|\^/| Maple 2016 (X86 64 LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | 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 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := sec_temp mod int_trunc(glob_sec_in_minute); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," 0.0 Seconds"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " 0.0 Seconds") end if; fprintf(fd, "\n") end proc # End Function number 7 # Begin Function number 8 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year)); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour)); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod int_trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" 0.0 Seconds\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" 0.0 Seconds\n") end if end proc # End Function number 8 # Begin Function number 9 > zero_ats_ar := proc(arr_a) > global ATS_MAX_TERMS; > local iii; > iii := 1; > while (iii <= ATS_MAX_TERMS) do # do number 1 > arr_a [iii] := glob__0; > iii := iii + 1; > od;# end do number 1 > end; zero_ats_ar := proc(arr_a) local iii; global ATS_MAX_TERMS; iii := 1; while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1 end do end proc # End Function number 9 # Begin Function number 10 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > global ATS_MAX_TERMS; > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := glob__0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 7 > ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]); > fi;# end if 7; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; global ATS_MAX_TERMS; ret_ats := glob__0; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]) end if; iii_ats := iii_ats + 1 end do end if; ret_ats end proc # End Function number 10 # Begin Function number 11 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global ATS_MAX_TERMS; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := glob__0; > if (jjj_att < mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 7 > ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / c(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global ATS_MAX_TERMS; ret_att := glob__0; if jjj_att < mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/c(mmm_att) end if; ret_att end proc # End Function number 11 # Begin Function number 12 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc # End Function number 12 # Begin Function number 13 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc # End Function number 13 # Begin Function number 14 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc # End Function number 14 # Begin Function number 15 > logitem_good_digits := proc(file,rel_error) > global glob_small_float,glob_prec; > local good_digits; > fprintf(file,""); > fprintf(file,"%d",glob_min_good_digits); > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float, glob_prec; fprintf(file, ""); fprintf(file, "%d", glob_min_good_digits); fprintf(file, "") end proc # End Function number 15 # Begin Function number 16 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc # End Function number 16 # Begin Function number 17 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc # End Function number 17 # Begin Function number 18 > logitem_h_reason := proc(file) > global glob_h_reason; > fprintf(file,""); > if (glob_h_reason = 1) then # if number 6 > fprintf(file,"Max H"); > elif > (glob_h_reason = 2) then # if number 7 > fprintf(file,"Display Interval"); > elif > (glob_h_reason = 3) then # if number 8 > fprintf(file,"Optimal"); > elif > (glob_h_reason = 4) then # if number 9 > fprintf(file,"Pole Accuracy"); > elif > (glob_h_reason = 5) then # if number 10 > fprintf(file,"Min H (Pole)"); > elif > (glob_h_reason = 6) then # if number 11 > fprintf(file,"Pole"); > elif > (glob_h_reason = 7) then # if number 12 > fprintf(file,"Opt Iter"); > else > fprintf(file,"Impossible"); > fi;# end if 12 > fprintf(file,""); > end; logitem_h_reason := proc(file) global glob_h_reason; fprintf(file, ""); if glob_h_reason = 1 then fprintf(file, "Max H") elif glob_h_reason = 2 then fprintf(file, "Display Interval") elif glob_h_reason = 3 then fprintf(file, "Optimal") elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy") elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)") elif glob_h_reason = 6 then fprintf(file, "Pole") elif glob_h_reason = 7 then fprintf(file, "Opt Iter") else fprintf(file, "Impossible") end if; fprintf(file, "") end proc # End Function number 18 # Begin Function number 19 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc # End Function number 19 # Begin Function number 20 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc # End Function number 20 # Begin Function number 21 > chk_data := proc() > global glob_max_iter,ALWAYS, ATS_MAX_TERMS; > local errflag; > errflag := false; > if (glob_max_iter < 2) then # if number 12 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 12; > if (errflag) then # if number 12 > quit; > fi;# end if 12 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, ATS_MAX_TERMS; errflag := false; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc # End Function number 21 # Begin Function number 22 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := c(clock_sec2); > sub1 := c(t_end2-t_start2); > sub2 := c(t2-t_start2); > if (sub1 = glob__0) then # if number 12 > sec_left := glob__0; > else > if (sub2 > glob__0) then # if number 13 > rrr := (sub1/sub2); > sec_left := rrr * c(ms2) - c(ms2); > else > sec_left := glob__0; > fi;# end if 13 > fi;# end if 12; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := c(clock_sec2); sub1 := c(t_end2 - t_start2); sub2 := c(t2 - t_start2); if sub1 = glob__0 then sec_left := glob__0 else if glob__0 < sub2 then rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2) else sec_left := glob__0 end if end if; sec_left end proc # End Function number 22 # Begin Function number 23 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 12 > rrr := (glob__100*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 12; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := glob__100*sub2/sub1 else rrr := 0. end if; rrr end proc # End Function number 23 # Begin Function number 24 > comp_rad_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 12 > ret := float_abs(term1 * glob_h / term2); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM TWO TERM RADIUS ANALYSIS > end; comp_rad_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2) else ret := glob_larger_float end if; ret end proc # End Function number 24 # Begin Function number 25 > comp_ord_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM ORDER ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 12 > ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no)); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM TWO TERM ORDER ANALYSIS > end; comp_ord_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)* c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no)) else ret := glob_larger_float end if; ret end proc # End Function number 25 # Begin Function number 26 > c := proc(in_val) > #To Force Conversion when needed > local ret; > ret := evalf(in_val); > ret; > #End Conversion > end; c := proc(in_val) local ret; ret := evalf(in_val); ret end proc # End Function number 26 # Begin Function number 27 > comp_rad_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret,temp; > temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3); > if (float_abs(temp) > glob__0) then # if number 12 > ret := float_abs((term2*glob_h*term1)/(temp)); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM THREE TERM RADIUS ANALYSIS > end; comp_rad_from_three_terms := proc(term1, term2, term3, last_no) local ret, temp; global glob_h, glob_larger_float; temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2 - term1*term3*c(last_no) + term1*term3); if glob__0 < float_abs(temp) then ret := float_abs(term2*glob_h*term1/temp) else ret := glob_larger_float end if; ret end proc # End Function number 27 # Begin Function number 28 > comp_ord_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM ORDER ANALYSIS > local ret; > ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3)); > ret; > #TOP THREE TERM ORDER ANALYSIS > end; comp_ord_from_three_terms := proc(term1, term2, term3, last_no) local ret; ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3 - glob__4*term2*term2*c(last_no) + glob__4*term2*term2 + term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no)) /(term2*term2*c(last_no) - glob__2*term2*term2 - term1*term3*c(last_no) + term1*term3)); ret end proc # End Function number 28 # Begin Function number 29 > comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > #TOP SIX TERM RADIUS ANALYSIS > global glob_h,glob_larger_float,glob_six_term_ord_save; > local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs; > if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 12 > rm0 := term6/term5; > rm1 := term5/term4; > rm2 := term4/term3; > rm3 := term3/term2; > rm4 := term2/term1; > nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2; > nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3; > dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; > dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; > ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; > ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; > if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 13 > rad_c := glob_larger_float; > ord_no := glob_larger_float; > else > if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2; > if (float_abs(rcs) <> glob__0) then # if number 15 > if (rcs > glob__0) then # if number 16 > rad_c := sqrt(rcs) * float_abs(glob_h); > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 16 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 15 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 14 > fi;# end if 13 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 12; > glob_six_term_ord_save := ord_no; > rad_c; > #BOTTOM SIX TERM RADIUS ANALYSIS > end; comp_rad_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no, ds1, rcs; global glob_h, glob_larger_float, glob_six_term_ord_save; if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and term2 <> glob__0 and term1 <> glob__0 then rm0 := term6/term5; rm1 := term5/term4; rm2 := term4/term3; rm3 := term3/term2; rm4 := term2/term1; nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1 + c(last_no - 3)*rm2; nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2 + c(last_no - 4)*rm3; dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; if float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0 then rad_c := glob_larger_float; ord_no := glob_larger_float else if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2; if float_abs(rcs) <> glob__0 then if glob__0 < rcs then rad_c := sqrt(rcs)*float_abs(glob_h) else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if; glob_six_term_ord_save := ord_no; rad_c end proc # End Function number 29 # Begin Function number 30 > comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > global glob_six_term_ord_save; > #TOP SIX TERM ORDER ANALYSIS > #TOP SAVED FROM SIX TERM RADIUS ANALYSIS > glob_six_term_ord_save; > #BOTTOM SIX TERM ORDER ANALYSIS > end; comp_ord_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) global glob_six_term_ord_save; glob_six_term_ord_save end proc # End Function number 30 # Begin Function number 31 > factorial_2 := proc(nnn) > ret := nnn!; > ret;; > end; Warning, `ret` is implicitly declared local to procedure `factorial_2` factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc # End Function number 31 # Begin Function number 32 > factorial_1 := proc(nnn) > global ATS_MAX_TERMS,array_fact_1; > local ret; > if (nnn <= ATS_MAX_TERMS) then # if number 12 > if (array_fact_1[nnn] = 0) then # if number 13 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 13; > else > ret := factorial_2(nnn); > fi;# end if 12; > ret; > end; factorial_1 := proc(nnn) local ret; global ATS_MAX_TERMS, array_fact_1; if nnn <= ATS_MAX_TERMS then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc # End Function number 32 # Begin Function number 33 > factorial_3 := proc(mmm,nnn) > global ATS_MAX_TERMS,array_fact_2; > local ret; > if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 12 > if (array_fact_2[mmm,nnn] = 0) then # if number 13 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 13; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 12; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global ATS_MAX_TERMS, array_fact_2; if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc # End Function number 33 # Begin Function number 34 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc # End Function number 34 # Begin Function number 35 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc # End Function number 35 # Begin Function number 36 > float_abs := proc(x) > abs(x); > end; float_abs := proc(x) abs(x) end proc # End Function number 36 # Begin Function number 37 > expt := proc(x,y) > x^y; > end; expt := proc(x, y) x^y end proc # End Function number 37 # Begin Function number 38 > neg := proc(x) > -x; > end; neg := proc(x) -x end proc # End Function number 38 # Begin Function number 39 > int_trunc := proc(x) > trunc(x); > end; int_trunc := proc(x) trunc(x) end proc # End Function number 39 # Begin Function number 40 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer))); > omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,""); > omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,""); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS))); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(glob__10, c(-glob_desired_digits_correct))* c(float_abs(c(estimated_answer))); omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, ""); omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "") ; omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := c(float_abs(desired_abs_gbl_error)/( sqrt(c(estimated_steps))*c(ATS_MAX_TERMS))); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc # End Function number 40 #END ATS LIBRARY BLOCK #BEGIN USER FUNCTION BLOCK #BEGIN BLOCK 3 #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(c(2.0) - sin(c(x))); > end; exact_soln_y := proc(x) return c(2.0) - sin(c(x)) end proc > exact_soln_yp := proc(x) > return(neg( cos(c(x)))); > end; exact_soln_yp := proc(x) return neg(cos(c(x))) end proc #END USER DEF BLOCK #END BLOCK 3 #END USER FUNCTION BLOCK # before write_aux functions # Begin Function number 2 > display_poles := proc() > local rad_given; > global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ; > if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1 > rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," "); > if (rad_given < glob_least_given_sing) then # if number 2 > glob_least_given_sing := rad_given; > fi;# end if 2; > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > elif > (glob_type_given_pole = 5) then # if number 3 > omniout_str(ALWAYS,"SOME POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 3; > if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," "); > if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4 > glob_least_ratio_sing := array_rad_test_poles[1,1]; > fi;# end if 4; > omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," "); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," "); > if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4 > glob_least_3_sing := array_rad_test_poles[1,2]; > fi;# end if 4; > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," "); > if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4 > glob_least_6_sing := array_rad_test_poles[1,3]; > fi;# end if 4; > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 3 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, glob_least_3_sing, glob_least_6_sing, glob_least_given_sing, glob_least_ratio_sing, array_x; if glob_type_given_pole = 1 or glob_type_given_pole = 2 then rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])* (array_x[1] - array_given_rad_poles[1, 1]) + array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " "); if rad_given < glob_least_given_sing then glob_least_given_sing := rad_given end if elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") elif glob_type_given_pole = 5 then omniout_str(ALWAYS, "SOME POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_rad_test_poles[1, 1] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1, 1], 4, " "); if array_rad_test_poles[1, 1] < glob_least_ratio_sing then glob_least_ratio_sing := array_rad_test_poles[1, 1] end if; omniout_float(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[1, 1], 4, " ") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 2] and array_rad_test_poles[1, 2] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1, 2], 4, " "); if array_rad_test_poles[1, 2] < glob_least_3_sing then glob_least_3_sing := array_rad_test_poles[1, 2] end if; omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 3] and array_rad_test_poles[1, 3] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1, 3], 4, " "); if array_rad_test_poles[1, 3] < glob_least_6_sing then glob_least_6_sing := array_rad_test_poles[1, 3] end if; omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[1, 3], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc # End Function number 2 # Begin Function number 3 > my_check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 3 > ret := glob__1; > else > ret := glob__m1; > fi;# end if 3; > ret;; > end; my_check_sign := proc(x0, xf) local ret; if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret end proc # End Function number 3 # Begin Function number 4 > est_size_answer := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_2, > array_const_0D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local min_size; > min_size := glob_estimated_size_answer; > if (float_abs(array_y[1]) < min_size) then # if number 3 > min_size := float_abs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > if (min_size < glob__1) then # if number 3 > min_size := glob__1; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > min_size; > end; est_size_answer := proc() local min_size; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_2, array_const_0D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; min_size := glob_estimated_size_answer; if float_abs(array_y[1]) < min_size then min_size := float_abs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < glob__1 then min_size := glob__1; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc # End Function number 4 # Begin Function number 5 > test_suggested_h := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_2, > array_const_0D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := glob__small; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 3 > max_estimated_step_error := est_tmp; > fi;# end if 3; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_2, array_const_0D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; max_estimated_step_error := glob__small; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := float_abs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc # End Function number 5 # Begin Function number 6 > track_estimated_error := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_2, > array_const_0D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3 > est_tmp := c(glob_prec) * c(float_abs(array_y[1])); > fi;# end if 3; > if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3 > array_max_est_error[1] := c(est_tmp); > fi;# end if 3 > ; > end; track_estimated_error := proc() local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_2, array_const_0D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; est_tmp := c(float_abs(array_y[no_terms - 3])) + c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y[1])) end if; if c(array_max_est_error[1]) <= c(est_tmp) then array_max_est_error[1] := c(est_tmp) end if end proc # End Function number 6 # Begin Function number 7 > reached_interval := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_2, > array_const_0D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local ret; > if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3 > ret := true; > else > ret := false; > fi;# end if 3; > return(ret); > end; reached_interval := proc() local ret; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_2, array_const_0D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if glob_check_sign*glob_next_display - glob_h/glob__10 <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc # End Function number 7 # Begin Function number 8 > display_alot := proc(iter) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_2, > array_const_0D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 3 > if (iter >= 0) then # if number 4 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > closed_form_val_y := evalf(exact_soln_y(ind_var)); > omniout_float(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := float_abs(numeric_val - closed_form_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 5 > relerr := abserr*glob__100/float_abs(closed_form_val_y); > if (c(relerr) > c(glob_prec)) then # if number 6 > glob_good_digits := -int_trunc(log10(c(relerr))) + 3; > else > glob_good_digits := Digits; > fi;# end if 6; > else > relerr := glob__m1 ; > glob_good_digits := -16; > fi;# end if 5; > if (glob_good_digits < glob_min_good_digits) then # if number 5 > glob_min_good_digits := glob_good_digits; > fi;# end if 5; > if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 5 > glob_min_apfp_est_good_digits := glob_apfp_est_good_digits; > fi;# end if 5; > if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 5 > est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*17*ATS_MAX_TERMS/float_abs(numeric_val)); > if (evalf(est_rel_err) > glob_prec) then # if number 6 > glob_est_digits := -int_trunc(log10(est_rel_err)) + 3; > else > glob_est_digits := Digits; > fi;# end if 6; > else > relerr := glob__m1 ; > glob_est_digits := -16; > fi;# end if 5; > array_est_digits[1] := glob_est_digits; > if (glob_iter = 1) then # if number 5 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 5; > array_est_rel_error[1] := est_rel_err; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," "); > omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," "); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 