3MB, time=100.39 memory used=9058.3MB, alloc=40.3MB, time=100.84 TOP MAIN SOLVE Loop x[1] = 1.35 y1[1] (closed_form) = 1.2190066870930415814200221730106 y1[1] (numeric) = 1.2190066870930415814200221730103 absolute error = 3e-31 relative error = 2.4610201336582354571266789408816e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9757233578266590692611135392652 y2[1] (numeric) = 1.9757233578266590692611135392662 absolute error = 1.0e-30 relative error = 5.0614373517354317078567354657180e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.95 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2137 Order of pole (three term test) = 32.05 NO COMPLEX POLE (six term test) for Equation 2 memory used=9099.9MB, alloc=40.3MB, time=101.31 memory used=9141.4MB, alloc=40.3MB, time=101.77 TOP MAIN SOLVE Loop x[1] = 1.36 y1[1] (closed_form) = 1.2092386658914193576759752523919 y1[1] (numeric) = 1.2092386658914193576759752523915 absolute error = 4e-31 relative error = 3.3078664392949292796602718264750e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9778646024353161856784924394266 y2[1] (numeric) = 1.9778646024353161856784924394277 absolute error = 1.1e-30 relative error = 5.5615536000067236657075199581456e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.96 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2046 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 2 memory used=9183.0MB, alloc=40.3MB, time=102.23 TOP MAIN SOLVE Loop x[1] = 1.37 y1[1] (closed_form) = 1.1994497209975729656881983896453 y1[1] (numeric) = 1.199449720997572965688198389645 absolute error = 3e-31 relative error = 2.5011469405361347109301122768487e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9799080613986142228876885048919 y2[1] (numeric) = 1.9799080613986142228876885048929 absolute error = 1.0e-30 relative error = 5.0507395747133651219664071195626e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.96 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1954 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 2 memory used=9224.5MB, alloc=40.3MB, time=102.70 memory used=9266.0MB, alloc=40.3MB, time=103.16 TOP MAIN SOLVE Loop x[1] = 1.38 y1[1] (closed_form) = 1.1896408312978343632091500735982 y1[1] (numeric) = 1.189640831297834363209150073598 absolute error = 2e-31 relative error = 1.6811796866606429706373023342143e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.981853530372359727878131085206 y2[1] (numeric) = 1.9818535303723597278781310852071 absolute error = 1.1e-30 relative error = 5.5503597170136329732435186414709e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.96 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1862 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 2 memory used=9307.5MB, alloc=40.3MB, time=103.62 memory used=9348.9MB, alloc=40.3MB, time=104.08 TOP MAIN SOLVE Loop x[1] = 1.39 y1[1] (closed_form) = 1.179812977672999476596163217804 y1[1] (numeric) = 1.179812977672999476596163217804 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9837008148112765448400382244429 y2[1] (numeric) = 1.983700814811276544840038224444 absolute error = 1.1e-30 relative error = 5.5451910478982727110899791208657e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.97 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1769 Order of pole (three term test) = 32.03 NO COMPLEX POLE (six term test) for Equation 2 memory used=9390.5MB, alloc=40.3MB, time=104.55 memory used=9432.0MB, alloc=40.3MB, time=105.00 TOP MAIN SOLVE Loop x[1] = 1.4 y1[1] (closed_form) = 1.1699671429002409386167480352036 y1[1] (numeric) = 1.1699671429002409386167480352037 absolute error = 1e-31 relative error = 8.5472485793155863828236215107460e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9854497299884601806594745788061 y2[1] (numeric) = 1.9854497299884601806594745788073 absolute error = 1.2e-30 relative error = 6.0439707028340356570045886922494e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.97 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1675 Order of pole (three term test) = 32.03 NO COMPLEX POLE (six term test) for Equation 2 memory used=9473.5MB, alloc=40.3MB, time=105.45 TOP MAIN SOLVE Loop x[1] = 1.41 y1[1] (closed_form) = 1.1601043115548311901635625493609 y1[1] (numeric) = 1.160104311554831190163562549361 absolute error = 1e-31 relative error = 8.6199145200981867290946985766988e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9871001010138503414290888619422 y2[1] (numeric) = 1.9871001010138503414290888619435 absolute error = 1.3e-30 relative error = 6.5421968391865067597220966184484e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.97 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.158 Order of pole (three term test) = 32.03 NO COMPLEX POLE (six term test) for