4; > #BOTTOM DISPLAY ALOT > fi;# end if 3; > end; display_alot := proc(iter) local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_2, array_const_0D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); closed_form_val_y := evalf(exact_soln_y(ind_var)); omniout_float(ALWAYS, "y[1] (closed_form) ", 33, closed_form_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := float_abs(numeric_val - closed_form_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if c(glob_prec) < c(float_abs(closed_form_val_y)) then relerr := abserr*glob__100/float_abs(closed_form_val_y); if c(glob_prec) < c(relerr) then glob_good_digits := -int_trunc(log10(c(relerr))) + 3 else glob_good_digits := Digits end if else relerr := glob__m1; glob_good_digits := -16 end if; if glob_good_digits < glob_min_good_digits then glob_min_good_digits := glob_good_digits end if; if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits then glob_min_apfp_est_good_digits := glob_apfp_est_good_digits end if; if glob_prec < evalf(float_abs(numeric_val)) then est_rel_err := evalf(array_max_est_error[1]*100.0* sqrt(glob_iter)*17*ATS_MAX_TERMS/float_abs(numeric_val)) ; if glob_prec < evalf(est_rel_err) then glob_est_digits := -int_trunc(log10(est_rel_err)) + 3 else glob_est_digits := Digits end if else relerr := glob__m1; glob_est_digits := -16 end if; array_est_digits[1] := glob_est_digits; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; array_est_rel_error[1] := est_rel_err; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Desired digits ", 32, glob_desired_digits_correct, 4, " "); omniout_int(INFO, "Estimated correct digits ", 32, glob_est_digits, 4, " "); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc # End Function number 8 # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_2, > array_const_0D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := (clock_sec1) - (glob_orig_start_sec); > glob_clock_sec := (clock_sec1) - (glob_clock_start_sec); > left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1); > expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec)); > opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); > percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr((total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr((glob_clock_sec)); > if (c(percent_done) < glob__100) then # if number 3 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr((expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr((glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr((glob_total_exp_sec)); > fi;# end if 3; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr((left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_2, array_const_0D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := clock_sec1 - glob_orig_start_sec; glob_clock_sec := clock_sec1 - glob_clock_start_sec; left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1; expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, clock_sec1 - glob_orig_start_sec); opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec; glob_optimal_expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec) ; glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(total_clock_sec); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(glob_clock_sec); if c(percent_done) < glob__100 then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(expect_sec); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(glob_optimal_expect_sec); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(glob_total_exp_sec) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(left_sec); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc # End Function number 9 # Begin Function number 10 > check_for_pole := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_2, > array_const_0D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no; > #TOP CHECK FOR POLE > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,1] := glob_larger_float; > array_ord_test_poles[1,1] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 2 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 3 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 3; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 4 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 5 > if (rad_c < array_rad_test_poles[1,1]) then # if number 6 > array_rad_test_poles[1,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,1] := rad_c; > array_ord_test_poles[1,1] := tmp_ord; > fi;# end if 6; > fi;# end if 5; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,2] := glob_larger_float; > array_ord_test_poles[1,2] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 2 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 5 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 5; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 6 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 7 > found_sing := 0; > fi;# end if 7; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 7 > if (rad_c < array_rad_test_poles[1,2]) then # if number 8 > array_rad_test_poles[1,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 9 > glob_min_pole_est := rad_c; > fi;# end if 9; > array_ord_test_poles[1,2] := tmp_ord; > fi;# end if 8; > fi;# end if 7; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,3] := glob_larger_float; > array_ord_test_poles[1,3] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 2 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 7 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 7; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 8 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 9 > found_sing := 0; > fi;# end if 9; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 9 > if (rad_c < array_rad_test_poles[1,3]) then # if number 10 > array_rad_test_poles[1,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 11 > glob_min_pole_est := rad_c; > fi;# end if 11; > array_ord_test_poles[1,3] := tmp_ord; > fi;# end if 10; > fi;# end if 9; > #BOTTOM general radius test1 > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 10; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 9; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 9 > display_poles(); > fi;# end if 9 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad, last_no; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_2, array_const_0D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 1] := glob_larger_float; array_ord_test_poles[1, 1] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 12; cnt := 0; while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 1] then array_rad_test_poles[1, 1] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 1] := rad_c; array_ord_test_poles[1, 1] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 2] := glob_larger_float; array_ord_test_poles[1, 2] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 12; cnt := 0; while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do tmp_rad := comp_rad_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 2] then array_rad_test_poles[1, 2] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 2] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 2] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 3] := glob_larger_float; array_ord_test_poles[1, 3] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 12; cnt := 0; while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 3] then array_rad_test_poles[1, 3] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_six_terms( array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 3] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 3] := tmp_ord end if end if; if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc # End Function number 10 # Begin Function number 11 > atomall := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_2, > array_const_0D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > # before write maple main top matter > # before generate constants assign > # before generate globals assign > #END OUTFILE1 > #BEGIN OUTFILE2 > #END OUTFILE2 > #BEGIN ATOMHDR1 > #emit pre sin 1 $eq_no = 1 > array_tmp1[1] := sin(array_x[1]); > array_tmp1_g[1] := cos(array_x[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp2[1]) * (expt((glob_h) , c(2))) * c(factorial_3(0,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y_higher[2,2] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(1); > array_y_higher[3,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre sin ID_LINEAR iii = 2 $eq_no = 1 > array_tmp1[2] := array_tmp1_g[1] * array_x[2] / c(1); > array_tmp1_g[2] := neg(array_tmp1[1]) * array_x[2] / c(1); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp2[2]) * (expt((glob_h) , c(2))) * c(factorial_3(1,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y_higher[2,3] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(2); > array_y_higher[3,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sin ID_LINEAR iii = 3 $eq_no = 1 > array_tmp1[3] := array_tmp1_g[2] * array_x[2] / c(2); > array_tmp1_g[3] := neg(array_tmp1[2]) * array_x[2] / c(2); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp2[3]) * (expt((glob_h) , c(2))) * c(factorial_3(2,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y_higher[2,4] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(3); > array_y_higher[3,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sin ID_LINEAR iii = 4 $eq_no = 1 > array_tmp1[4] := array_tmp1_g[3] * array_x[2] / c(3); > array_tmp1_g[4] := neg(array_tmp1[3]) * array_x[2] / c(3); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp2[4]) * (expt((glob_h) , c(2))) * c(factorial_3(3,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y_higher[2,5] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(4); > array_y_higher[3,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sin ID_LINEAR iii = 5 $eq_no = 1 > array_tmp1[5] := array_tmp1_g[4] * array_x[2] / c(4); > array_tmp1_g[5] := neg(array_tmp1[4]) * array_x[2] / c(4); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,7]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp2[5]) * (expt((glob_h) , c(2))) * c(factorial_3(4,6)); > if (7 <= ATS_MAX_TERMS) then # if number 3 > array_y[7] := temporary; > array_y_higher[1,7] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(6); > array_y_higher[2,6] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(5); > array_y_higher[3,5] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= ATS_MAX_TERMS) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sin LINEAR $eq_no = 1 > array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / c(kkk - 1); > array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1]) * array_x[2] / c(kkk - 1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 2; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := c(array_tmp2[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_y[kkk + order_d] := c(temporary); > array_y_higher[1,kkk + order_d] := c(temporary); > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := c(temporary) / c(glob_h) * c(adj2); > else > temporary := c(temporary); > fi;# end if 4; > array_y_higher[adj3,term] := c(temporary); > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_2, array_const_0D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; array_tmp1[1] := sin(array_x[1]); array_tmp1_g[1] := cos(array_x[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_set_initial[1, 3] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp2[1])*expt(glob_h, c(2))*c(factorial_3(0, 2)); if 3 <= ATS_MAX_TERMS then array_y[3] := temporary; array_y_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y_higher[2, 2] := c(temporary); temporary := c(temporary)*c(1)/c(glob_h); array_y_higher[3, 1] := c(temporary) end if end if; kkk := 2; array_tmp1[2] := array_tmp1_g[1]*array_x[2]/c(1); array_tmp1_g[2] := neg(array_tmp1[1])*array_x[2]/c(1); array_tmp2[2] := array_tmp1[2]; if not array_y_set_initial[1, 4] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp2[2])*expt(glob_h, c(2))*c(factorial_3(1, 3)); if 4 <= ATS_MAX_TERMS then array_y[4] := temporary; array_y_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y_higher[2, 3] := c(temporary); temporary := c(temporary)*c(2)/c(glob_h); array_y_higher[3, 2] := c(temporary) end if end if; kkk := 3; array_tmp1[3] := array_tmp1_g[2]*array_x[2]/c(2); array_tmp1_g[3] := neg(array_tmp1[2])*array_x[2]/c(2); array_tmp2[3] := array_tmp1[3]; if not array_y_set_initial[1, 5] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp2[3])*expt(glob_h, c(2))*c(factorial_3(2, 4)); if 5 <= ATS_MAX_TERMS then array_y[5] := temporary; array_y_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y_higher[2, 4] := c(temporary); temporary := c(temporary)*c(3)/c(glob_h); array_y_higher[3, 3] := c(temporary) end if end if; kkk := 4; array_tmp1[4] := array_tmp1_g[3]*array_x[2]/c(3); array_tmp1_g[4] := neg(array_tmp1[3])*array_x[2]/c(3); array_tmp2[4] := array_tmp1[4]; if not array_y_set_initial[1, 6] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp2[4])*expt(glob_h, c(2))*c(factorial_3(3, 5)); if 6 <= ATS_MAX_TERMS then array_y[6] := temporary; array_y_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y_higher[2, 5] := c(temporary); temporary := c(temporary)*c(4)/c(glob_h); array_y_higher[3, 4] := c(temporary) end if end if; kkk := 5; array_tmp1[5] := array_tmp1_g[4]*array_x[2]/c(4); array_tmp1_g[5] := neg(array_tmp1[4])*array_x[2]/c(4); array_tmp2[5] := array_tmp1[5]; if not array_y_set_initial[1, 7] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp2[5])*expt(glob_h, c(2))*c(factorial_3(4, 6)); if 7 <= ATS_MAX_TERMS then array_y[7] := temporary; array_y_higher[1, 7] := temporary end if; temporary := c(temporary)*c(6)/c(glob_h); array_y_higher[2, 6] := c(temporary); temporary := c(temporary)*c(5)/c(glob_h); array_y_higher[3, 5] := c(temporary) end if end if; kkk := 6; while kkk <= ATS_MAX_TERMS do array_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/c(kkk - 1); array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1])*array_x[2]/c(kkk - 1) ; array_tmp2[kkk] := array_tmp1[kkk]; order_d := 2; if kkk + order_d <= ATS_MAX_TERMS then if not array_y_set_initial[1, kkk + order_d] then temporary := c(array_tmp2[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_y[kkk + order_d] := c(temporary); array_y_higher[1, kkk + order_d] := c(temporary); term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1 do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := c(temporary)*c(adj2)/c(glob_h) else temporary := c(temporary) end if; array_y_higher[adj3, term] := c(temporary) end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc # End Function number 12 #END OUTFILE5 # Begin Function number 12 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it; > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 40; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=40; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_y_init:= Array(0..(40),[]); > array_norms:= Array(0..(40),[]); > array_fact_1:= Array(0..(40),[]); > array_1st_rel_error:= Array(0..(2),[]); > array_last_rel_error:= Array(0..(2),[]); > array_est_rel_error:= Array(0..(2),[]); > array_max_est_error:= Array(0..(2),[]); > array_type_pole:= Array(0..(2),[]); > array_type_real_pole:= Array(0..(2),[]); > array_type_complex_pole:= Array(0..(2),[]); > array_est_digits:= Array(0..(2),[]); > array_y:= Array(0..(40),[]); > array_x:= Array(0..(40),[]); > array_tmp0:= Array(0..(40),[]); > array_tmp1_g:= Array(0..(40),[]); > array_tmp1:= Array(0..(40),[]); > array_tmp2:= Array(0..(40),[]); > array_m1:= Array(0..(40),[]); > array_y_higher := Array(0..(3) ,(0..40+ 1),[]); > array_y_higher_work := Array(0..(3) ,(0..40+ 1),[]); > array_y_higher_work2 := Array(0..(3) ,(0..40+ 1),[]); > array_y_set_initial := Array(0..(2) ,(0..40+ 1),[]); > array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]); > array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_fact_2 := Array(0..(40) ,(0..40+ 1),[]); > # before generate constants > # before generate globals definition > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > # before generate const definition > # before arrays initialized > term := 1; > while (term <= 40) do # do number 1 > array_y_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_norms[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_fact_1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_max_est_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_digits[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_y[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_x[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp1_g[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=3) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_higher[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=3) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_higher_work[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=3) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_higher_work2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_set_initial[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_rad_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_ord_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=40) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_fact_2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > # before symbols initialized > #BEGIN SYMBOLS INITIALIZATED > zero_ats_ar(array_y); > zero_ats_ar(array_x); > zero_ats_ar(array_tmp0); > zero_ats_ar(array_tmp1_g); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_2); > array_const_2[1] := c(2); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_h := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 1000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := true; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > array_y_set_initial[1,31] := false; > array_y_set_initial[1,32] := false; > array_y_set_initial[1,33] := false; > array_y_set_initial[1,34] := false; > array_y_set_initial[1,35] := false; > array_y_set_initial[1,36] := false; > array_y_set_initial[1,37] := false; > array_y_set_initial[1,38] := false; > array_y_set_initial[1,39] := false; > array_y_set_initial[1,40] := false; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 40; > glob_iolevel := INFO; > # set default block > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := (0.0); > glob_max_minutes := (15.0); > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/h2sinpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 2 ) = sin ( x ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=40;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := c(0.1);"); > omniout_str(ALWAYS,"x_end := c(5.0) ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"array_y_init[1 + 1] := exact_soln_yp(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(1.000001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);"); > omniout_str(ALWAYS,"glob_look_poles:=false;"); > omniout_str(ALWAYS,"glob_h:=c(0.001);"); > omniout_str(ALWAYS,"glob_display_interval:=c(0.01);"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(c(2.0) - sin(c(x)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_yp := proc(x)"); > omniout_str(ALWAYS,"return(neg( cos(c(x))));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := glob__0; > glob_smallish_float := glob__0; > glob_large_float := c(1.0e100); > glob_larger_float := c( 1.1e100); > glob_almost_1 := c( 0.99); > # before second block > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN BLOCK 2 > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := c(0.1); > x_end := c(5.0) ; > array_y_init[0 + 1] := exact_soln_y(x_start); > array_y_init[1 + 1] := exact_soln_yp(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(1.000001); > glob_lower_ratio_limit:=c(0.999999); > glob_look_poles:=false; > glob_h:=c(0.001); > glob_display_interval:=c(0.01); > #END OVERRIDE BLOCK > #END BLOCK 2 > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours); > # after second input block > glob_check_sign := c(my_check_sign(x_start,x_end)); > glob__pi := arccos(glob__m1); > glob_prec = expt(10.0,c(-Digits)); > if (glob_optimize) then # if number 9 > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > found_h := false; > glob_min_pole_est := glob_larger_float; > last_min_pole_est := glob_larger_float; > glob_least_given_sing := glob_larger_float; > glob_least_ratio_sing := glob_larger_float; > glob_least_3_sing := glob_larger_float; > glob_least_6_sing := glob_larger_float; > glob_min_h := float_abs(glob_min_h) * glob_check_sign; > glob_max_h := float_abs(glob_max_h) * glob_check_sign; > glob_h := float_abs(glob_min_h) * glob_check_sign; > glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign)); > display_max := c(x_end) - c(x_start)/glob__10; > if ((glob_display_interval) > (display_max)) then # if number 10 > glob_display_interval := c(display_max); > fi;# end if 10; > chk_data(); > min_value := glob_larger_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := glob_small_float; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := c(x_start); > array_x[2] := c(glob_h); > glob_next_display := c(x_start); > order_diff := 2; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 10 > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 10; > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > atomall(); > if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > glob_h := glob_check_sign * float_abs(glob_min_h); > glob_h_reason := 1; > found_h := true; > fi;# end if 10; > if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL"); > glob_h_reason := 2; > glob_h := glob_display_interval; > found_h := true; > fi;# end if 10; > if (glob_look_poles) then # if number 10 > check_for_pole(); > fi;# end if 10; > if ( not found_h) then # if number 10 > est_answer := est_size_answer(); > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (estimated_step_error < est_needed_step_err) then # if number 11 > omniout_str(ALWAYS,"Double H and LOOP"); > glob_h := glob_h*glob__2; > else > omniout_str(ALWAYS,"Found H for OPTIMAL"); > found_h := true; > glob_h_reason := 3; > glob_h := glob_h/glob__2; > fi;# end if 11; > fi;# end if 10; > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 10 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 10; > if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MAX H"); > glob_h := glob_check_sign * float_abs(glob_max_h); > glob_h_reason := 1; > found_h := true; > fi;# end if 10; > else > found_h := true; > glob_h := glob_h * glob_check_sign; > fi;# end if 9; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 9 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 9; > #BEGIN SOLUTION CODE > if (found_h) then # if number 9 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := c(x_start); > array_x[2] := c(glob_h); > glob_next_display := c(x_start); > glob_min_pole_est := glob_larger_float; > glob_least_given_sing := glob_larger_float; > glob_least_ratio_sing := glob_larger_float; > glob_least_3_sing := glob_larger_float; > glob_least_6_sing := glob_larger_float; > order_diff := 2; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 10 > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 10; > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_iter < glob_max_iter) and (glob_check_sign * array_x[1] < glob_check_sign * x_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 10 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 10; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > track_estimated_error(); > atomall(); > track_estimated_error(); > display_alot(current_iter); > if (glob_look_poles) then # if number 10 > check_for_pole(); > fi;# end if 10; > if (reached_interval()) then # if number 10 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 10; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 3; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[3,iii] := array_y_higher[3,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 := 3; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 2; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 2; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 3; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 3; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := ATS_MAX_TERMS; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 10 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 10; > if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 10; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 2 ) = sin ( x ) ; "); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 10 > logstart(html_log_file); > logitem_str(html_log_file,"2016-08-26T16:36:03-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"h2sin") > ; > logitem_str(html_log_file,"diff ( y , x , 2 ) = sin ( x ) ; ") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_h_reason(html_log_file) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_float(html_log_file,glob_desired_digits_correct) > ; > if (array_est_digits[1] <> -16) then # if number 11 > logitem_integer(html_log_file,array_est_digits[1]) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_min_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_min_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > logitem_integer(html_log_file,ATS_MAX_TERMS) > ; > if (glob_type_given_pole = 0) then # if number 11 > logitem_str(html_log_file,"Not Given") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 4) then # if number 12 > logitem_str(html_log_file,"No Solution") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 5) then # if number 13 > logitem_str(html_log_file,"Some Pole") > ; > logitem_str(html_log_file,"????") > ; > elif > (glob_type_given_pole = 3) then # if number 14 > logitem_str(html_log_file,"No Pole") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 1) then # if number 15 > logitem_str(html_log_file,"Real Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > elif > (glob_type_given_pole = 2) then # if number 16 > logitem_str(html_log_file,"Complex Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > fi;# end if 16; > if (glob_least_ratio_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_ratio_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_3_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_3_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_6_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_6_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,(glob_clock_sec)) > ; > if (c(glob_percent_done) < glob__100) then # if number 16 > logitem_time(html_log_file,(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 16; > log_revs(html_log_file," 308.maple.seems.ok ") > ; > logitem_str(html_log_file,"h2sin diffeq.mxt") > ; > logitem_str(html_log_file,"h2sin maple results") > ; > logitem_str(html_log_file,"OK") > ; > logend(html_log_file) > ; > ; > fi;# end if 15; > if (glob_html_log) then # if number 15 > fclose(html_log_file); > fi;# end if 15 > ; > ;; > fi;# end if 14 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, found_h, repeat_it; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_2, array_const_0D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 40; Digits := 32; max_terms := 40; glob_html_log := true; array_y_init := Array(0 .. 40, []); array_norms := Array(0 .. 40, []); array_fact_1 := Array(0 .. 40, []); array_1st_rel_error := Array(0 .. 2, []); array_last_rel_error := Array(0 .. 2, []); array_est_rel_error := Array(0 .. 2, []); array_max_est_error := Array(0 .. 2, []); array_type_pole := Array(0 .. 2, []); array_type_real_pole := Array(0 .. 2, []); array_type_complex_pole := Array(0 .. 2, []); array_est_digits := Array(0 .. 2, []); array_y := Array(0 .. 40, []); array_x := Array(0 .. 40, []); array_tmp0 := Array(0 .. 40, []); array_tmp1_g := Array(0 .. 40, []); array_tmp1 := Array(0 .. 40, []); array_tmp2 := Array(0 .. 40, []); array_m1 := Array(0 .. 40, []); array_y_higher := Array(0 .. 3, 0 .. 41, []); array_y_higher_work := Array(0 .. 3, 0 .. 41, []); array_y_higher_work2 := Array(0 .. 3, 0 .. 41, []); array_y_set_initial := Array(0 .. 2, 0 .. 41, []); array_given_rad_poles := Array(0 .. 2, 0 .. 4, []); array_given_ord_poles := Array(0 .. 2, 0 .. 4, []); array_rad_test_poles := Array(0 .. 2, 0 .. 5, []); array_ord_test_poles := Array(0 .. 2, 0 .. 5, []); array_fact_2 := Array(0 .. 40, 0 .. 41, []); term := 1; while term <= 40 do array_y_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 40 do array_fact_1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_real_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do ; term := 1; while term <= 40 do array_y[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_x[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp1_g[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 40 do array_y_higher[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 40 do array_y_higher_work[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 40 do array_y_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_rad_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_ord_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 40 do term := 1; while term <= 40 do array_fact_2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; zero_ats_ar(array_y); zero_ats_ar(array_x); zero_ats_ar(array_tmp0); zero_ats_ar(array_tmp1_g); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2); zero_ats_ar(array_m1); zero_ats_ar(array_const_2); array_const_2[1] := c(2); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_h := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 1000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := true; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; array_y_set_initial[1, 31] := false; array_y_set_initial[1, 32] := false; array_y_set_initial[1, 33] := false; array_y_set_initial[1, 34] := false; array_y_set_initial[1, 35] := false; array_y_set_initial[1, 36] := false; array_y_set_initial[1, 37] := false; array_y_set_initial[1, 38] := false; array_y_set_initial[1, 39] := false; array_y_set_initial[1, 40] := false; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 40; glob_iolevel := INFO; glob_orig_start_sec := elapsed_time_seconds(); glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/h2sinpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 2 ) = sin ( x ) ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=40;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := c(0.1);"); omniout_str(ALWAYS, "x_end := c(5.0) ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "array_y_init[1 + 1] := exact_soln_yp(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(1.000001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);"); omniout_str(ALWAYS, "glob_look_poles:=false;"); omniout_str(ALWAYS, "glob_h:=c(0.001);"); omniout_str(ALWAYS, "glob_display_interval:=c(0.01);"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(c(2.0) - sin(c(x)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_yp := proc(x)"); omniout_str(ALWAYS, "return(neg( cos(c(x))));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := glob__0; glob_smallish_float := glob__0; glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := c(0.1); x_end := c(5.0); array_y_init[1] := exact_soln_y(x_start); array_y_init[2] := exact_soln_yp(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(1.000001); glob_lower_ratio_limit := c(0.999999); glob_look_poles := false; glob_h := c(0.001); glob_display_interval := c(0.01); glob_last_good_h := glob_h; glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours; glob_check_sign := c(my_check_sign(x_start, x_end)); glob__pi := arccos(glob__m1); glob_prec = expt(10.0, c(-Digits)); if glob_optimize then omniout_str(ALWAYS, "START of Optimize"); found_h := false; glob_min_pole_est := glob_larger_float; last_min_pole_est := glob_larger_float; glob_least_given_sing := glob_larger_float; glob_least_ratio_sing := glob_larger_float; glob_least_3_sing := glob_larger_float; glob_least_6_sing := glob_larger_float; glob_min_h := float_abs(glob_min_h)*glob_check_sign; glob_max_h := float_abs(glob_max_h)*glob_check_sign; glob_h := float_abs(glob_min_h)*glob_check_sign; glob_display_interval := c(float_abs(c(glob_display_interval))*glob_check_sign); display_max := c(x_end) - c(x_start)/glob__10; if display_max < glob_display_interval then glob_display_interval := c(display_max) end if; chk_data(); min_value := glob_larger_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer) ; omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := glob_small_float; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); order_diff := 2; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y_higher[r_order, term_no] := array_y_init[it]*expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); glob_h := float_abs(glob_min_h)*glob_check_sign; glob_h_reason := 1; found_h := true end if; if glob_check_sign*glob_display_interval <= glob_check_sign*glob_h then omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL"); glob_h_reason := 2; glob_h := glob_display_interval; found_h := true end if; if glob_look_poles then check_for_pole() end if; if not found_h then est_answer := est_size_answer(); est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if estimated_step_error < est_needed_step_err then omniout_str(ALWAYS, "Double H and LOOP"); glob_h := glob_h*glob__2 else omniout_str(ALWAYS, "Found H for OPTIMAL"); found_h := true; glob_h_reason := 3; glob_h := glob_h/glob__2 end if end if; opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then omniout_str(ALWAYS, "SETTING H FOR MAX H"); glob_h := float_abs(glob_max_h)*glob_check_sign; glob_h_reason := 1; found_h := true end if else found_h := true; glob_h := glob_check_sign*glob_h end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); glob_min_pole_est := glob_larger_float; glob_least_given_sing := glob_larger_float; glob_least_ratio_sing := glob_larger_float; glob_least_3_sing := glob_larger_float; glob_least_6_sing := glob_larger_float; order_diff := 2; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and glob_clock_sec - glob_orig_start_sec < glob_max_sec do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); track_estimated_error(); atomall(); track_estimated_error(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 3; ord := 3; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[3, iii] := array_y_higher[3, 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 := 3; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 2; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 3; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 3; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); term_no := ATS_MAX_TERMS; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 2 ) = sin ( x ) ; "); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2016-08-26T16:36:03-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "h2sin"); logitem_str(html_log_file, "diff ( y , x , 2 ) = sin ( x ) ; "); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_h_reason(html_log_file); logitem_integer(html_log_file, Digits); logitem_float(html_log_file, glob_desired_digits_correct); if array_est_digits[1] <> -16 then logitem_integer(html_log_file, array_est_digits[1]) else logitem_str(html_log_file, "Unknown") end if; if glob_min_good_digits <> -16 then logitem_integer(html_log_file, glob_min_good_digits) else logitem_str(html_log_file, "Unknown") end if; if glob_good_digits <> -16 then logitem_integer(html_log_file, glob_good_digits) else logitem_str(html_log_file, "Unknown") end if; logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); logitem_integer(html_log_file, ATS_MAX_TERMS); if glob_type_given_pole = 0 then logitem_str(html_log_file, "Not Given"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 4 then logitem_str(html_log_file, "No Solution"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 5 then logitem_str(html_log_file, "Some Pole"); logitem_str(html_log_file, "????") elif glob_type_given_pole = 3 then logitem_str(html_log_file, "No Pole"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 1 then logitem_str(html_log_file, "Real Sing"); logitem_float(html_log_file, glob_least_given_sing) elif glob_type_given_pole = 2 then logitem_str(html_log_file, "Complex Sing"); logitem_float(html_log_file, glob_least_given_sing) end if; if glob_least_ratio_sing < glob_large_float then logitem_float(html_log_file, glob_least_ratio_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_3_sing < glob_large_float then logitem_float(html_log_file, glob_least_3_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_6_sing < glob_large_float then logitem_float(html_log_file, glob_least_6_sing) else logitem_str(html_log_file, "NONE") end if; logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, glob_clock_sec); if c(glob_percent_done) < glob__100 then logitem_time(html_log_file, glob_total_exp_sec); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 308.maple.seems.ok "); logitem_str(html_log_file, "h2sin diffeq.mxt"); logitem_str(html_log_file, "h2sin maple results") ; logitem_str(html_log_file, "OK"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc # End Function number 12 > main(); ##############ECHO OF PROBLEM################# ##############temp/h2sinpostode.ode################# diff ( y , x , 2 ) = sin ( x ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=40; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := c(0.1); x_end := c(5.0) ; array_y_init[0 + 1] := exact_soln_y(x_start); array_y_init[1 + 1] := exact_soln_yp(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(1.000001); glob_lower_ratio_limit:=c(0.999999); glob_look_poles:=false; glob_h:=c(0.001); glob_display_interval:=c(0.01); #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(c(2.0) - sin(c(x))); end; exact_soln_yp := proc(x) return(neg( cos(c(x)))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 1.9001665833531718476931858015894 y[1] (numeric) = 1.9001665833531718476931858015894 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 32 h = 0.001 memory used=4.4MB, alloc=40.3MB, time=0.09 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (closed_form) = 1.8902216991628251913350505099166 y[1] (numeric) = 1.8902216991628251913350505099166 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = 1.880287792711080640032649385729 y[1] (numeric) = 1.8802877927110806400326493857291 absolute error = 1e-31 relative error = 5.3183347989413713575080521335103e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = 1.8703658573803051404587941892917 y[1] (numeric) = 1.8703658573803051404587941892919 absolute error = 2e-31 relative error = 1.0693095108147796435612868030825e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = 1.8604568853557635182820116482946 y[1] (numeric) = 1.860456885355763518282011648295 absolute error = 4e-31 relative error = 2.1500095119028275958707097122784e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 1.8505618675264007785022745613124 y[1] (numeric) = 1.8505618675264007785022745613126 absolute error = 2e-31 relative error = 1.0807528432828616488115254639861e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 memory used=36.7MB, alloc=40.3MB, time=0.48 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (closed_form) = 1.840681793385754036688536840314 y[1] (numeric) = 1.8406817933857540366885368403143 absolute error = 3e-31 relative error = 1.6298308652696529196356648939333e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (closed_form) = 1.8308176509330039898423756233292 y[1] (numeric) = 1.8308176509330039898423756233294 absolute error = 2e-31 relative error = 1.0924080827933786306996316837436e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (closed_form) = 1.8209704265741758216581972603008 y[1] (numeric) = 1.8209704265741758216581972603011 absolute error = 3e-31 relative error = 1.6474732133041575899218996089712e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (closed_form) = 1.8111411050234994220071488470187 y[1] (numeric) = 1.811141105023499422007148847019 absolute error = 3e-31 relative error = 1.6564142858217969834431003781778e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (closed_form) = 1.8013306692049387845405873728816 y[1] (numeric) = 1.8013306692049387845405873728819 absolute error = 3e-31 relative error = 1.6654354757220245151306827526882e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (closed_form) = 1.7915401001539004293912875737724 y[1] (numeric) = 1.7915401001539004293912875737726 absolute error = 2e-31 relative error = 1.1163579312727591389234061052369e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (closed_form) = 1.781770376919130680048208994543 y[1] (numeric) = 1.7817703769191306800482089945433 absolute error = 3e-31 relative error = 1.6837186423467860705132474041951e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (closed_form) = 1.7720224764648116045953827876399 y[1] (numeric) = 1.7720224764648116045953827876402 absolute error = 3e-31 relative error = 1.6929807831698647628359242871244e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 memory used=77.2MB, alloc=44.3MB, time=0.95 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (closed_form) = 1.7622973735728654116392079155102 y[1] (numeric) = 1.7622973735728654116392079155104 absolute error = 2e-31 relative error = 1.1348822451827289964707718309936e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (closed_form) = 1.7525960407454770704031512951506 y[1] (numeric) = 1.7525960407454770704031512951508 absolute error = 2e-31 relative error = 1.1411642805887477614396416108152e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (closed_form) = 1.7429194481078449026466115356348 y[1] (numeric) = 1.7429194481078449026466115356351 absolute error = 3e-31 relative error = 1.7212499425930853274353749814797e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (closed_form) = 1.7332685633111688712677134789795 y[1] (numeric) = 1.7332685633111688712677134789798 absolute error = 3e-31 relative error = 1.7308339073945451618302692677121e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (closed_form) = 1.7236443514358862666803304415422 y[1] (numeric) = 1.7236443514358862666803304415424 absolute error = 2e-31 relative error = 1.1603321754478497634892724964499e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (closed_form) = 1.7140477748951644673160597944956 y[1] (numeric) = 1.7140477748951644673160597944958 absolute error = 2e-31 relative error = 1.1668286201196026172264104191836e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (closed_form) = 1.704479793338660424894679254315 y[1] (numeric) = 1.7044797933386604248946792543152 absolute error = 2e-31 relative error = 1.1733785333309745651762247616123e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=117.5MB, alloc=44.3MB, time=1.41 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (closed_form) = 1.694941363556556498434356676041 y[1] (numeric) = 1.6949413635565564984343566760413 absolute error = 3e-31 relative error = 1.7699727344579000474754640509181e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (closed_form) = 1.6854334393838822333382424565828 y[1] (numeric) = 1.6854334393838822333382424565832 absolute error = 4e-31 relative error = 2.3732767527516351951433962429444e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (closed_form) = 1.6759569716051316532998043038298 y[1] (numeric) = 1.6759569716051316532998043038301 absolute error = 3e-31 relative error = 1.7900220893659214199591941211775e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (closed_form) = 1.6665129078591856032182285129692 y[1] (numeric) = 1.6665129078591856032182285129694 absolute error = 2e-31 relative error = 1.2001107165555736977364670074092e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.35 y[1] (closed_form) = 1.6571021925445486508103650930824 y[1] (numeric) = 1.6571021925445486508103650930826 absolute error = 2e-31 relative error = 1.2069261684633448263132598423937e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (closed_form) = 1.6477257667249100231500865640793 y[1] (numeric) = 1.6477257667249100231500865640795 absolute error = 2e-31 relative error = 1.2137942128411848899071324974386e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (closed_form) = 1.6383845680350380219627075308728 y[1] (numeric) = 1.638384568035038021962707530873 absolute error = 2e-31 relative error = 1.2207146228181688868516605552692e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=157.9MB, alloc=44.3MB, time=1.88 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (closed_form) = 1.6290795305870173281545145336508 y[1] (numeric) = 