Equation 2 memory used=9515.1MB, alloc=40.3MB, time=105.92 memory used=9556.6MB, alloc=40.3MB, time=106.38 TOP MAIN SOLVE Loop x[1] = 1.42 y1[1] (closed_form) = 1.1502254699116857734869821029759 y1[1] (numeric) = 1.150225469911685773486982102976 absolute error = 1e-31 relative error = 8.6939476316480796242789546185500e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9886517628517197927362734733357 y2[1] (numeric) = 1.9886517628517197927362734733369 absolute error = 1.2e-30 relative error = 6.0342389875198869636122954247078e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.98 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1485 Order of pole (three term test) = 32.02 NO COMPLEX POLE (six term test) for Equation 2 memory used=9598.1MB, alloc=40.3MB, time=106.84 memory used=9639.6MB, alloc=40.3MB, time=107.30 TOP MAIN SOLVE Loop x[1] = 1.43 y1[1] (closed_form) = 1.1403316058467366625338976245749 y1[1] (numeric) = 1.140331605846736662533897624575 absolute error = 1e-31 relative error = 8.7693789672475536804733641222893e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9901045603371777948572914954818 y2[1] (numeric) = 1.9901045603371777948572914954829 absolute error = 1.1e-30 relative error = 5.5273477681676690736892003731658e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.98 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1389 Order of pole (three term test) = 32.02 NO COMPLEX POLE (six term test) for Equation 2 memory used=9681.1MB, alloc=40.3MB, time=107.75 memory used=9722.5MB, alloc=40.3MB, time=108.22 TOP MAIN SOLVE Loop x[1] = 1.44 y1[1] (closed_form) = 1.1304237087381454929775201561292 y1[1] (numeric) = 1.1304237087381454929775201561293 absolute error = 1e-31 relative error = 8.8462405049542604262797632342193e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.991458348191686462527604463958 y2[1] (numeric) = 1.9914583481916864625276044639592 absolute error = 1.2e-30 relative error = 6.0257348645511054392812963653261e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.98 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1293 Order of pole (three term test) = 32.02 NO COMPLEX POLE (six term test) for Equation 2 memory used=9764.0MB, alloc=40.3MB, time=108.67 TOP MAIN SOLVE Loop x[1] = 1.45 y1[1] (closed_form) = 1.120502769367366570532866627248 y1[1] (numeric) = 1.120502769367366570532866627248 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.992712991037588497665354134323 y2[1] (numeric) = 1.9927129910375884976653541343244 absolute error = 1.4e-30 relative error = 7.0255977970567254326730166466215e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1196 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 2 memory used=9805.5MB, alloc=40.3MB, time=109.14 memory used=9847.0MB, alloc=40.3MB, time=109.59 TOP MAIN SOLVE Loop x[1] = 1.46 y1[1] (closed_form) = 1.1105697798200695511746481091234 y1[1] (numeric) = 1.1105697798200695511746481091232 absolute error = 2e-31 relative error = 1.8008773841514332183699371263908e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.99386836341164484228683230125 y2[1] (numeric) = 1.9938683634116448422868323012513 absolute error = 1.3e-30 relative error = 6.5199891018663402677453310778834e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1099 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 2 memory used=9888.5MB, alloc=40.3MB, time=110.05 memory used=9930.0MB, alloc=40.3MB, time=110.51 TOP MAIN SOLVE Loop x[1] = 1.47 y1[1] (closed_form) = 1.1006257333869317009069746014624 y1[1] (numeric) = 1.1006257333869317009069746014622 absolute error = 2e-31 relative error = 1.8171481361292938086225480976158e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9949243497775808978599284627356 y2[1] (numeric) = 1.9949243497775808978599284627369 absolute error = 1.3e-30 relative error = 6.5165378333516268393615406838906e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1001 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 2 memory used=9971.6MB, alloc=40.3MB, time=110.97 memory used=10013.0MB, alloc=40.3MB, time=111.42 TOP MAIN SOLVE Loop x[1] = 1.48 y1[1] (closed_form) = 1.0906716244643096557762265406478 y1[1] (numeric) = 1.0906716244643096557762265406477 absolute error = 1e-31 relative error = 9.1686624788754029971031479664537e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9958808445376400564840751325627 y2[1] (numeric) = 1.9958808445376400564840751325639 absolute error = 1.2e-30 relative error = 6.0123829700764952481122072872922e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0903 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 2 memory used=10054.7MB, alloc=40.3MB, time=111.89 TOP MAIN SOLVE Loop x[1] = 1.49 y1[1] (closed_form) = 1.0807084484548006148683184845637 y1[1] (numeric) = 1.0807084484548006148683184845636 absolute error = 1e-31 relative error = 9.2531894372603662245462113142182e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9967377520431433885532007170437 y2[1] (numeric) = 1.996737752043143388553200717045 absolute error = 1.3e-30 relative error = 6.5106196277893131194106809452181e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08045 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 2 memory used=10096.2MB, alloc=40.3MB, time=112.36 memory used=10137.7MB, alloc=40.3MB, time=112.81 TOP MAIN SOLVE Loop x[1] = 1.5 y1[1] (closed_form) = 1.0707372016677029100881898514343 y1[1] (numeric) = 1.0707372016677029100881898514342 absolute error = 1e-31 relative error = 9.3393598209016390280655430800655e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9974949866040544309417233711415 y2[1] (numeric) = 1.9974949866040544309417233711426 absolute error = 1.1e-30 relative error = 5.5068974259110026167229077966595e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.07056 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 2 memory used=10179.2MB, alloc=40.3MB, time=113.26 memory used=10220.7MB, alloc=40.3MB, time=113.73 TOP MAIN SOLVE Loop x[1] = 1.51 y1[1] (closed_form) = 1.0607588812193859065815955149162 y1[1] (numeric) = 1.0607588812193859065815955149161 absolute error = 1e-31 relative error = 9.4272130802285522527302635247474e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9981524724975481192427378648367 y2[1] (numeric) = 1.9981524724975481192427378648378 absolute error = 1.1e-30 relative error = 5.5050853983383882197484659921568e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 33 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.06065 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 2 memory used=10262.2MB, alloc=40.3MB, time=114.19 memory used=10303.7MB, alloc=40.3MB, time=114.66 TOP MAIN SOLVE Loop x[1] = 1.52 y1[1] (closed_form) = 1.0507744849335791967261292701527 y1[1] (numeric) = 1.0507744849335791967261292701526 absolute error = 1e-31 relative error = 9.5167898948670349845863684406231e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9987101439755830071723123941168 y2[1] (numeric) = 1.9987101439755830071723123941179 absolute error = 1.1e-30 relative error = 5.5035493931702285521896375316990e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 33 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.05071 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 2 memory used=10345.3MB, alloc=40.3MB, time=115.11 TOP MAIN SOLVE Loop x[1] = 1.53 y1[1] (closed_form) = 1.0407850112415910586889890070761 y1[1] (numeric) = 1.040785011241591058688989007076 absolute error = 1e-31 relative error = 9.6081322194202517825138776403092e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.999167945271476015924265068709 y2[1] (numeric) = 1.9991679452714760159242650687099 absolute error = 9e-31 relative error = 4.5018729023177937560825372378242e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 33 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.04075 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 2 memory used=10386.9MB, alloc=40.3MB, time=115.56 memory used=10428.4MB, alloc=40.3MB, time=116.03 TOP MAIN SOLVE Loop x[1] = 1.54 y1[1] (closed_form) = 1.0307914590824661576224768070764 y1[1] (numeric) = 1.0307914590824661576224768070763 absolute error = 1e-31 relative error = 9.7012833312581535851318673240320e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.99952583060547905600596353844 y2[1] (numeric) = 1.9995258306054790560059635384409 absolute error = 9e-31 relative error = 4.5010671341388463686923932564950e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 33 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.03078 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 2 memory used=10470.0MB, alloc=40.3MB, time=116.48 memory used=10511.5MB, alloc=40.3MB, time=116.95 TOP MAIN SOLVE Loop x[1] = 1.55 y1[1] (closed_form) = 1.0207948278030924736439127746956 y1[1] (numeric) = 1.0207948278030924736439127746954 absolute error = 2e-31 relative error = 1.9592575760834405038747057926026e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9997837641893569638976113476345 y2[1] (numeric) = 1.9997837641893569638976113476353 absolute error = 8e-31 relative error = 4.0004325183842677922859062475748e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 33 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.02079 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 2 memory used=10552.9MB, alloc=40.3MB, time=117.41 TOP MAIN SOLVE Loop memory used=10594.4MB, alloc=40.3MB, time=117.87 x[1] = 1.56 y1[1] (closed_form) = 1.0107961170582674458239206637609 y1[1] (numeric) = 1.0107961170582674458239206637606 