1.6290795305870173281545145336508 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (closed_form) = 1.6198115848768385717688179021528 y[1] (numeric) = 1.6198115848768385717688179021528 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (closed_form) = 1.6105816576913495083336882432043 y[1] (numeric) = 1.6105816576913495083336882432042 absolute error = 1e-31 relative error = 6.2089369714630088311655157104526e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (closed_form) = 1.6013906720155771064062023599489 y[1] (numeric) = 1.6013906720155771064062023599487 absolute error = 2e-31 relative error = 1.2489144809884002660391396951597e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (closed_form) = 1.5922395469404298140272128419137 y[1] (numeric) = 1.5922395469404298140272128419136 absolute error = 1e-31 relative error = 6.2804620191826753380330015869096e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (closed_form) = 1.5831291975707892337830813273754 y[1] (numeric) = 1.5831291975707892337830813273754 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (closed_form) = 1.5740605349340003972302792492201 y[1] (numeric) = 1.57406053493400039723027924922 absolute error = 1e-31 relative error = 6.3529958207225462269565027346511e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=198.2MB, alloc=44.3MB, time=2.34 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (closed_form) = 1.5650344658887697895791557537681 y[1] (numeric) = 1.5650344658887697895791557537679 absolute error = 2e-31 relative error = 1.2779271278631023473796889558184e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (closed_form) = 1.5560518930344802347584863560711 y[1] (numeric) = 1.5560518930344802347584863560709 absolute error = 2e-31 relative error = 1.2853041784485540998541945251957e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (closed_form) = 1.5471137146209317092967251996036 y[1] (numeric) = 1.5471137146209317092967251996034 absolute error = 2e-31 relative error = 1.2927297981390029076962460417967e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (closed_form) = 1.5382208244585171108633570574114 y[1] (numeric) = 1.5382208244585171108633570574111 absolute error = 3e-31 relative error = 1.9503051527442796575101980316703e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (closed_form) = 1.529374111828841963818641662812 y[1] (numeric) = 1.5293741118288419638186416628119 absolute error = 1e-31 relative error = 6.5386225140439266104400847887623e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (closed_form) = 1.5205744613957969997267120647844 y[1] (numeric) = 1.5205744613957969997267120647843 absolute error = 1e-31 relative error = 6.5764618924485909237902113823204e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (closed_form) = 1.5118227531170925054998697623254 y[1] (numeric) = 1.5118227531170925054998697623253 absolute error = 1e-31 relative error = 6.6145320140088458331137476957297e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=238.6MB, alloc=44.3MB, time=2.81 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (closed_form) = 1.5031198621562632856655410574522 y[1] (numeric) = 1.5031198621562632856655410574521 absolute error = 1e-31 relative error = 6.6528293928966837244105802564533e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (closed_form) = 1.4944666587951530381863389775339 y[1] (numeric) = 1.4944666587951530381863389775338 absolute error = 1e-31 relative error = 6.6913503497375131401807390081828e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (closed_form) = 1.4858640083468868953227193170418 y[1] (numeric) = 1.4858640083468868953227193170416 absolute error = 2e-31 relative error = 1.3460182013730316597572758732152e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (closed_form) = 1.4773127710693408322116218922427 y[1] (numeric) = 1.4773127710693408322116218922424 absolute error = 3e-31 relative error = 2.0307141850729919591435611967470e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (closed_form) = 1.468813802079116596148130558888 y[1] (numeric) = 1.4688138020791165961481305588877 absolute error = 3e-31 relative error = 2.0424644674181834543956504934294e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.57 y[1] (closed_form) = 1.4603679512660307590055365069212 y[1] (numeric) = 1.4603679512660307590055365069208 absolute error = 4e-31 relative error = 2.7390357317361672540175748812887e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (closed_form) = 1.4519760632081264438173039404235 y[1] (numeric) = 1.4519760632081264438173039404231 absolute error = 4e-31 relative error = 2.7548663516959366450861212055144e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (closed_form) = 1.4436389770872162242774566211242 y[1] (numeric) = 1.4436389770872162242774566211239 absolute error = 3e-31 relative error = 2.0780818803140125695425957680170e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=279.1MB, alloc=44.3MB, time=3.28 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (closed_form) = 1.4353575266049646427990545543413 y[1] (numeric) = 1.4353575266049646427990545543409 absolute error = 4e-31 relative error = 2.7867621312866599639651269593536e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (closed_form) = 1.4271325398995187388090239678373 y[1] (numeric) = 1.4271325398995187388090239678369 absolute error = 4e-31 relative error = 2.8028230652505696468048682758890e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (closed_form) = 1.4189648394626949241570367724178 y[1] (numeric) = 1.4189648394626949241570367724174 absolute error = 4e-31 relative error = 2.8189563890213372562502079806098e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (closed_form) = 1.4108552420577304868818879092054 y[1] (numeric) = 1.4108552420577304868818879092049 absolute error = 5e-31 relative error = 3.5439496916122356221279214201077e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (closed_form) = 1.4028045586376079481164537607921 y[1] (numeric) = 1.4028045586376079481164537607915 absolute error = 6e-31 relative error = 4.2771460664678405420215913207156e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (closed_form) = 1.3948135942639604396274783213941 y[1] (numeric) = 1.3948135942639604396274783213935 absolute error = 6e-31 relative error = 4.3016500732961271637342386911410e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (closed_form) = 1.3868831480265662113848545206037 y[1] (numeric) = 1.3868831480265662113848545206031 absolute error = 6e-31 relative error = 4.3262476788600130785208507534859e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=319.6MB, alloc=44.3MB, time=3.75 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (closed_form) = 1.3790140129634403196425560858734 y[1] (numeric) = 1.3790140129634403196425560858729 absolute error = 5e-31 relative error = 3.6257789645336673746984577257419e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (closed_form) = 1.3712069759815314862958218125798 y[1] (numeric) = 1.3712069759815314862958218125794 absolute error = 4e-31 relative error = 2.9171380178668775992720398930406e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (closed_form) = 1.3634628177780320597625707929913 y[1] (numeric) = 1.3634628177780320597625707929909 absolute error = 4e-31 relative error = 2.9337066972743724888688117719370e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (closed_form) = 1.3557823127623089463273856486013 y[1] (numeric) = 1.3557823127623089463273856486009 absolute error = 4e-31 relative error = 2.9503261418496363946400731270079e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (closed_form) = 1.3481662289784633187898720271472 y[1] (numeric) = 1.3481662289784633187898720271468 absolute error = 4e-31 relative error = 2.9669931748927521801618208864246e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (closed_form) = 1.3406153280285268463819961673518 y[1] (numeric) = 1.3406153280285268463819961673514 absolute error = 4e-31 relative error = 2.9837045096913022314800558706507e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (closed_form) = 1.3331303649963021262674058692385 y[1] (numeric) = 1.3331303649963021262674058692381 absolute error = 4e-31 relative error = 3.0004567482874004675418797304405e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=359.9MB, alloc=44.3MB, time=4.22 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (closed_form) = 1.3257120883718549325161188423918 y[1] (numeric) = 1.3257120883718549325161188423913 absolute error = 5e-31 relative error = 3.7715579754127787387062366092748e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (closed_form) = 1.3183612399766658332667580472201 y[1] (numeric) = 1.3183612399766658332667580472197 absolute error = 4e-31 relative error = 3.0340697820202886806456419207843e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (closed_form) = 1.3110785548894486608522443612303 y[1] (numeric) = 1.3110785548894486608522443612299 absolute error = 4e-31 relative error = 3.0509232151518820678689361671888e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (closed_form) = 1.3038647613726432529801162655478 y[1] (numeric) = 1.3038647613726432529801162655475 absolute error = 3e-31 relative error = 2.3008521196951061564049891568921e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (closed_form) = 1.2967205807995898156321026748821 y[1] (numeric) = 1.2967205807995898156321026748818 absolute error = 3e-31 relative error = 2.3135284844095912981432877129788e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (closed_form) = 1.2896467275823921901859711250308 y[1] (numeric) = 1.2896467275823921901859711250305 absolute error = 3e-31 relative error = 2.3262184409399338919347304183806e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (closed_form) = 1.2826439091004772383728253894186 y[1] (numeric) = 1.2826439091004772383728253894181 absolute error = 5e-31 relative error = 3.8981980614608133021229012236116e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=400.2MB, alloc=44.3MB, time=4.69 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (closed_form) = 1.2757128256298574890718231474855 y[1] (numeric) = 1.275712825629857489071823147485 absolute error = 5e-31 relative error = 3.9193773861537770468305016854874e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (closed_form) = 1.2688541702731041206186866353123 y[1] (numeric) = 1.2688541702731041206186866353118 absolute error = 5e-31 relative error = 3.9405631609531739673326614824137e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (closed_form) = 1.2620686288900372812714197738619 y[1] (numeric) = 1.2620686288900372812714197738615 absolute error = 4e-31 relative error = 3.1693997524666432490169449290483e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.84 y[1] (closed_form) = 1.2553568800291406787434273293704 y[1] (numeric) = 1.2553568800291406787434273293699 absolute error = 5e-31 relative error = 3.9829311326066374714157099468024e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (closed_form) = 1.2487195948597072972879284757645 y[1] (numeric) = 1.2487195948597072972879284757641 absolute error = 4e-31 relative error = 3.2032811981695514090478968952503e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (closed_form) = 1.2421574371047230277054112704714 y[1] (numeric) = 1.242157437104723027705411270471 absolute error = 4e-31 relative error = 3.2202037201688231059519807841364e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (closed_form) = 1.2356710629744949218551971762772 y[1] (numeric) = 1.2356710629744949218551971762768 absolute error = 4e-31 relative error = 3.2371074470023117134360838596829e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=440.5MB, alloc=44.3MB, time=5.15 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (closed_form) = 1.229261121101030708790354869244 y[1] (numeric) = 1.2292611211010307087903548692437 absolute error = 3e-31 relative error = 2.4404904283582523897515253718208e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (closed_form) = 1.2229282524731761345096662870268 y[1] (numeric) = 1.2229282524731761345096662870264 absolute error = 4e-31 relative error = 3.2708378368973338557959500271721e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (closed_form) = 1.2166730903725166115386176842864 y[1] (numeric) = 1.216673090372516611538617684286 absolute error = 4e-31 relative error = 3.2876538748590998413761921107075e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (closed_form) = 1.2104962603100495881210424821284 y[1] (numeric) = 1.2104962603100495881210424821279 absolute error = 5e-31 relative error = 4.1305373374051800869000094499650e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (closed_form) = 1.2043983799636339697317238975184 y[1] (numeric) = 1.2043983799636339697317238975179 absolute error = 5e-31 relative error = 4.1514502868651913719689518828438e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (closed_form) = 1.1983800591162228479156807840894 y[1] (numeric) = 1.1983800591162228479156807840888 absolute error = 6e-31 relative error = 5.0067588778345152891024153325247e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (closed_form) = 1.1924418995948857131297802013658 y[1] (numeric) = 1.1924418995948857131297802013652 absolute error = 6e-31 relative error = 5.0316916925163483367739507738116e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=480.9MB, alloc=44.3MB, time=5.62 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (closed_form) = 1.1865844952106262493145778978974 y[1] (numeric) = 1.1865844952106262493145778978968 absolute error = 6e-31 relative error = 5.0565299177745973065931437016105e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (closed_form) = 1.1808084316990017283667778535696 y[1] (numeric) = 1.180808431699001728366777853569 absolute error = 6e-31 relative error = 5.0812645293927337411310175738367e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (closed_form) = 1.1751142866615499425233799621437 y[1] (numeric) = 1.1751142866615499425233799621431 absolute error = 6e-31 relative error = 5.1058863534420525088821020902928e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (closed_form) = 1.1695026295080295319154667122808 y[1] (numeric) = 1.1695026295080295319154667122803 absolute error = 5e-31 relative error = 4.2753217255298793389809728669857e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (closed_form) = 1.1639740213994794832107405884529 y[1] (numeric) = 1.1639740213994794832107405884523 absolute error = 6e-31 relative error = 5.1547542210487028109513799409674e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = 1.1585290151921034933474976783697 y[1] (numeric) = 1.1585290151921034933474976783692 absolute error = 5e-31 relative error = 4.3158176743384509434221727174092e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = 1.153168155381984809876901215218 y[1] (numeric) = 1.1531681553819848098769012152176 absolute error = 4e-31 relative error = 3.4687048730330291062845015935679e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (closed_form) = 1.1478919780506370763834500145446 y[1] (numeric) = 1.1478919780506370763834500145441 absolute error = 5e-31 relative error = 4.3558105602332508747174385036559e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=521.4MB, alloc=44.3MB, time=6.08 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (closed_form) = 1.1427010108113966278537256147056 y[1] (numeric) = 1.1427010108113966278537256147048 absolute error = 8e-31 relative error = 7.0009564394446868943292134318479e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (closed_form) = 1.1375957727566615967192083078838 y[1] (numeric) = 1.1375957727566615967192083078831 absolute error = 7e-31 relative error = 6.1533280692819003883921203687843e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (closed_form) = 1.1325767744059831056185905149997 y[1] (numeric) = 1.132576774405983105618590514999 absolute error = 7e-31 relative error = 6.1805964577292154990950163142505e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (closed_form) = 1.1276445176550137377170540780026 y[1] (numeric) = 1.1276445176550137377170540780019 absolute error = 7e-31 relative error = 6.2076300557526827710516065624155e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (closed_form) = 1.1227994957253183896929367422232 y[1] (numeric) = 1.1227994957253183896929367422224 absolute error = 8e-31 relative error = 7.1250477315471822980013772582265e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (closed_form) = 1.1180421931150525262646650123752 y[1] (numeric) = 1.1180421931150525262646650123745 absolute error = 7e-31 relative error = 6.2609443928916755387560077168470e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.09 y[1] (closed_form) = 1.113373085550512768391399371364 y[1] (numeric) = 1.1133730855505127683913993713632 absolute error = 8e-31 relative error = 7.1853721846027568258772657534518e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=561.8MB, alloc=44.3MB, time=6.55 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (closed_form) = 1.1087926399385646600481974221283 y[1] (numeric) = 1.1087926399385646600481974221275 absolute error = 8e-31 relative error = 7.2150551075476649658345317900782e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (closed_form) = 1.1043013143199523707593740406606 y[1] (numeric) = 1.1043013143199523707593740406599 absolute error = 7e-31 relative error = 6.3388496502068547086136021510845e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (closed_form) = 1.0998995578234950028808967526608 y[1] (numeric) = 1.0998995578234950028808967526601 absolute error = 7e-31 relative error = 6.3642174871419633657433824988738e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (closed_form) = 1.0955878106211740839629184775886 y[1] (numeric) = 1.095587810621174083962918477588 absolute error = 6e-31 relative error = 5.4765121899249066645891573796767e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (closed_form) = 1.0913665038841167354057844218978 y[1] (numeric) = 1.0913665038841167354057844218973 absolute error = 5e-31 relative error = 4.5814123689936053065554758655278e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (closed_form) = 1.0872360597394789190559669502463 y[1] (numeric) = 1.087236059739478919055966950246 absolute error = 3e-31 relative error = 2.7592903796061117696312018247819e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (closed_form) = 1.0831968912282330733813383331257 y[1] (numeric) = 1.0831968912282330733813383331255 absolute error = 2e-31 relative error = 1.8463863921657005190449176946966e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=602.3MB, alloc=44.3MB, time=7.01 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (closed_form) = 1.079249402263864360426986991038 y[1] (numeric) = 1.0792494022638643604269869910379 absolute error = 1e-31 relative error = 9.2656989005726706769964517663026e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (closed_form) = 1.0753939875919796538924619741252 y[1] (numeric) = 1.075393987591979653892461974125 absolute error = 2e-31 relative error = 1.8597835054651891075896518749800e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (closed_form) = 1.0716310327508333073979788883973 y[1] (numeric) = 1.0716310327508333073979788883972 absolute error = 1e-31 relative error = 9.3315700034650978930241833766916e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (closed_form) = 1.0679609140327736503298655645052 y[1] (numeric) = 1.0679609140327736503298655645051 absolute error = 1e-31 relative error = 9.3636385644850663363063136267275e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (closed_form) = 1.0643839984466140665835351114564 y[1] (numeric) = 1.0643839984466140665835351114562 absolute error = 2e-31 relative error = 1.8790211079073388529101166100304e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (closed_form) = 1.0609006436809324190647547281116 y[1] (numeric) = 1.0609006436809324190647547281116 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (closed_form) = 1.0575111980683024899761764346108 y[1] (numeric) = 1.0575111980683024899761764346107 absolute error = 1e-31 relative error = 9.4561646422907385698499835728707e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=642.8MB, alloc=44.3MB, time=7.48 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (closed_form) = 1.0542160005504610137152940369182 y[1] (numeric) = 1.054216000550461013715294036918 absolute error = 2e-31 relative error = 1.8971444172310949188085370996792e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (closed_form) = 1.051015380644413785651509152964 y[1] (numeric) = 1.0510153806444137856515091529638 absolute error = 2e-31 relative error = 1.9029217239178088983737124935182e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (closed_form) = 1.0479096584094842361431837785746 y[1] (numeric) = 1.0479096584094842361431837785744 absolute error = 2e-31 relative error = 1.9085614718310709219314623010111e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (closed_form) = 1.0448991444153077649098182578171 y[1] (numeric) = 1.0448991444153077649098182578168 absolute error = 3e-31 relative error = 2.8710904933113944864797566045650e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (closed_form) = 1.0419841397107750362992461408397 y[1] (numeric) = 1.0419841397107750362992461408394 absolute error = 3e-31 relative error = 2.8791225179614673460840089601111e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (closed_form) = 1.0391649357939273410944387087146 y[1] (numeric) = 1.0391649357939273410944387087143 absolute error = 3e-31 relative error = 2.8869334372873008962892542947282e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (closed_form) = 1.0364418145828070352986513699604 y[1] (numeric) = 1.0364418145828070352986513699601 absolute error = 3e-31 relative error = 2.8945184937444585365249207893449e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=683.2MB, alloc=44.3MB, time=7.95 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (closed_form) = 1.0338150483872659708307421940625 y[1] (numeric) = 1.0338150483872659708307421940621 absolute error = 4e-31 relative error = 3.8691640310710629501340716132869e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (closed_form) = 1.0312848998817347372641001540272 y[1] (numeric) = 1.0312848998817347372641001540268 absolute error = 4e-31 relative error = 3.8786566160899964149229952343450e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (closed_form) = 1.0288516220789554376623169622362 y[1] (numeric) = 1.0288516220789554376623169622357 absolute error = 5e-31 relative error = 4.8597872547420578108940289658081e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (closed_form) = 1.0265154583046806252121296519104 y[1] (numeric) = 1.0265154583046806252121296519097 absolute error = 7e-31 relative error = 6.8191861538653284451586056664790e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (closed_form) = 1.0242766421733409307388864607348 y[1] (numeric) = 1.0242766421733409307388864607341 absolute error = 7e-31 relative error = 6.8340912130410294647498388972148e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (closed_form) = 1.0221353975646838143215075605734 y[1] (numeric) = 1.0221353975646838143215075605726 absolute error = 8e-31 relative error = 7.8267517386254455039536141381466e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (closed_form) = 1.0200919386013857771123114951081 y[1] (numeric) = 1.0200919386013857771123114951074 absolute error = 7e-31 relative error = 6.8621265741963100168466464782675e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=723.7MB, alloc=44.3MB, time=8.42 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (closed_form) = 1.018146469627640272121868914794 y[1] (numeric) = 1.0181464696276402721218689147932 absolute error = 8e-31 relative error = 7.8574156456347436451200609802514e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (closed_form) = 1.0162991851887234551599617755571 y[1] (numeric) = 1.0162991851887234551599617755563 absolute error = 8e-31 relative error = 7.8716977407734770587131429116058e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (closed_form) = 1.0145502700115398193405254211939 y[1] (numeric) = 1.014550270011539819340525421193 absolute error = 9e-31 relative error = 8.8709256367332405527513811256582e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (closed_form) = 1.0128998989861496585709111380578 y[1] (numeric) = 1.0128998989861496585709111380568 absolute error = 1.0e-30 relative error = 9.8726438910788552548757343046722e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (closed_form) = 1.0113482371482802072637265266643 y[1] (numeric) = 1.0113482371482802072637265266634 absolute error = 9e-31 relative error = 8.8990119025445561444611722681767e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (closed_form) = 1.0098954396628222051427085045182 y[1] (numeric) = 1.0098954396628222051427085045174 absolute error = 8e-31 relative error = 7.9216121647910319522176824206799e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (closed_form) = 1.008541651808313537472395536042 y[1] (numeric) = 1.0085416518083135374723955360411 absolute error = 9e-31 relative error = 8.9237762107921023119377606765352e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=764.0MB, alloc=44.3MB, time=8.89 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (closed_form) = 1.007287008962411502334645865677 y[1] (numeric) = 1.0072870089624115023346458656759 absolute error = 1.1e-30 relative error = 1.0920422781319204213245538848916e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (closed_form) = 1.00613163658835515771316769875 y[1] (numeric) = 1.006131636588355157713167698749 absolute error = 1.0e-30 relative error = 9.9390573125287398947933891831885e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (closed_form) = 1.0050756502224191021400715372644 y[1] (numeric) = 1.0050756502224191021400715372634 absolute error = 1.0e-30 relative error = 9.9494998190305786270997754811358e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.48 y[1] (closed_form) = 1.0041191554623599435159248674373 y[1] (numeric) = 1.0041191554623599435159248674364 absolute error = 9e-31 relative error = 8.9630796813709135792680008571199e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (closed_form) = 1.0032622479568566114467992829563 y[1] (numeric) = 1.0032622479568566114467992829553 absolute error = 1.0e-30 relative error = 9.9674835970006827344738832079132e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (closed_form) = 1.0025050133959455690582766288585 y[1] (numeric) = 1.0025050133959455690582766288577 absolute error = 8e-31 relative error = 7.9800099681300550385158277633208e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.51 y[1] (closed_form) = 1.0018475275024518807572621351633 y[1] (numeric) = 1.0018475275024518807572621351625 absolute error = 8e-31 relative error = 7.9852470364862193328607630345089e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=804.5MB, alloc=44.3MB, time=9.36 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (closed_form) = 1.0012898560244169928276876058832 y[1] (numeric) = 1.0012898560244169928276876058824 absolute error = 8e-31 relative error = 7.9896944444875267847051199407156e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.53 y[1] (closed_form) = 1.000832054728523984075734931291 y[1] (numeric) = 1.0008320547285239840757349312904 absolute error = 6e-31 relative error = 5.9950118220658928883660882368356e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (closed_form) = 1.00047416939452094399403646156 y[1] (numeric) = 1.0004741693945209439940364615594 absolute error = 6e-31 relative error = 5.9971563320132018547040952699862e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (closed_form) = 1.0002162358106430361023886523655 y[1] (numeric) = 1.000216235810643036102388652365 absolute error = 5e-31 relative error = 4.9989190546858710809461744593095e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.56 y[1] (closed_form) = 1.0000582797700337042548299765865 y[1] (numeric) = 1.0000582797700337042548299765861 absolute error = 4e-31 relative error = 3.9997668945051998135283906151737e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (closed_form) = 1.0000003170681653797894700761767 y[1] (numeric) = 1.0000003170681653797894700761763 absolute error = 4e-31 relative error = 3.9999987317277406096006066896968e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (closed_form) = 1.0000423535012599474482057677483 y[1] (numeric) = 1.0000423535012599474482057677479 absolute error = 4e-31 relative error = 3.9998305931699326009104675195683e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=844.9MB, alloc=44.3MB, time=9.82 TOP MAIN SOLVE Loop x[1] = 1.59 y[1] (closed_form) = 1.0001843848657091280184156562545 y[1] (numeric) = 1.0001843848657091280184156562539 absolute error = 6e-31 relative error = 5.9988938947548123259809004172559e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (closed_form) = 1.0004263969584948356578861744538 y[1] (numeric) = 1.0004263969584948356578861744532 absolute error = 6e-31 relative error = 5.9974427086702759655948703385069e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (closed_form) = 1.0007683655786094678675868521557 y[1] (numeric) = 1.0007683655786094678675868521551 absolute error = 6e-31 relative error = 5.9953933461226151431586495989740e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (closed_form) = 1.0012102565294759860844811087532 y[1] (numeric) = 1.0012102565294759860844811087524 absolute error = 8e-31 relative error = 7.9903296513667677897843192575325e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (closed_form) = 1.0017520256223675448883300150669 y[1] (numeric) = 1.0017520256223675448883300150662 absolute error = 7e-31 relative error = 6.9877572702196900110661544869184e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.64 y[1] (closed_form) = 1.0023936186808263278624180256321 y[1] (numeric) = 1.0023936186808263278624180256314 absolute error = 7e-31 relative error = 6.9832846793380082507153596678108e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.65 y[1] (closed_form) = 1.0031349715460811482282969597978 y[1] (numeric) = 1.0031349715460811482282969597971 absolute error = 7e-31 relative error = 6.9781237805030905990253706586754e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=885.1MB, alloc=44.3MB, time=10.29 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (closed_form) = 1.003976010083463272498999409387 y[1] (numeric) = 1.0039760100834632724989994093863 absolute error = 7e-31 relative error = 6.9722781517638761594318490185029e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.67 y[1] (closed_form) = 1.0049166501898198255737027534658 y[1] (numeric) = 1.0049166501898198255737027534649 absolute error = 9e-31 relative error = 8.9559666448953552253533303520111e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.68 y[1] (closed_form) = 1.0059567978019240359395121308064 y[1] (numeric) = 1.0059567978019240359395121308054 absolute error = 1.0e-30 relative error = 9.9407847552207013604854046055065e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (closed_form) = 1.0070963489058814799628507060544 y[1] (numeric) = 1.0070963489058814799628507060534 absolute error = 1.0e-30 relative error = 9.9295365442085951641114556557187e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (closed_form) = 1.0083351895475313846538666013521 y[1] (numeric) = 1.008335189547531384653866601351 absolute error = 1.1e-30 relative error = 1.0909070826870588709441980120709e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (closed_form) = 1.0096731958438419487822477761389 y[1] (numeric) = 1.0096731958438419487822477761377 absolute error = 1.2e-30 relative error = 1.1885033741012516398081885750189e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (closed_form) = 1.0111102339952985428218293429145 y[1] (numeric) = 1.0111102339952985428218293429132 absolute error = 1.3e-30 relative error = 1.2857154010430525776888916591379e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop memory used=925.3MB, alloc=44.3MB, time=10.76 x[1] = 1.73 y[1] (closed_form) = 1.0126461602992835489143223237779 y[1] (numeric) = 1.0126461602992835489143223237766 absolute error = 1.3e-30 relative error = 1.2837652982516520534341354791726e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (closed_form) = 1.0142808211644465028793173043344 y[1] (numeric) = 1.0142808211644465028793173043329 absolute error = 1.5e-30 relative error = 1.4788803738573336331894459958459e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (closed_form) = 1.016014053126063101268337063032 y[1] (numeric) = 1.0160140531260631012683370630304 absolute error = 1.6e-30 relative error = 1.5747813675186224781390987001240e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.76 y[1] (closed_form) = 1.017845682862381537575031900544 y[1] (numeric) = 1.0178456828623815375750319005425 absolute error = 1.5e-30 relative error = 1.4737008028385069434548816466156e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (closed_form) = 1.0197755272119545329815185511016 y[1] (numeric) = 1.0197755272119545329815185511001 absolute error = 1.5e-30 relative error = 1.4709119408866080255644730468777e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (closed_form) = 1.0218033931919553284522313526944 y[1] (numeric) = 1.021803393191955328452231352693 absolute error = 1.4e-30 relative error = 1.3701265912091142372663058462667e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.79 y[1] (closed_form) = 1.0239290780174758065913395668914 y[1] (numeric) = 1.0239290780174758065913395668901 absolute error = 1.3e-30 relative error = 1.2696191835054149919399055386141e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (closed_form) = 1.0261523691218048134676268211566 y[1] (numeric) = 1.0261523691218048134676268211554 absolute error = 1.2e-30 relative error = 1.1694169755968856350430985936127e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=965.6MB, alloc=44.3MB, time=11.22 TOP MAIN SOLVE Loop x[1] = 1.81 y[1] (closed_form) = 1.0284730441776846525915487309096 y[1] (numeric) = 1.0284730441776846525915487309084 absolute error = 1.2e-30 relative error = 1.1667782707513347411662265235456e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.82 y[1] (closed_form) = 1.030890871119543625412784681502 y[1] (numeric) = 1.0308908711195436254127846815006 absolute error = 1.4e-30 relative error = 1.3580486928549529621055550375138e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (closed_form) = 1.0334056081667023951027610702572 y[1] (numeric) = 1.0334056081667023951027610702557 absolute error = 1.5e-30 relative error = 1.4515113796034572869292873598671e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (closed_form) = 1.0360170038475518530051063282729 y[1] (numeric) = 1.0360170038475518530051063282713 absolute error = 1.6e-30 relative error = 1.5443761965855121133055099517294e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.85 y[1] (closed_form) = 1.0387247970247000699875408313639 y[1] (numeric) = 1.0387247970247000699875408313623 absolute error = 1.6e-30 relative error = 1.5403502492508159897507278638791e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (closed_form) = 1.0415287169210858180210222340968 y[1] (numeric) = 1.0415287169210858180210222340951 absolute error = 1.7e-30 relative error = 1.6322161572514807605274806286032e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.87 y[1] (closed_form) = 1.0444284831470560506557495078274 y[1] (numeric) = 1.0444284831470560506557495078257 absolute error = 1.7e-30 relative error = 1.6276844488936052438469607174820e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1005.8MB, alloc=44.3MB, time=11.69 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (closed_form) = 1.0474238057284046346685425741849 y[1] (numeric) = 1.0474238057284046346685425741833 absolute error = 1.6e-30 relative error = 1.5275574139613144461121781502530e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (closed_form) = 1.0505143851353695290317983278617 y[1] (numeric) = 1.05051438513536952903179832786 absolute error = 1.7e-30 relative error = 1.6182548511993366020777744235668e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (closed_form) = 1.053699912312585511510290388365 y[1] (numeric) = 1.0536999123125855115102903883635 absolute error = 1.5e-30 relative error = 1.4235552100482829560148227444542e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (closed_form) = 1.0569800687099894576381134230518 y[1] (numeric) = 1.0569800687099894576381134230502 absolute error = 1.6e-30 relative error = 1.5137466139288218465962076278606e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.92 y[1] (closed_form) = 1.060354526314675081573628660313 y[1] (numeric) = 1.0603545263146750815736286603113 absolute error = 1.7e-30 relative error = 1.6032373680795711060299385605202e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.93 y[1] (closed_form) = 1.0638229476836939533848706272512 y[1] (numeric) = 1.0638229476836939533848706272495 absolute error = 1.7e-30 relative error = 1.5980102738914223085409094607684e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (closed_form) = 1.0673849859777995126910206611343 y[1] (numeric) = 1.0673849859777995126910206611325 absolute error = 1.8e-30 relative error = 1.6863643611691556157962024111235e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1046.0MB, alloc=44.3MB, time=12.16 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (closed_form) = 1.0710402849961307042867029649085 y[1] (numeric) = 1.0710402849961307042867029649067 absolute error = 1.8e-30 relative error = 1.6806090538475896575708920833743e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (closed_form) = 1.07478847921183176741444371051 y[1] (numeric) = 1.0747884792118317674144437105082 absolute error = 1.8e-30 relative error = 1.6747481339956149109425532764207e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.97 y[1] (closed_form) = 1.0786291938086046167360490028468 y[1] (numeric) = 1.078629193808604616736049002845 absolute error = 1.8e-30 relative error = 1.6687847967884667747704065754096e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (closed_form) = 1.082562044718190159795264782598 y[1] (numeric) = 1.0825620447181901597952647825963 absolute error = 1.7e-30 relative error = 1.5703487927498324055417342215366e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (closed_form) = 1.0865866386587748028712067289424 y[1] (numeric) = 1.0865866386587748028712067289407 absolute error = 1.7e-30 relative error = 1.5645323985378563780641736750142e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = 1.0907025731743183046039801340883 y[1] (numeric) = 1.0907025731743183046039801340866 absolute error = 1.7e-30 relative error = 1.5586283940381816086938303062970e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (closed_form) = 1.0949094366747990446399002897263 y[1] (numeric) = 1.0949094366747990446399002897246 absolute error = 1.7e-30 relative error = 1.5526398285166300521745795115995e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1086.3MB, alloc=44.3MB, time=12.62 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (closed_form) = 1.0992068084773726828029864754463 y[1] (numeric) = 1.0992068084773726828029864754445 absolute error = 1.8e-30 relative error = 1.6375444421540382384893370028780e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (closed_form) = 1.1035942588484400929611111680324 y[1] (numeric) = 1.1035942588484400929611111680307 absolute error = 1.7e-30 relative error = 1.5404212067702194298011724330832e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.04 y[1] (closed_form) = 1.1080713490466203648284743514158 y[1] (numeric) = 1.1080713490466203648284743514143 absolute error = 1.5e-30 relative error = 1.3537034427346156855014491306127e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (closed_form) = 1.1126376313666245764400333953197 y[1] (numeric) = 1.1126376313666245764400333953181 absolute error = 1.6e-30 relative error = 1.4380243440398115870987894126869e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (closed_form) = 1.1172926491840259499572024148001 y[1] (numeric) = 1.1172926491840259499572024147985 absolute error = 1.6e-30 relative error = 1.4320330498625421079172748371283e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (closed_form) = 1.1220359370009219138265488795562 y[1] (numeric) = 1.1220359370009219138265488795545 absolute error = 1.7e-30 relative error = 1.5151029872928242989131365352276e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (closed_form) = 1.1268670204924835051233231949754 y[1] (numeric) = 1.1268670204924835051233231949736 absolute error = 1.8e-30 relative error = 1.5973490813612877990747059233249e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1126.4MB, alloc=44.3MB, time=13.09 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (closed_form) = 1.1317854165543874571783779412725 y[1] (numeric) = 1.1317854165543874571783779412706 absolute error = 1.9e-30 relative error = 1.6787634583456362501173834905355e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (closed_form) = 1.136790633351126229319240686731 y[1] (numeric) = 1.1367906333511262293192406867293 absolute error = 1.7e-30 relative error = 1.4954380781521732211862933688134e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (closed_form) = 1.1418821703651911477626244916893 y[1] (numeric) = 1.1418821703651911477626244916876 absolute error = 1.7e-30 relative error = 1.4887700711329211392873613403939e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (closed_form) = 1.1470595184471237393852726663458 y[1] (numeric) = 1.1470595184471237393852726663441 absolute error = 1.7e-30 relative error = 1.4820503841870741447131215293844e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (closed_form) = 1.1523221598664302532814700036841 y[1] (numeric) = 1.1523221598664302532814700036824 absolute error = 1.7e-30 relative error = 1.4752818779403261903554181885423e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (closed_form) = 1.1576695683633542786974933629311 y[1] (numeric) = 1.1576695683633542786974933629295 absolute error = 1.6e-30 relative error = 1.3820869475406412290515957984115e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (closed_form) = 1.1631012092015022821243518629562 y[1] (numeric) = 1.1631012092015022821243518629547 absolute error = 1.5e-30 relative error = 1.2896556104776015681489065466154e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1166.6MB, alloc=44.3MB, time=13.56 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (closed_form) = 1.1686165392213168010389618796537 y[1] (numeric) = 1.1686165392213168010389618796522 absolute error = 1.5e-30 relative error = 1.2835690319764716319236436281554e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (closed_form) = 1.1742150068943919470189435760566 y[1] (numeric) = 1.1742150068943919470189435760551 absolute error = 1.5e-30 relative error = 1.2774491819579588467044888533925e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (closed_form) = 1.1798960523786257867259902539161 y[1] (numeric) = 1.1798960523786257867259902539145 absolute error = 1.6e-30 relative error = 1.3560516596139639202196247076219e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (closed_form) = 1.185659107574204085565672354095 y[1] (numeric) = 1.1856591075742040855656723540933 absolute error = 1.7e-30 relative error = 1.4338016628389168416407560985665e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (closed_form) = 1.1915035961804098156959630895839 y[1] (numeric) = 1.1915035961804098156959630895822 absolute error = 1.7e-30 relative error = 1.4267686689739515711790053432990e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (closed_form) = 1.197428933753252747481025957444 y[1] (numeric) = 1.1974289337532527474810259574423 absolute error = 1.7e-30 relative error = 1.4197084704404755635035476928129e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (closed_form) = 1.2034345277639133614791432503908 y[1] (numeric) = 1.2034345277639133614791432503891 absolute error = 1.7e-30 relative error = 1.4126235875571467351829545776655e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1206.8MB, alloc=44.3MB, time=14.02 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (closed_form) = 1.2095197776579952366222898728115 y[1] (numeric) = 1.2095197776579952366222898728097 absolute error = 1.8e-30 relative error = 1.4881939371717900220583088787409e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (closed_form) = 1.2156840749155799893979113293955 y[1] (numeric) = 1.2156840749155799893979113293938 absolute error = 1.7e-30 relative error = 1.3983896269415654450620797806866e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (closed_form) = 