absolute error = 3e-31 relative error = 2.9679575825151935089528063740599e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 y2[1] (closed_form) = 1.9999417202299662957451700234135 y2[1] (numeric) = 1.9999417202299662957451700234142 absolute error = 7e-31 relative error = 3.5001019925696107334760124941429e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 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) = 33 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0108 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 2 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE memory used=10636.7MB, alloc=40.3MB, time=118.33 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE memory used=10679.3MB, alloc=40.3MB, time=118.78 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE memory used=10721.9MB, alloc=40.3MB, time=119.23 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE memory used=10764.5MB, alloc=40.3MB, time=119.70 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.5700148795998165846586783591267 y1[1] (closed_form) = 1.000781447115546982946813332392 y1[1] (numeric) = 1.0007814471155469829468133323916 absolute error = 4e-31 relative error = 3.9968766522688873963705389380156e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 8.6827417631646129007656443771738e-05 y2[1] (closed_form) = 1.9999996946701561884933806294143 y2[1] (numeric) = 1.9999996946701561884933806294153 absolute error = 1.0e-30 relative error = 5.0000007633247260616762413628058e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 8.6827417631646129007656443771738e-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 = 0.0007814 Order of pole (three term test) = 33 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0007814 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 2 memory used=10807.1MB, alloc=40.3MB, time=120.16 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE memory used=10849.6MB, alloc=40.3MB, time=120.63 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE memory used=10892.2MB, alloc=40.3MB, time=121.08 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE memory used=10934.7MB, alloc=40.3MB, time=121.53 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE memory used=10977.3MB, alloc=40.3MB, time=121.98 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE memory used=11019.8MB, alloc=40.3MB, time=122.45 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE memory used=11062.4MB, alloc=40.3MB, time=122.91 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE memory used=11105.0MB, alloc=40.3MB, time=123.36 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=11147.1MB, alloc=40.3MB, time=123.81 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=11188.5MB, alloc=40.3MB, time=124.28 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=11229.9MB, alloc=40.3MB, time=124.73 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=11271.4MB, alloc=40.3MB, time=125.19 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=11312.7MB, alloc=40.3MB, time=125.64 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=11354.2MB, alloc=40.3MB, time=126.11 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=11395.6MB, alloc=40.3MB, time=126.56 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=11437.1MB, alloc=40.3MB, time=127.03 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=11478.5MB, alloc=40.3MB, time=127.48 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=11520.0MB, alloc=40.3MB, time=127.94 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=11561.5MB, alloc=40.3MB, time=128.41 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=11603.0MB, alloc=40.3MB, time=128.86 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=11644.5MB, alloc=40.3MB, time=129.33 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=11686.0MB, alloc=40.3MB, time=129.78 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=11727.5MB, alloc=40.3MB, time=130.23 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=11768.8MB, alloc=40.3MB, time=130.70 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=11810.3MB, alloc=40.3MB, time=131.16 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=11851.8MB, alloc=40.3MB, time=131.61 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=11893.2MB, alloc=40.3MB, time=132.06 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=11934.7MB, alloc=40.3MB, time=132.53 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=11976.1MB, alloc=40.3MB, time=132.98 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12017.5MB, alloc=40.3MB, time=133.45 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12059.0MB, alloc=40.3MB, time=133.91 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12100.4MB, alloc=40.3MB, time=134.36 