1.2219268031120787585890333244122 y[1] (numeric) = 1.2219268031120787585890333244105 absolute error = 1.7e-30 relative error = 1.3912453640188060812248378546554e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (closed_form) = 1.2282473379798741504749383622597 y[1] (numeric) = 1.2282473379798741504749383622578 absolute error = 1.9e-30 relative error = 1.5469196970741841518655658276193e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (closed_form) = 1.2346450474707464803492573980653 y[1] (numeric) = 1.2346450474707464803492573980633 absolute error = 2.0e-30 relative error = 1.6198987750342778098315573693644e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (closed_form) = 1.2411192918190780677833464236991 y[1] (numeric) = 1.2411192918190780677833464236971 absolute error = 2.0e-30 relative error = 1.6114486441256175416561918111773e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (closed_form) = 1.2476694236058292652580917220264 y[1] (numeric) = 1.2476694236058292652580917220243 absolute error = 2.1e-30 relative error = 1.6831381456242561567597139903348e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1246.9MB, alloc=44.3MB, time=14.49 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (closed_form) = 1.2542947878232798226145937883565 y[1] (numeric) = 1.2542947878232798226145937883545 absolute error = 2.0e-30 relative error = 1.5945214948001395357834523084085e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (closed_form) = 1.2609947219405291132412358079017 y[1] (numeric) = 1.2609947219405291132412358078998 absolute error = 1.9e-30 relative error = 1.5067469886599633043798779928486e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (closed_form) = 1.2677685559697486720291013222753 y[1] (numeric) = 1.2677685559697486720291013222734 absolute error = 1.9e-30 relative error = 1.4986962652237744507113689222147e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (closed_form) = 1.2746156125331804198971558075246 y[1] (numeric) = 1.2746156125331804198971558075228 absolute error = 1.8e-30 relative error = 1.4121904535773469727333570627973e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (closed_form) = 1.281535206930873875120571313206 y[1] (numeric) = 1.2815352069308738751205713132042 absolute error = 1.8e-30 relative error = 1.4045653917778726797580371939986e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (closed_form) = 1.2885266472091555777975088179868 y[1] (numeric) = 1.2885266472091555777975088179849 absolute error = 1.9e-30 relative error = 1.4745523533527585250953893557779e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (closed_form) = 1.2955892342298238805689692870673 y[1] (numeric) = 1.2955892342298238805689692870654 absolute error = 1.9e-30 relative error = 1.4665141927715030837526886034040e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1287.2MB, alloc=44.3MB, time=14.95 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (closed_form) = 1.3027222617400621861703035797108 y[1] (numeric) = 1.3027222617400621861703035797088 absolute error = 2.0e-30 relative error = 1.5352466590450180394948277279094e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (closed_form) = 1.3099250164430636405488868929798 y[1] (numeric) = 1.3099250164430636405488868929778 absolute error = 2.0e-30 relative error = 1.5268049505846892232996978194540e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (closed_form) = 1.317196778069360219137499688987 y[1] (numeric) = 1.3171967780693602191374996889848 absolute error = 2.2e-30 relative error = 1.6702136207959609944135130109700e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (closed_form) = 1.3245368194488490734342284746587 y[1] (numeric) = 1.3245368194488490734342284746565 absolute error = 2.2e-30 relative error = 1.6609579799491255589525799022715e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (closed_form) = 1.3319444065835089353142501993453 y[1] (numeric) = 1.3319444065835089353142501993429 absolute error = 2.4e-30 relative error = 1.8018770063805415812825312235530e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.42 y[1] (closed_form) = 1.3394187987207993074936658934398 y[1] (numeric) = 1.3394187987207993074936658934374 absolute error = 2.4e-30 relative error = 1.7918219471699963265170739034374e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (closed_form) = 1.3469592484277351002875029528101 y[1] (numeric) = 1.3469592484277351002875029528077 absolute error = 2.4e-30 relative error = 1.7817910993234929743319788973516e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1327.3MB, alloc=44.3MB, time=15.42 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (closed_form) = 1.3545650016656293072599389270175 y[1] (numeric) = 1.354565001665629307259938927015 absolute error = 2.5e-30 relative error = 1.8456109503241972968001902463746e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (closed_form) = 1.3622352978654962455614671443662 y[1] (numeric) = 1.3622352978654962455614671443639 absolute error = 2.3e-30 relative error = 1.6884014117119848181136919984300e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (closed_form) = 1.3699693700041078206918062813841 y[1] (numeric) = 1.3699693700041078206918062813819 absolute error = 2.2e-30 relative error = 1.6058753196747773653752411433639e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (closed_form) = 1.3777664446806952101254575951442 y[1] (numeric) = 1.377766444680695210125457595142 absolute error = 2.2e-30 relative error = 1.5967873281380879052294412290146e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (closed_form) = 1.3856257421942882956954651193344 y[1] (numeric) = 1.385625742194288295695465119332 absolute error = 2.4e-30 relative error = 1.7320694375952775716715940908346e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (closed_form) = 1.3935464766216851108565897602082 y[1] (numeric) = 1.3935464766216851108565897602059 absolute error = 2.3e-30 relative error = 1.6504652256563349403661331339226e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (closed_form) = 1.4015278558960435059481452978138 y[1] (numeric) = 1.4015278558960435059481452978115 absolute error = 2.3e-30 relative error = 1.6410662052303864370732367631253e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1367.4MB, alloc=44.3MB, time=15.88 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (closed_form) = 1.409569081886087172355462844976 y[1] (numeric) = 1.4095690818860871723554628449738 absolute error = 2.2e-30 relative error = 1.5607606808857280699323017623698e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (closed_form) = 1.4176693504759181050335724177029 y[1] (numeric) = 1.4176693504759181050335724177006 absolute error = 2.3e-30 relative error = 1.6223811280309329166954824607026e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (closed_form) = 1.4258278516454275222133594125978 y[1] (numeric) = 1.4258278516454275222133594125955 absolute error = 2.3e-30 relative error = 1.6130979608413205136969679183585e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (closed_form) = 1.434043769551297201265234252018 y[1] (numeric) = 1.4340437695512972012652342520158 absolute error = 2.2e-30 relative error = 1.5341233278314548452048059425165e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (closed_form) = 1.4423162826085831306542297182338 y[1] (numeric) = 1.4423162826085831306542297182316 absolute error = 2.2e-30 relative error = 1.5253242485906523195790216207503e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (closed_form) = 1.4506445635728733196893166168627 y[1] (numeric) = 1.4506445635728733196893166168606 absolute error = 2.1e-30 relative error = 1.4476323509790661583343158579891e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (closed_form) = 1.4590277796230115503544274512542 y[1] (numeric) = 1.459027779623011550354427451252 absolute error = 2.2e-30 relative error = 1.5078534012343776730722368341894e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1407.6MB, alloc=44.3MB, time=16.35 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (closed_form) = 1.4674650924443787989149412355284 y[1] (numeric) = 1.4674650924443787989149412355261 absolute error = 2.3e-30 relative error = 1.5673285939421258832363110537435e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (closed_form) = 1.4759556583127239992268697511241 y[1] (numeric) = 1.4759556583127239992268697511217 absolute error = 2.4e-30 relative error = 1.6260651100749331696888191492558e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (closed_form) = 1.4844986281785357647422730647906 y[1] (numeric) = 1.4844986281785357647422730647881 absolute error = 2.5e-30 relative error = 1.6840702662470451452218252803972e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (closed_form) = 1.4930931477519466321090133004445 y[1] (numeric) = 1.493093147751946632109013300442 absolute error = 2.5e-30 relative error = 1.6743764471520665747730126341335e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (closed_form) = 1.5017383575881613360112399900024 y[1] (numeric) = 1.5017383575881613360112399899998 absolute error = 2.6e-30 relative error = 1.7313268898423032444380496019397e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (closed_form) = 1.5104333931734005724943129463884 y[1] (numeric) = 1.5104333931734005724943129463858 absolute error = 2.6e-30 relative error = 1.7213602478275684862045070074953e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (closed_form) = 1.5191773850113516564694497304671 y[1] (numeric) = 1.5191773850113516564694497304645 absolute error = 2.6e-30 relative error = 1.7114525437597744246696202357688e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1447.8MB, alloc=44.3MB, time=16.81 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (closed_form) = 1.5279694587101174284043892216026 y[1] (numeric) = 1.5279694587101174284043892216 absolute error = 2.6e-30 relative error = 1.7016046918862306552968461373648e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (closed_form) = 1.5368087350696547153818594062036 y[1] (numeric) = 1.5368087350696547153818594062009 absolute error = 2.7e-30 relative error = 1.7568874632129316364094886922167e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (closed_form) = 1.5456943301696936027526086788087 y[1] (numeric) = 1.5456943301696936027526086788059 absolute error = 2.8e-30 relative error = 1.8114836454712250991258786027085e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (closed_form) = 1.5546253554581287245291011680706 y[1] (numeric) = 1.5546253554581287245291011680678 absolute error = 2.8e-30 relative error = 1.8010770184401597404561391535434e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (closed_form) = 1.563600917839873733464495881239 y[1] (numeric) = 1.5636009178398737334644958812362 absolute error = 2.8e-30 relative error = 1.7907382683480518609242894107763e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (closed_form) = 1.5726201197661700654439469141421 y[1] (numeric) = 1.5726201197661700654439469141394 absolute error = 2.7e-30 relative error = 1.7168799801451465172644092405225e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (closed_form) = 1.5816820593243410673862093188914 y[1] (numeric) = 1.5816820593243410673862093188887 absolute error = 2.7e-30 relative error = 1.7070434504096095998137066477545e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1487.9MB, alloc=44.3MB, time=17.28 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (closed_form) = 1.5907858303279825133175553259926 y[1] (numeric) = 1.5907858303279825133175553259899 absolute error = 2.7e-30 relative error = 1.6972743587006452591068908634423e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (closed_form) = 1.5999305224075804896415520421056 y[1] (numeric) = 1.5999305224075804896415520421029 absolute error = 2.7e-30 relative error = 1.6875732803303430297937391447428e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (closed_form) = 1.6091152211015475878916882983597 y[1] (numeric) = 1.6091152211015475878916882983571 absolute error = 2.6e-30 relative error = 1.6157947957388192128503765578357e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (closed_form) = 1.6183390079476683014234386276222 y[1] (numeric) = 1.6183390079476683014234386276198 absolute error = 2.4e-30 relative error = 1.4830020089817967324943021750606e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (closed_form) = 1.6276009605749444815822994075502 y[1] (numeric) = 1.6276009605749444815822994075479 absolute error = 2.3e-30 relative error = 1.4131227836014134900548040045437e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (closed_form) = 1.6369001527958316688787179908275 y[1] (numeric) = 1.636900152795831668878717990825 absolute error = 2.5e-30 relative error = 1.5272770276977435177165141928852e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (closed_form) = 1.6462356546988570756136606827727 y[1] (numeric) = 1.64623565469885707561366068277 absolute error = 2.7e-30 relative error = 1.6401054079307413244224220349577e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1528.1MB, alloc=44.3MB, time=17.74 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (closed_form) = 1.6556065327416099582337384044377 y[1] (numeric) = 1.6556065327416099582337384044351 absolute error = 2.6e-30 relative error = 1.5704214428862617095133279242678e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (closed_form) = 1.6650118498440950804561462472876 y[1] (numeric) = 1.6650118498440950804561462472849 absolute error = 2.7e-30 relative error = 1.6216100805846018388067595735662e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (closed_form) = 1.6744506654824399318948987187937 y[1] (numeric) = 1.6744506654824399318948987187909 absolute error = 2.8e-30 relative error = 1.6721902040591137224329057103850e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (closed_form) = 1.6839220357829463315445871439754 y[1] (numeric) = 1.6839220357829463315445871439726 absolute error = 2.8e-30 relative error = 1.6627848204968282421958944757175e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (closed_form) = 1.6934250136164770110396869221319 y[1] (numeric) = 1.6934250136164770110396869221292 absolute error = 2.7e-30 relative error = 1.5944018650308479315285043222114e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (closed_form) = 1.7029586486931677391097439319027 y[1] (numeric) = 1.7029586486931677391097439319 absolute error = 2.7e-30 relative error = 1.5854759609529868118872663785404e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (closed_form) = 1.7125219876574555160969210733083 y[1] (numeric) = 1.7125219876574555160969210733056 absolute error = 2.7e-30 relative error = 1.5766220927144458953709282961617e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1568.3MB, alloc=44.3MB, time=18.21 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (closed_form) = 1.7221140741834133357956430902468 y[1] (numeric) = 1.7221140741834133357956430902441 absolute error = 2.7e-30 relative error = 1.5678403890173637616152404590606e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (closed_form) = 1.7317339490703819812176010790129 y[1] (numeric) = 1.73173394907038198121760107901 absolute error = 2.9e-30 relative error = 1.6746221332420946703237356475597e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (closed_form) = 1.7413806503388892911822330798823 y[1] (numeric) = 1.7413806503388892911822330798794 absolute error = 2.9e-30 relative error = 1.6653452531677277610614843115552e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (closed_form) = 1.7510532133268473058859541594195 y[1] (numeric) = 1.7510532133268473058859541594166 absolute error = 2.9e-30 relative error = 1.6561461284721637410087205400115e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (closed_form) = 1.7607506707860176718157430812604 y[1] (numeric) = 1.7607506707860176718157430812574 absolute error = 3.0e-30 relative error = 1.7038187460469734514064612664989e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (closed_form) = 1.770472052978735659546981776173 y[1] (numeric) = 1.77047205297873565954698177617 absolute error = 3.0e-30 relative error = 1.6944633466270431129408163968218e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (closed_form) = 1.7802163877748831221043709069354 y[1] (numeric) = 1.7802163877748831221043709069323 absolute error = 3.1e-30 relative error = 1.7413613430863494718282182305327e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1608.5MB, alloc=44.3MB, time=18.68 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (closed_form) = 1.7899827007491006966708959657409 y[1] (numeric) = 1.7899827007491006966708959657379 absolute error = 3.0e-30 relative error = 1.6759938510827573018095474544628e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (closed_form) = 1.7997700152782295285056829055769 y[1] (numeric) = 1.799770015278229528505682905574 absolute error = 2.9e-30 relative error = 1.6113169879384194730973426072264e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (closed_form) = 1.8095773526389727729795526859426 y[1] (numeric) = 1.8095773526389727729795526859399 absolute error = 2.7e-30 relative error = 1.4920611136420840730997157464954e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (closed_form) = 1.8194037321057671096594554911986 y[1] (numeric) = 1.8194037321057671096594554911959 absolute error = 2.7e-30 relative error = 1.4840026720595081898234542215161e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (closed_form) = 1.829248171048854481371935501332 y[1] (numeric) = 1.8292481710488544813719355013292 absolute error = 2.8e-30 relative error = 1.5306835039198293949101451543242e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (closed_form) = 1.8391096850325442511534460454587 y[1] (numeric) = 1.8391096850325442511534460454557 absolute error = 3.0e-30 relative error = 1.6312240778324828591849165635149e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (closed_form) = 1.8489872879136559509537049643895 y[1] (numeric) = 1.8489872879136559509537049643867 absolute error = 2.8e-30 relative error = 1.5143424826676009367979708496303e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1648.6MB, alloc=44.3MB, time=19.14 TOP MAIN SOLVE Loop x[1] = 3 y[1] (closed_form) = 1.8588799919401327778992551971919 y[1] (numeric) = 1.8588799919401327778992551971891 absolute error = 2.8e-30 relative error = 1.5062833599481644216097802229678e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (closed_form) = 1.8687868078498159768497818753152 y[1] (numeric) = 1.8687868078498159768497818753124 absolute error = 2.8e-30 relative error = 1.4982982479535035645203357168019e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (closed_form) = 1.8787067449693702318912420036609 y[1] (numeric) = 1.8787067449693702318912420036581 absolute error = 2.8e-30 relative error = 1.4903869417074191674426650714599e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (closed_form) = 1.8886388113133501743090949670827 y[1] (numeric) = 1.8886388113133501743090949670798 absolute error = 2.9e-30 relative error = 1.5354974083071787618028474204980e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (closed_form) = 1.8985820136833981004733916873912 y[1] (numeric) = 1.8985820136833981004733916873883 absolute error = 2.9e-30 relative error = 1.5274557428118537889072509672396e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (closed_form) = 1.9085353577675629799465984113036 y[1] (numeric) = 1.9085353577675629799465984113007 absolute error = 2.9e-30 relative error = 1.5194897952491513023408529669585e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (closed_form) = 1.9184978482397308219961099111643 y[1] (numeric) = 1.9184978482397308219961099111614 absolute error = 2.9e-30 relative error = 1.5115992976801207534314639555814e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1688.8MB, alloc=44.3MB, time=19.61 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (closed_form) = 1.9284684888591564575576592096811 y[1] (numeric) = 1.9284684888591564575576592096782 absolute error = 2.9e-30 relative error = 1.5037839698980937102511576931000e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (closed_form) = 1.9384462825700867835543703628643 y[1] (numeric) = 1.9384462825700867835543703628614 absolute error = 2.9e-30 relative error = 1.4960435200479418606857791841563e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (closed_form) = 1.9484302316014655073300414894254 y[1] (numeric) = 1.9484302316014655073300414894224 absolute error = 3.0e-30 relative error = 1.5397010123037466613286953054743e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (closed_form) = 1.9584193375667094208053017284033 y[1] (numeric) = 1.9584193375667094208053017284005 absolute error = 2.8e-30 relative error = 1.4297244447549905334710845464704e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (closed_form) = 1.9684126015635462268123731272966 y[1] (numeric) = 1.9684126015635462268123731272938 absolute error = 2.8e-30 relative error = 1.4224660001545959686954822904368e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (closed_form) = 1.9784090242739039339090018957981 y[1] (numeric) = 1.9784090242739039339090018957952 absolute error = 2.9e-30 relative error = 1.4658242883138532232106683955328e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (closed_form) = 1.9884076060638418308153185168817 y[1] (numeric) = 1.9884076060638418308153185168788 absolute error = 2.9e-30 relative error = 1.4584534836600749049056703260745e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1729.0MB, alloc=44.3MB, time=20.08 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (closed_form) = 1.9984073470835130474594585636756 y[1] (numeric) = 1.9984073470835130474594585636728 absolute error = 2.8e-30 relative error = 1.4011157455392344262866579858630e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (closed_form) = 2.0084072473671487064591415165711 y[1] (numeric) = 2.0084072473671487064591415165682 absolute error = 2.9e-30 relative error = 1.4439302605592833098448025899037e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.16 y[1] (closed_form) = 2.0184063069330536667073792711874 y[1] (numeric) = 2.0184063069330536667073792711844 absolute error = 3.0e-30 relative error = 1.4863211582798050341417576216364e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (closed_form) = 2.0284035258836038595712852748967 y[1] (numeric) = 2.0284035258836038595712852748937 absolute error = 3.0e-30 relative error = 1.4789956543253166213803497275027e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (closed_form) = 2.0383979045052352180536952467261 y[1] (numeric) = 2.0383979045052352180536952467232 absolute error = 2.9e-30 relative error = 1.4226859209335259248359332076308e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (closed_form) = 2.0483884433684142001080071484512 y[1] (numeric) = 2.0483884433684142001080071484484 absolute error = 2.8e-30 relative error = 1.3669282352499604625065422688226e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (closed_form) = 2.0583741434275799091372174146191 y[1] (numeric) = 2.0583741434275799091372174146163 absolute error = 2.8e-30 relative error = 1.3602969163504325890219098984763e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (closed_form) = 2.0683540061210478175483883606769 y[1] (numeric) = 2.0683540061210478175483883606742 absolute error = 2.7e-30 relative error = 1.3053858246749207083579375053851e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1769.2MB, alloc=44.3MB, time=20.54 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (closed_form) = 2.078327033470865103073444147916 y[1] (numeric) = 2.0783270334708651030734441479133 absolute error = 2.7e-30 relative error = 1.2991218208286130058389971856218e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.23 y[1] (closed_form) = 2.0882922281826076124058757285297 y[1] (numeric) = 2.088292228182607612405875728527 absolute error = 2.7e-30 relative error = 1.2929224959812006301174758267848e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.24 y[1] (closed_form) = 2.0982485937451084725401549594376 y[1] (numeric) = 2.098248593745108472540154959435 absolute error = 2.6e-30 relative error = 1.2391286751010416264888956981854e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (closed_form) = 2.1081951345301083770358308425608 y[1] (numeric) = 2.1081951345301083770358308425582 absolute error = 2.6e-30 relative error = 1.2332824212591255593133842728261e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (closed_form) = 2.1181308558918175822607231103361 y[1] (numeric) = 2.1181308558918175822607231103334 absolute error = 2.7e-30 relative error = 1.2747087803804228598495234171913e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (closed_form) = 2.1280547642663796574965568907536 y[1] (numeric) = 2.128054764266379657496556890751 absolute error = 2.6e-30 relative error = 1.2217730688412605665365986730631e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.28 y[1] (closed_form) = 2.1379658672712270426149140705852 y[1] (numeric) = 2.1379658672712270426149140705825 absolute error = 2.7e-30 relative error = 1.2628826499677097387820796210459e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1809.4MB, alloc=44.3MB, time=21.01 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (closed_form) = 2.1478631738043184778505297837426 y[1] (numeric) = 2.14786317380431847785052978374 absolute error = 2.6e-30 relative error = 1.2105054138038280561084322540872e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (closed_form) = 2.1577456941432483820116542776025 y[1] (numeric) = 2.1577456941432483820116542775999 absolute error = 2.6e-30 relative error = 1.2049612737298741411143761369672e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (closed_form) = 2.167612440044218268272249994317 y[1] (numeric) = 2.1676124400442182682722499943145 absolute error = 2.5e-30 relative error = 1.1533427073102612304431652755469e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (closed_form) = 2.1774624248408603004869205523084 y[1] (numeric) = 2.1774624248408603004869205523059 absolute error = 2.5e-30 relative error = 1.1481254378856674586191529258328e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.33 y[1] (closed_form) = 2.187294663542903107755292824136 y[1] (numeric) = 2.1872946635429031077552928241336 absolute error = 2.4e-30 relative error = 1.0972458535205148151326622146784e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (closed_form) = 2.1971081729346699907366169105927 y[1] (numeric) = 2.1971081729346699907366169105904 absolute error = 2.3e-30 relative error = 1.0468305695335417837912793927906e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (closed_form) = 2.2069019716733996699760341160255 y[1] (numeric) = 2.2069019716733996699760341160232 absolute error = 2.3e-30 relative error = 1.0421849404828833718164428519303e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1849.5MB, alloc=44.3MB, time=21.48 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (closed_form) = 2.2166750803873797442496139819055 y[1] (numeric) = 2.2166750803873797442496139819032 absolute error = 2.3e-30 relative error = 1.0375900466197592806901102534984e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (closed_form) = 2.2264265217738830456641034843086 y[1] (numeric) = 2.2264265217738830456641034843062 absolute error = 2.4e-30 relative error = 1.0779605688885811614183045277001e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (closed_form) = 2.2361553206968970979574917775896 y[1] (numeric) = 2.2361553206968970979574917775872 absolute error = 2.4e-30 relative error = 1.0732707061028483296921150089811e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (closed_form) = 2.2458605042846369051360013715579 y[1] (numeric) = 2.2458605042846369051360013715554 absolute error = 2.5e-30 relative error = 1.1131590743194056571563752970465e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (closed_form) = 2.2555411020268313192499024293637 y[1] (numeric) = 2.2555411020268313192499024293611 absolute error = 2.6e-30 relative error = 1.1527167461783948856537302598341e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (closed_form) = 2.2651961458717732587524443075741 y[1] (numeric) = 2.2651961458717732587524443075714 absolute error = 2.7e-30 relative error = 1.1919497589295473899849843106397e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.42 y[1] (closed_form) = 2.2748246703231240725009433576662 y[1] (numeric) = 2.2748246703231240725009433576635 absolute error = 2.7e-30 relative error = 1.1869046591693954738317660285982e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1889.7MB, alloc=44.3MB, time=21.94 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (closed_form) = 2.2844257125364623690442969145914 y[1] (numeric) = 2.2844257125364623690442969145887 absolute error = 2.7e-30 relative error = 1.1819163062221505841429526037855e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (closed_form) = 2.2939983124155676563944518105603 y[1] (numeric) = 2.2939983124155676563944518105576 absolute error = 2.7e-30 relative error = 1.1769843008981618607497426058827e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.45 y[1] (closed_form) = 2.3035415127084291639980863662199 y[1] (numeric) = 2.303541512708429163998086366217 absolute error = 2.9e-30 relative error = 1.2589310780817118214900063427425e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.46 y[1] (closed_form) = 2.3130543591029702461063157759749 y[1] (numeric) = 2.3130543591029702461063157759721 absolute error = 2.8e-30 relative error = 1.2105206213510144288410628540356e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.47 y[1] (closed_form) = 2.3225359003224787941818539871573 y[1] (numeric) = 2.3225359003224787941818539871544 absolute error = 2.9e-30 relative error = 1.2486351662410650518760646693598e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (closed_form) = 2.3319851882207341153819164354428 y[1] (numeric) = 2.3319851882207341153819164354399 absolute error = 2.9e-30 relative error = 1.2435756516158028138513611630202e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (closed_form) = 2.3414012778768207645082874807375 y[1] (numeric) = 2.3414012778768207645082874807347 absolute error = 2.8e-30 relative error = 1.1958650686904193894919921273958e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1929.9MB, alloc=44.3MB, time=22.41 TOP MAIN SOLVE Loop x[1] = 3.5 y[1] (closed_form) = 2.3507832276896198481203688000436 y[1] (numeric) = 2.3507832276896198481203688000409 absolute error = 2.7e-30 relative error = 1.1485533707221464699196850744590e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.51 y[1] (closed_form) = 2.3601300994719683517595399234174 y[1] (numeric) = 2.3601300994719683517595399234148 absolute error = 2.6e-30 relative error = 1.1016341855822684159534434444463e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.52 y[1] (closed_form) = 2.369440958544477074430574321433 y[1] (numeric) = 2.3694409585444770744305743214305 absolute error = 2.5e-30 relative error = 1.0551012005531144300809598776468e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (closed_form) = 2.3787148738289977886248442540066 y[1] (numeric) = 2.3787148738289977886248442540042 absolute error = 2.4e-30 relative error = 1.0089481620538823632353142992333e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (closed_form) = 2.3879509179417302792472011004845 y[1] (numeric) = 2.3879509179417302792472011004822 absolute error = 2.3e-30 relative error = 9.6316887533955736916189974312872e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (closed_form) = 2.397148167285959950820227423437 y[1] (numeric) = 2.3971481672859599508202274234344 absolute error = 2.6e-30 relative error = 1.0846221503878535611672768507788e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.56 y[1] (closed_form) = 2.4063057021444167292824214226859 y[1] (numeric) = 2.4063057021444167292824214226834 absolute error = 2.5e-30 relative error = 1.0389369886677682477461347841289e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1970.0MB, alloc=44.3MB, time=22.88 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (closed_form) = 2.4154226067712460225670994560663 y[1] (numeric) = 2.4154226067712460225670994560637 absolute error = 2.6e-30 relative error = 1.0764161901570852047885973311756e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (closed_form) = 2.4244979694835825429426009483438 y[1] (numeric) = 2.4244979694835825429426009483411 absolute error = 2.7e-30 relative error = 1.1136326093005964942883454119084e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (closed_form) = 2.433530882752717833807872932044 y[1] (numeric) = 2.4335308827527178338078729320412 absolute error = 2.8e-30 relative error = 1.1505915210875590781384080178351e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (closed_form) = 2.4425204432948523842667273474927 y[1] (numeric) = 2.4425204432948523842667273474898 absolute error = 2.9e-30 relative error = 1.1872981485010736960611745874030e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (closed_form) = 2.4514657521614232563449401863925 y[1] (numeric) = 2.4514657521614232563449401863897 absolute error = 2.8e-30 relative error = 1.1421738188801042580685572013106e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.62 y[1] (closed_form) = 2.4603659148289981921627435407948 y[1] (numeric) = 2.4603659148289981921627435407921 absolute error = 2.7e-30 relative error = 1.0973977422328487256084998620371e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (closed_form) = 2.4692200412887272117269048145319 y[1] (numeric) = 2.4692200412887272117269048145292 absolute error = 2.7e-30 relative error = 1.0934626946373012874189546744708e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=2010.2MB, alloc=44.3MB, time=23.34 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (closed_form) = 2.4780272461353427562571566388729 y[1] (numeric) = 2.4780272461353427562571566388703 absolute error = 2.6e-30 relative error = 1.0492217162078755614309988594203e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (closed_form) = 2.4867866486556994771068113882953 y[1] (numeric) = 2.4867866486556994771068113882928 absolute error = 2.5e-30 relative error = 1.0053134237918815276231952018364e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (closed_form) = 2.4954973729168448163724511464104 y[1] (numeric) = 2.4954973729168448163724511464078 absolute error = 2.6e-30 relative error = 1.0418764724889323413393310834037e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (closed_form) = 2.5041585478536115722080240589139 y[1] (numeric) = 2.5041585478536115722080240589113 absolute error = 2.6e-30 relative error = 1.0382729169558920196342782971609e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.68 y[1] (closed_form) = 2.512769307355723689659809225044 y[1] (numeric) = 2.5127693073557236896598092250413 absolute error = 2.7e-30 relative error = 1.0745116919791199663625081869907e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (closed_form) = 2.5213287903544065665157545481247 y[1] (numeric) = 2.521328790354406566515754548122 absolute error = 2.7e-30 relative error = 1.0708639072893300835278778639772e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (closed_form) = 2.5298361409084932132107776257012 y[1] (numeric) = 2.5298361409084932132107776256985 absolute error = 2.7e-30 relative error = 1.0672627987006300695301701414933e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=2050.4MB, alloc=44.3MB, time=23.81 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (closed_form) = 2.5382905082900176562437940432504 y[1] (numeric) = 2.5382905082900176562437940432475 absolute error = 2.9e-30 relative error = 1.1425012190403914452956021187251e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (closed_form) = 2.5466910470692870258374589670562 y[1] (numeric) = 2.5466910470692870258374589670534 absolute error = 2.8e-30 relative error = 1.0994659141014450964150453277702e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (closed_form) = 2.5550369171994238207027492321657 y[1] (numeric) = 2.5550369171994238207027492321628 absolute error = 2.9e-30 relative error = 1.1350129544032930229813113900196e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.74 y[1] (closed_form) = 2.5633272841003698957523611196795 y[1] (numeric) = 2.5633272841003698957523611196766 absolute error = 2.9e-30 relative error = 1.1313420716846890606438641169172e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (closed_form) = 2.5715613187423437724341555733503 y[1] (numeric) = 2.5715613187423437724341555733474 absolute error = 2.9e-30 relative error = 1.1277195604335359687736527157174e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (closed_form) = 2.579738197728742926023165037754 y[1] (numeric) = 2.579738197728742926023165037751 absolute error = 3.0e-30 relative error = 1.1629087023796696178972914497436e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (closed_form) = 2.5878571033784827597125177264744 y[1] (numeric) = 2.5878571033784827597125177264714 absolute error = 3.0e-30 relative error = 1.1592602992195585548628426020946e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=2090.5MB, alloc=44.3MB, time=24.28 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (closed_form) = 2.5959172238077640316744858109002 y[1] (numeric) = 2.5959172238077640316744858108972 absolute error = 3.0e-30 relative error = 1.1556608864436424686095521294342e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (closed_form) = 2.6039177530112605584170907202327 y[1] (numeric) = 2.6039177530112605584170907202298 absolute error = 2.9e-30 relative error = 1.1137064512296287737036055178368e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (closed_form) = 2.6118578909427190757335860861189 y[1] (numeric) = 2.6118578909427190757335860861159 absolute error = 3.0e-30 relative error = 1.1486076675163921882818963805210e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (closed_form) = 2.6197368435949631973258897105178 y[1] (numeric) = 2.6197368435949631973258897105148 absolute error = 3.0e-30 relative error = 1.1451531887008988396406559635614e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (closed_form) = 2.6275538230792934707727719568899 y[1] (numeric) = 2.6275538230792934707727719568869 absolute error = 3.0e-30 relative error = 1.1417463549744636263429696650872e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.83 y[1] (closed_form) = 2.6353080477042755909033702386223 y[1] (numeric) = 2.6353080477042755909033702386192 absolute error = 3.1e-30 relative error = 1.1763330676656706363673869227138e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (closed_form) = 2.6429987420539088918203488788627 y[1] (numeric) = 2.6429987420539088918203488788596 absolute error = 3.1e-30 relative error = 1.1729101307066644508636482591307e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=2130.6MB, alloc=44.3MB, time=24.74 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (closed_form) = 2.650625137065167300788642218662 y[1] (numeric) = 2.6506251370651673007886422186589 absolute error = 3.1e-30 relative error = 1.1695354264361918835460209170871e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (closed_form) = 2.6581864701049049999590093452957 y[1] (numeric) = 2.6581864701049049999590093452925 absolute error = 3.2e-30 relative error = 1.2038282626100765595124843243824e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (closed_form) = 2.6656819850461191054243159231035 y[1] (numeric) = 2.6656819850461191054243159231003 absolute error = 3.2e-30 relative error = 1.2004432704093307777882144806791e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (closed_form) = 2.6731109323435617374041895193685 y[1] (numeric) = 2.6731109323435617374041895193654 absolute error = 3.1e-30 relative error = 1.1596974755111181897071182628691e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (closed_form) = 2.6804725691086939204140398081587 y[1] (numeric) = 2.6804725691086939204140398081555 absolute error = 3.2e-30 relative error = 1.1938193424840972865778624562833e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (closed_form) = 2.6877661591839738180908881253787 y[1] (numeric) = 2.6877661591839738180908881253754 absolute error = 3.3e-30 relative error = 1.2277853818212760805543578295002e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (closed_form) = 2.6949909732164718739144304480765 y[1] (numeric) = 2.6949909732164718739144304480731 absolute error = 3.4e-30 relative error = 1.2615997729825787928575897039334e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=2170.8MB, alloc=44.3MB, time=25.21 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (closed_form) = 2.7021462887308054963706074378206 y[1] (numeric) = 2.7021462887308054963706074378174 absolute error = 3.2e-30 relative error = 1.1842438040255162228934498967835e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (closed_form) = 2.7092313902013859951499438928516 y[1] (numeric) = 2.7092313902013859951499438928482 absolute error = 3.4e-30 relative error = 1.2549684800999101533934563762145e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (closed_form) = 2.7162455691239705437472433545408 y[1] (numeric) = 2.7162455691239705437472433545375 absolute error = 3.3e-30 relative error = 1.2149122441327346233361425591677e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (closed_form) = 2.7231881240865120133260043354428 y[1] (numeric) = 2.7231881240865120133260043354394 absolute error = 3.4e-30 relative error = 1.2485365847210879604822355994567e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (closed_form) = 2.7300583608392995929232130587317 y[1] (numeric) = 2.7300583608392995929232130587282 absolute error = 3.5e-30 relative error = 1.2820238754617677415537367265230e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (closed_form) = 2.7368555923643831819909425517513 y[1] (numeric) = 2.7368555923643831819909425517478 absolute error = 3.5e-30 relative error = 1.2788398517498442663768306354940e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (closed_form) = 2.7435791389442746128933574013766 y[1] (numeric) = 2.743579138944274612893357401373 absolute error = 3.6e-30 relative error = 1.3121546045087931845803468262682e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=2211.0MB, alloc=44.3MB, time=25.68 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (closed_form) = 2.7502283282299188332941252986201 y[1] (numeric) = 2.7502283282299188332941252986166 absolute error = 3.5e-30 relative error = 1.2726216089311550151590381883432e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4 y[1] (closed_form) = 2.7568024953079282513726390945118 y[1] (numeric) = 2.7568024953079282513726390945084 absolute error = 3.4e-30 relative error = 1.2333128709027188123854176987367e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.01 y[1] (closed_form) = 2.7633009827670735204905561792977 y[1] (numeric) = 2.7633009827670735204905561792944 absolute error = 3.3e-30 relative error = 1.1942238723106792172134012071344e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (closed_form) = 2.7697231407640241142855973335445 y[1] (numeric) = 2.7697231407640241142855973335412 absolute error = 3.3e-30 relative error = 1.1914548250081413489623563754503e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.03 y[1] (closed_form) = 2.7760683270883321181898793012325 y[1] (numeric) = 2.776068327088332118189879301229 absolute error = 3.5e-30 relative error = 1.2607758843136835354902466393811e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (closed_form) = 2.7823359072266527390477822306665 y[1] (numeric) = 2.782335907226652739047782230663 absolute error = 3.5e-30 relative error = 1.2579358196504364061064146653780e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (closed_form) = 2.7885252544261951108359071094194 y[1] (numeric) = 2.7885252544261951108359071094158 absolute error = 3.6e-30 relative error = 1.2910049834713743596527274552548e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=2251.2MB, alloc=44.3MB, time=26.14 TOP MAIN SOLVE Loop x[1] = 4.06 y[1] (closed_form) = 2.7946357497573970514574266927463 y[1] (numeric) = 2.7946357497573970514574266927427 absolute error = 3.6e-30 relative error = 1.2881821898658946152540612956156e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.07 y[1] (closed_form) = 2.8006667821758175031873792802757 y[1] (numeric) = 2.800666782175817503187379280272 absolute error = 3.7e-30 relative error = 1.3211139659840208156097283044046e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (closed_form) = 2.8066177485832404675764376733801 y[1] (numeric) = 2.8066177485832404675764376733764 absolute error = 3.7e-30 relative error = 1.3183127634205734551104246343204e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (closed_form) = 