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12141.9MB, alloc=40.3MB, time=134.83 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12183.3MB, alloc=40.3MB, time=135.28 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12224.8MB, alloc=40.3MB, time=135.75 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12266.2MB, alloc=40.3MB, time=136.20 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12307.6MB, alloc=40.3MB, time=136.66 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12349.1MB, alloc=40.3MB, time=137.11 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12390.4MB, alloc=40.3MB, time=137.56 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12431.9MB, alloc=40.3MB, time=138.03 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12473.3MB, alloc=40.3MB, time=138.48 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12514.9MB, alloc=40.3MB, time=138.94 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12556.4MB, alloc=40.3MB, time=139.41 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12598.0MB, alloc=40.3MB, time=139.86 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12639.5MB, alloc=40.3MB, time=140.33 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12680.9MB, alloc=40.3MB, time=140.78 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12722.5MB, alloc=40.3MB, time=141.25 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12763.9MB, alloc=40.3MB, time=141.70 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12805.4MB, alloc=40.3MB, time=142.16 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12846.9MB, alloc=40.3MB, time=142.63 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12888.5MB, alloc=40.3MB, time=143.08 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12929.9MB, alloc=40.3MB, time=143.53 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=12971.4MB, alloc=40.3MB, time=144.00 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13012.8MB, alloc=40.3MB, time=144.45 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13054.3MB, alloc=40.3MB, time=144.92 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13095.9MB, alloc=40.3MB, time=145.38 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13137.4MB, alloc=40.3MB, time=145.83 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13178.9MB, alloc=40.3MB, time=146.30 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13220.4MB, alloc=40.3MB, time=146.75 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13261.8MB, alloc=40.3MB, time=147.22 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13303.3MB, alloc=40.3MB, time=147.67 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13344.8MB, alloc=40.3MB, time=148.13 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13386.2MB, alloc=40.3MB, time=148.58 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13427.6MB, alloc=40.3MB, time=149.05 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13469.1MB, alloc=40.3MB, time=149.50 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13510.6MB, alloc=40.3MB, time=149.95 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13552.0MB, alloc=40.3MB, time=150.42 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13593.5MB, alloc=40.3MB, time=150.88 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13635.0MB, alloc=40.3MB, time=151.34 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13676.4MB, alloc=40.3MB, time=151.81 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13717.8MB, alloc=40.3MB, time=152.26 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13759.2MB, alloc=40.3MB, time=152.72 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13800.7MB, alloc=40.3MB, time=153.19 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13842.1MB, alloc=40.3MB, time=153.64 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13883.6MB, alloc=40.3MB, time=154.09 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13925.1MB, alloc=40.3MB, time=154.56 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=13966.6MB, alloc=40.3MB, time=155.01 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14008.0MB, alloc=40.3MB, time=155.48 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14049.4MB, alloc=40.3MB, time=155.94 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14090.8MB, alloc=40.3MB, time=156.39 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14132.3MB, alloc=40.3MB, time=156.86 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14173.8MB, alloc=40.3MB, time=157.30 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14215.3MB, alloc=40.3MB, time=157.75 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14256.8MB, alloc=40.3MB, time=158.22 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14298.1MB, alloc=40.3MB, time=158.67 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14339.6MB, alloc=40.3MB, time=159.14 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14381.2MB, alloc=40.3MB, time=159.59 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14422.7MB, alloc=40.3MB, time=160.06 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14464.1MB, alloc=40.3MB, time=160.51 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14505.6MB, alloc=40.3MB, time=160.98 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14547.1MB, alloc=40.3MB, time=161.44 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14588.5MB, alloc=40.3MB, time=161.91 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14629.9MB, alloc=40.3MB, time=162.36 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14671.4MB, alloc=40.3MB, time=162.81 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14712.8MB, alloc=40.3MB, time=163.39 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14754.3MB, alloc=40.3MB, time=163.86 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14795.7MB, alloc=40.3MB, time=164.36 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14837.2MB, alloc=40.3MB, time=164.81 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14878.8MB, alloc=40.3MB, time=165.28 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14920.2MB, alloc=40.3MB, time=165.75 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=14961.7MB, alloc=40.3MB, time=166.20 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15003.2MB, alloc=40.3MB, time=166.66 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15044.5MB, alloc=40.3MB, time=167.13 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15085.9MB, alloc=40.3MB, time=167.58 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15127.4MB, alloc=40.3MB, time=168.03 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15168.9MB, alloc=40.3MB, time=168.50 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15210.4MB, alloc=40.3MB, time=168.98 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15251.9MB, alloc=40.3MB, time=169.45 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15293.4MB, alloc=40.3MB, time=169.91 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15334.9MB, alloc=40.3MB, time=170.38 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15376.4MB, alloc=40.3MB, time=170.83 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15418.0MB, alloc=40.3MB, time=171.30 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15459.6MB, alloc=40.3MB, time=171.75 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15501.1MB, alloc=40.3MB, time=172.22 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15542.6MB, alloc=40.3MB, time=172.67 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15584.0MB, alloc=40.3MB, time=173.14 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15625.5MB, alloc=40.3MB, time=173.59 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15667.0MB, alloc=40.3MB, time=174.05 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15708.5MB, alloc=40.3MB, time=174.51 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15750.0MB, alloc=40.3MB, time=174.97 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15791.5MB, alloc=40.3MB, time=175.44 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15832.8MB, alloc=40.3MB, time=175.89 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15874.3MB, alloc=40.3MB, time=176.36 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15915.6MB, alloc=40.3MB, time=176.81 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15957.1MB, alloc=40.3MB, time=177.27 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=15998.5MB, alloc=40.3MB, time=177.72 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=16040.1MB, alloc=40.3MB, time=178.19 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=16081.5MB, alloc=40.3MB, time=178.64 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=16123.0MB, alloc=40.3MB, time=179.11 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=16164.5MB, alloc=40.3MB, time=179.56 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H memory used=16205.9MB, alloc=40.3MB, time=180.03 SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H SETTING H FOR POLE SETTING H FOR MIN H Finished! Maximum Time Reached before Solution Completed! diff ( y1 , x , 1 ) = neg ( y2 ) + 1.0 ; diff ( y2 , x , 1 ) = y1 - 1.0 ; Iterations = 2225 Total Elapsed Time = 3 Minutes 0 Seconds Elapsed Time(since restart) = 3 Minutes 0 Seconds Expected Time Remaining = 17 Minutes 11 Seconds Optimized Time Remaining = 17 Minutes 11 Seconds Expected Total Time = 20 Minutes 11 Seconds Time to Timeout 0.0 Seconds Percent Done = 14.86 % > quit memory used=16223.4MB, alloc=40.3MB, time=180.22