2.8124880538879843244705827123527 y[1] (numeric) = 2.812488053887984324470582712349 absolute error = 3.7e-30 relative error = 1.3155611434100560521631748209904e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (closed_form) = 2.8182771110644105042650370243584 y[1] (numeric) = 2.8182771110644105042650370243548 absolute error = 3.6e-30 relative error = 1.2773761621476418247289709796943e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (closed_form) = 2.823984341211625562574823983696 y[1] (numeric) = 2.8239843412116255625748239836924 absolute error = 3.6e-30 relative error = 1.2747946040152001235044855741453e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (closed_form) = 2.8296091736113707871634030609722 y[1] (numeric) = 2.8296091736113707871634030609687 absolute error = 3.5e-30 relative error = 1.2369199367321189005143141567613e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=2291.4MB, alloc=44.3MB, time=26.61 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (closed_form) = 2.8351510457850935482169298759564 y[1] (numeric) = 2.8351510457850935482169298759527 absolute error = 3.7e-30 relative error = 1.3050451070325311385082437834849e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (closed_form) = 2.8406094035501946848766728281409 y[1] (numeric) = 2.8406094035501946848766728281373 absolute error = 3.6e-30 relative error = 1.2673336909681136260268191678562e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (closed_form) = 2.8459837010754463033378057292122 y[1] (numeric) = 2.8459837010754463033378057292087 absolute error = 3.5e-30 relative error = 1.2298032482327332524270188747165e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (closed_form) = 2.8512734009355744447809479026467 y[1] (numeric) = 2.8512734009355744447809479026432 absolute error = 3.5e-30 relative error = 1.2275217097215447869610489953217e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (closed_form) = 2.8564779741650011649151440014129 y[1] (numeric) = 2.8564779741650011649151440014094 absolute error = 3.5e-30 relative error = 1.2252851349302322768000808937047e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (closed_form) = 2.8615969003107406509691141628009 y[1] (numeric) = 2.8615969003107406509691141627973 absolute error = 3.6e-30 relative error = 1.2580388242694406737727787543880e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (closed_form) = 2.8666296674844440865631553259225 y[1] (numeric) = 2.866629667484444086563155325919 absolute error = 3.5e-30 relative error = 1.2209459909313496735957403252437e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=2331.6MB, alloc=44.3MB, time=27.07 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (closed_form) = 2.8715757724135880600185770979088 y[1] (numeric) = 2.8715757724135880600185770979052 absolute error = 3.6e-30 relative error = 1.2536670752637546164783912391403e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (closed_form) = 2.8764347204918013973064980899522 y[1] (numeric) = 2.8764347204918013973064980899486 absolute error = 3.6e-30 relative error = 1.2515493483490166888556805016227e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (closed_form) = 2.8812060258283253869946467312212 y[1] (numeric) = 2.8812060258283253869946467312177 absolute error = 3.5e-30 relative error = 1.2147690823302981013895470903519e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (closed_form) = 2.8858892112966024512108885972993 y[1] (numeric) = 2.8858892112966024512108885972956 absolute error = 3.7e-30 relative error = 1.2821004997408148420698916002558e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (closed_form) = 2.8904838085819884037968743245822 y[1] (numeric) = 2.8904838085819884037968743245787 absolute error = 3.5e-30 relative error = 1.2108699552678095221933500348844e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (closed_form) = 2.8949893582285835244657528284383 y[1] (numeric) = 2.8949893582285835244657528284348 absolute error = 3.5e-30 relative error = 1.2089854458538033236386556888105e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (closed_form) = 2.8994054096851777658955598188531 y[1] (numeric) = 2.8994054096851777658955598188497 absolute error = 3.4e-30 relative error = 1.1726542237393347564146351721260e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=2371.8MB, alloc=44.3MB, time=27.54 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (closed_form) = 2.9037315213503054992758598196613 y[1] (numeric) = 2.9037315213503054992758598196579 absolute error = 3.4e-30 relative error = 1.1709071499898577524919628407471e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (closed_form) = 2.9079672606164052928706325232994 y[1] (numeric) = 2.907967260616405292870632523296 absolute error = 3.4e-30 relative error = 1.1692016089889877026285118021917e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.29 y[1] (closed_form) = 2.912112203913080307656346885248 y[1] (numeric) = 2.9121122039130803076563468852447 absolute error = 3.3e-30 relative error = 1.1331980943473623208390244872217e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (closed_form) = 2.9161659367494549840317093602846 y[1] (numeric) = 2.9161659367494549840317093602812 absolute error = 3.4e-30 relative error = 1.1659144485412436439577775179690e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (closed_form) = 2.920128053755623783965712426991 y[1] (numeric) = 2.9201280537556237839657124269876 absolute error = 3.4e-30 relative error = 1.1643325009761832762400830353462e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (closed_form) = 2.923998158723187843744309098984 y[1] (numeric) = 2.9239981587231878437443090989805 absolute error = 3.5e-30 relative error = 1.1969911778358755488381235597045e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (closed_form) = 2.927775864644875483684219186773 y[1] (numeric) = 2.9277758646448754836842191867695 absolute error = 3.5e-30 relative error = 1.1954467014586625235524315500292e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=2411.9MB, alloc=44.3MB, time=28.01 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (closed_form) = 2.9314607937532426127959129109888 y[1] (numeric) = 2.9314607937532426127959129109854 absolute error = 3.4e-30 relative error = 1.1598313056907275637914428674745e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (closed_form) = 2.9350525775584491583875557983414 y[1] (numeric) = 2.935052577558449158387555798338 absolute error = 3.4e-30 relative error = 1.1584119569089020164418479224556e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (closed_form) = 2.938550856885107742998434718885 y[1] (numeric) = 2.9385508568851077429984347188816 absolute error = 3.4e-30 relative error = 1.1570328932826545668099340313270e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (closed_form) = 2.9419552819082009238248788504083 y[1] (numeric) = 2.9419552819082009238248788504047 absolute error = 3.6e-30 relative error = 1.2236759756813775812195504594866e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (closed_form) = 2.9452655121880634029446639109382 y[1] (numeric) = 2.9452655121880634029446639109348 absolute error = 3.4e-30 relative error = 1.1543950743762012767459632665982e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (closed_form) = 2.9484812167044257101480289636141 y[1] (numeric) = 2.9484812167044257101480289636106 absolute error = 3.5e-30 relative error = 1.1870518218569550410206523343323e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (closed_form) = 2.9516020738895159540353923333804 y[1] (numeric) = 2.9516020738895159540353923333769 absolute error = 3.5e-30 relative error = 1.1857967003620595833567915752595e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=2452.1MB, alloc=44.3MB, time=28.48 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (closed_form) = 2.9546277716602163312342415645362 y[1] (numeric) = 2.9546277716602163312342415645327 absolute error = 3.5e-30 relative error = 1.1845823807556432009630582356443e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (closed_form) = 2.9575580074492711781110727318389 y[1] (numeric) = 2.9575580074492711781110727318355 absolute error = 3.4e-30 relative error = 1.1495970633327697139579575651816e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (closed_form) = 2.9603924882355434441992145343005 y[1] (numeric) = 2.9603924882355434441992145342971 absolute error = 3.4e-30 relative error = 1.1484963610438262980315576828044e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (closed_form) = 2.9631309305733165617204080330778 y[1] (numeric) = 2.9631309305733165617204080330744 absolute error = 3.4e-30 relative error = 1.1474349529813576405005194903335e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (closed_form) = 2.9657730606206387810376080186917 y[1] (numeric) = 2.9657730606206387810376080186884 absolute error = 3.3e-30 relative error = 1.1126947114791778810616649439483e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (closed_form) = 2.9683186141667071376290809282464 y[1] (numeric) = 2.9683186141667071376290809282433 absolute error = 3.1e-30 relative error = 1.0443622814629216058305322388105e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (closed_form) = 2.9707673366582883122099217992716 y[1] (numeric) = 2.9707673366582883122099217992686 absolute error = 3.0e-30 relative error = 1.0098401052754923859497781856614e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=2492.2MB, alloc=44.3MB, time=28.94 TOP MAIN SOLVE Loop x[1] = 4.48 y[1] (closed_form) = 2.9731189832251737419369954185327 y[1] (numeric) = 2.9731189832251737419369954185297 absolute error = 3.0e-30 relative error = 1.0090413525077514137572148279733e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (closed_form) = 2.9753733187046664372073936936592 y[1] (numeric) = 2.9753733187046664372073936936561 absolute error = 3.1e-30 relative error = 1.0418860653592168357097873752604e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (closed_form) = 2.9775301176650970553891350144986 y[1] (numeric) = 2.9775301176650970553891350144956 absolute error = 3.0e-30 relative error = 1.0075464836448147337278994982054e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.51 y[1] (closed_form) = 2.9795891644283668798963291970477 y[1] (numeric) = 2.9795891644283668798963291970447 absolute error = 3.0e-30 relative error = 1.0068502180821794375263737471788e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.52 y[1] (closed_form) = 2.9815502530915154503296862467421 y[1] (numeric) = 2.9815502530915154503296862467391 absolute error = 3.0e-30 relative error = 1.0061879711366106746969257696792e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (closed_form) = 2.983413187547310686937327855437 y[1] (numeric) = 2.9834131875473106869373278554339 absolute error = 3.1e-30 relative error = 1.0390783324748042430877415529069e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (closed_form) = 2.9851777815038594504006139307825 y[1] (numeric) = 2.9851777815038594504006139307795 absolute error = 3.0e-30 relative error = 1.0049652716122901996682547862613e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=2532.5MB, alloc=44.3MB, time=29.41 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (closed_form) = 2.9868438585032365759053476540251 y[1] (numeric) = 2.9868438585032365759053476540222 absolute error = 2.9e-30 relative error = 9.7092454021123298334854740244577e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (closed_form) = 2.9884112519391305186104760890381 y[1] (numeric) = 2.9884112519391305186104760890351 absolute error = 3.0e-30 relative error = 1.0038778960068998986985297341644e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.57 y[1] (closed_form) = 2.9898798050735038459644441280651 y[1] (numeric) = 2.9898798050735038459644441280621 absolute error = 3.0e-30 relative error = 1.0033848166435731877169452909035e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (closed_form) = 2.9912493710522669108338538360973 y[1] (numeric) = 2.9912493710522669108338538360945 absolute error = 2.8e-30 relative error = 9.3606371541501106136015220386538e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (closed_form) = 2.9925198129199631380901776786878 y[1] (numeric) = 2.9925198129199631380901776786851 absolute error = 2.7e-30 relative error = 9.0224966543010595328018728155459e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (closed_form) = 2.9936910036334644561381046599088 y[1] (numeric) = 2.9936910036334644561381046599061 absolute error = 2.7e-30 relative error = 9.0189668764177413178077600396121e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.61 y[1] (closed_form) = 2.9947628260746755038537793574031 y[1] (numeric) = 2.9947628260746755038537793574006 absolute error = 2.5e-30 relative error = 8.3479064793816216141077303620114e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=2572.7MB, alloc=44.3MB, time=29.89 TOP MAIN SOLVE Loop x[1] = 4.62 y[1] (closed_form) = 2.9957351730622453425228268344515 y[1] (numeric) = 2.9957351730622453425228268344488 absolute error = 2.7e-30 relative error = 9.0128126954561728833689693911385e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (closed_form) = 2.9966079473622855016167293539807 y[1] (numeric) = 2.996607947362285501616729353978 absolute error = 2.7e-30 relative error = 9.0101876769586434116842327422627e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (closed_form) = 2.9973810616980932866119089318828 y[1] (numeric) = 2.99738106169809328661190893188 absolute error = 2.8e-30 relative error = 9.3414882604673833155989772839008e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (closed_form) = 2.998054438758879376528836550896 y[1] (numeric) = 2.9980544387588793765288365508931 absolute error = 2.9e-30 relative error = 9.6729397655651926829711876588616e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.66 y[1] (closed_form) = 2.9986280112074988384386870978325 y[1] (numeric) = 2.9986280112074988384386870978296 absolute error = 2.9e-30 relative error = 9.6710895421543703286530907871443e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.67 y[1] (closed_form) = 2.9991017216871847858425318492734 y[1] (numeric) = 2.9991017216871847858425318492704 absolute error = 3.0e-30 relative error = 1.0002995157871170423917214205723e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (closed_form) = 2.9994755228272840075628419497597 y[1] (numeric) = 2.9994755228272840075628419497566 absolute error = 3.1e-30 relative error = 1.0335140181700707278436953471178e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop memory used=2612.8MB, alloc=44.3MB, time=30.36 x[1] = 4.69 y[1] (closed_form) = 2.9997493772479939935891934069429 y[1] (numeric) = 2.9997493772479939935891934069398 absolute error = 3.1e-30 relative error = 1.0334196661602367356489034651092e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (closed_form) = 2.999923257564100884179536541575 y[1] (numeric) = 2.9999232575641008841795365415718 absolute error = 3.2e-30 relative error = 1.0666939535641184562627347519509e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (closed_form) = 2.9999971463877179684252347125936 y[1] (numeric) = 2.9999971463877179684252347125902 absolute error = 3.4e-30 relative error = 1.1333344113656653073625607407067e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (closed_form) = 2.9999710363300244584322978879616 y[1] (numeric) = 2.9999710363300244584322978879581 absolute error = 3.5e-30 relative error = 1.1666779304248481910498769764664e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (closed_form) = 2.9998449300020043652428419115577 y[1] (numeric) = 2.9998449300020043652428419115543 absolute error = 3.4e-30 relative error = 1.1333919183608361611652771740535e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (closed_form) = 2.9996188400141854026097970480728 y[1] (numeric) = 2.9996188400141854026097970480694 absolute error = 3.4e-30 relative error = 1.1334773454029649872136337663422e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (closed_form) = 2.9992927889753779447342707555971 y[1] (numeric) = 2.9992927889753779447342707555936 absolute error = 3.5e-30 relative error = 1.1669417580254558150301310967144e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (closed_form) = 2.9988668094904141640687400845694 y[1] (numeric) = 2.998866809490414164068740084566 absolute error = 3.4e-30 relative error = 1.1337615892910391866405123819766e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=2653.2MB, alloc=44.3MB, time=30.82 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (closed_form) = 2.9983409441568875752704093382995 y[1] (numeric) = 2.9983409441568875752704093382961 absolute error = 3.4e-30 relative error = 1.1339604345616059122091119900206e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (closed_form) = 2.9977152455608933113476206216477 y[1] (numeric) = 2.9977152455608933113476206216442 absolute error = 3.5e-30 relative error = 1.1675558594776155024004900161201e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (closed_form) = 2.9969897762717695579681528787627 y[1] (numeric) = 2.9969897762717695579681528787592 absolute error = 3.5e-30 relative error = 1.1678384850394688337243851299420e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (closed_form) = 2.9961646088358406717815964665036 y[1] (numeric) = 2.9961646088358406717815964665001 absolute error = 3.5e-30 relative error = 1.1681601169970178965082896528989e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (closed_form) = 2.995239825769162608438756975404 y[1] (numeric) = 2.9952398257691626084387569754005 absolute error = 3.5e-30 relative error = 1.1685207875136400815788091736038e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (closed_form) = 2.9942155195492713857592409012983 y[1] (numeric) = 2.9942155195492713857592409012948 absolute error = 3.5e-30 relative error = 1.1689205326565356697642961634140e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (closed_form) = 2.9930917926059354071940301512694 y[1] (numeric) = 2.9930917926059354071940301512658 absolute error = 3.6e-30 relative error = 1.2027696607545938156279704535000e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=2693.4MB, alloc=44.3MB, time=31.29 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (closed_form) = 2.9918687573109125703429927550405 y[1] (numeric) = 2.991868757310912570342992755037 absolute error = 3.5e-30 relative error = 1.1698374106308710799433522059318e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (closed_form) = 2.9905465359667131848079423162912 y[1] (numeric) = 2.9905465359667131848079423162876 absolute error = 3.6e-30 relative error = 1.2037933390112844732555931273187e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (closed_form) = 2.9891252607943698230800966940429 y[1] (numeric) = 2.9891252607943698230800966940393 absolute error = 3.6e-30 relative error = 1.2043657210415090517994964741608e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (closed_form) = 2.9876050739202153274666554112925 y[1] (numeric) = 2.9876050739202153274666554112891 absolute error = 3.4e-30 relative error = 1.1380352877559739252086304892071e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (closed_form) = 2.9859861273616702952447848423184 y[1] (numeric) = 2.9859861273616702952447848423149 absolute error = 3.5e-30 relative error = 1.1721420832897496669004983131534e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (closed_form) = 2.9842685830120414632826520572489 y[1] (numeric) = 2.9842685830120414632826520572455 absolute error = 3.4e-30 relative error = 1.1393076411937286640901921768603e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (closed_form) = 2.9824526126243325122763772499183 y[1] (numeric) = 2.9824526126243325122763772499149 absolute error = 3.4e-30 relative error = 1.1400013484231883226114752960623e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=2733.6MB, alloc=44.3MB, time=31.76 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (closed_form) = 2.9805383977940689095089901022697 y[1] (numeric) = 2.9805383977940689095089901022662 absolute error = 3.5e-30 relative error = 1.1742844858467150285366291409368e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (closed_form) = 2.9785261299411385076328016063411 y[1] (numeric) = 2.9785261299411385076328016063378 absolute error = 3.3e-30 relative error = 1.1079305186640126752111884073043e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.93 y[1] (closed_form) = 2.9764160102906497154001803227491 y[1] (numeric) = 2.976416010290649715400180322746 absolute error = 3.1e-30 relative error = 1.0415210740978651691334523385058e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (closed_form) = 2.9742082498528091545097085268232 y[1] (numeric) = 2.9742082498528091545097085268201 absolute error = 3.1e-30 relative error = 1.0422941971711013054083347957018e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (closed_form) = 2.9719030694018208147852650633774 y[1] (numeric) = 2.9719030694018208147852650633742 absolute error = 3.2e-30 relative error = 1.0767511339608024685649369880363e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (closed_form) = 2.9695006994538088177549330230967 y[1] (numeric) = 2.9695006994538088177549330230936 absolute error = 3.1e-30 relative error = 1.0439465464918713096882078418866e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (closed_form) = 2.9670013802437659963349767140779 y[1] (numeric) = 2.9670013802437659963349767140747 absolute error = 3.2e-30 relative error = 1.0785300004602933686066009490568e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=2773.7MB, alloc=44.3MB, time=32.22 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (closed_form) = 2.9644053617015305957417100779289 y[1] (numeric) = 2.9644053617015305957417100779256 absolute error = 3.3e-30 relative error = 1.1132080796486761152836746615152e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (closed_form) = 2.9617129034267934979411460144111 y[1] (numeric) = 2.9617129034267934979411460144077 absolute error = 3.4e-30 relative error = 1.1479843289557521817175792924235e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Finished! diff ( y , x , 2 ) = sin ( x ) ; Iterations = 4900 Total Elapsed Time = 32 Seconds Elapsed Time(since restart) = 32 Seconds Time to Timeout = 2 Minutes 27 Seconds Percent Done = 100 % > quit memory used=2789.8MB, alloc=44.3MB, time=32.40