|\^/| 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)/exp(c(x))); > end; exact_soln_y := proc(x) return c(-2.0)/exp(c(x)) end proc #END USER DEF BLOCK #END BLOCK 3 #END USER FUNCTION BLOCK # before write_aux functions # Begin Function number 2 > display_poles := proc() > local rad_given; > global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ; > if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1 > rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," "); > if (rad_given < glob_least_given_sing) then # if number 2 > glob_least_given_sing := rad_given; > fi;# end if 2; > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > elif > (glob_type_given_pole = 5) then # if number 3 > omniout_str(ALWAYS,"SOME POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 3; > if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," "); > if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4 > glob_least_ratio_sing := array_rad_test_poles[1,1]; > fi;# end if 4; > omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," "); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," "); > if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4 > glob_least_3_sing := array_rad_test_poles[1,2]; > fi;# end if 4; > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," "); > if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4 > glob_least_6_sing := array_rad_test_poles[1,3]; > fi;# end if 4; > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 3 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, glob_least_3_sing, glob_least_6_sing, glob_least_given_sing, glob_least_ratio_sing, array_x; if glob_type_given_pole = 1 or glob_type_given_pole = 2 then rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])* (array_x[1] - array_given_rad_poles[1, 1]) + array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " "); if rad_given < glob_least_given_sing then glob_least_given_sing := rad_given end if elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") elif glob_type_given_pole = 5 then omniout_str(ALWAYS, "SOME POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_rad_test_poles[1, 1] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1, 1], 4, " "); if array_rad_test_poles[1, 1] < glob_least_ratio_sing then glob_least_ratio_sing := array_rad_test_poles[1, 1] end if; omniout_float(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[1, 1], 4, " ") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 2] and array_rad_test_poles[1, 2] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1, 2], 4, " "); if array_rad_test_poles[1, 2] < glob_least_3_sing then glob_least_3_sing := array_rad_test_poles[1, 2] end if; omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 3] and array_rad_test_poles[1, 3] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1, 3], 4, " "); if array_rad_test_poles[1, 3] < glob_least_6_sing then glob_least_6_sing := array_rad_test_poles[1, 3] end if; omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[1, 3], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc # End Function number 2 # Begin Function number 3 > my_check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 3 > ret := glob__1; > else > ret := glob__m1; > fi;# end if 3; > ret;; > end; my_check_sign := proc(x0, xf) local ret; if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret end proc # End Function number 3 # Begin Function number 4 > est_size_answer := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local min_size; > min_size := glob_estimated_size_answer; > if (float_abs(array_y[1]) < min_size) then # if number 3 > min_size := float_abs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > if (min_size < glob__1) then # if number 3 > min_size := glob__1; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > min_size; > end; est_size_answer := proc() local min_size; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; min_size := glob_estimated_size_answer; if float_abs(array_y[1]) < min_size then min_size := float_abs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < glob__1 then min_size := glob__1; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc # End Function number 4 # Begin Function number 5 > test_suggested_h := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := glob__small; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 3 > max_estimated_step_error := est_tmp; > fi;# end if 3; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; max_estimated_step_error := glob__small; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := float_abs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc # End Function number 5 # Begin Function number 6 > track_estimated_error := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3 > est_tmp := c(glob_prec) * c(float_abs(array_y[1])); > fi;# end if 3; > if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3 > array_max_est_error[1] := c(est_tmp); > fi;# end if 3 > ; > end; track_estimated_error := proc() local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; est_tmp := c(float_abs(array_y[no_terms - 3])) + c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y[1])) end if; if c(array_max_est_error[1]) <= c(est_tmp) then array_max_est_error[1] := c(est_tmp) end if end proc # End Function number 6 # Begin Function number 7 > reached_interval := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local ret; > if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3 > ret := true; > else > ret := false; > fi;# end if 3; > return(ret); > end; reached_interval := proc() local ret; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if glob_check_sign*glob_next_display - glob_h/glob__10 <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc # End Function number 7 # Begin Function number 8 > display_alot := proc(iter) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_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)*19*ATS_MAX_TERMS/float_abs(numeric_val)); > if (evalf(est_rel_err) > glob_prec) then # if number 6 > glob_est_digits := -int_trunc(log10(est_rel_err)) + 3; > else > glob_est_digits := Digits; > fi;# end if 6; > else > relerr := glob__m1 ; > glob_est_digits := -16; > fi;# end if 5; > array_est_digits[1] := glob_est_digits; > if (glob_iter = 1) then # if number 5 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 5; > array_est_rel_error[1] := est_rel_err; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," "); > omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," "); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 4; > #BOTTOM DISPLAY ALOT > fi;# end if 3; > end; display_alot := proc(iter) local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_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)*19*ATS_MAX_TERMS/float_abs(numeric_val)) ; if glob_prec < evalf(est_rel_err) then glob_est_digits := -int_trunc(log10(est_rel_err)) + 3 else glob_est_digits := Digits end if else relerr := glob__m1; glob_est_digits := -16 end if; array_est_digits[1] := glob_est_digits; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; array_est_rel_error[1] := est_rel_err; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Desired digits ", 32, glob_desired_digits_correct, 4, " "); omniout_int(INFO, "Estimated correct digits ", 32, glob_est_digits, 4, " "); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc # End Function number 8 # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := (clock_sec1) - (glob_orig_start_sec); > glob_clock_sec := (clock_sec1) - (glob_clock_start_sec); > left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1); > expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec)); > opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); > percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr((total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr((glob_clock_sec)); > if (c(percent_done) < glob__100) then # if number 3 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr((expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr((glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr((glob_total_exp_sec)); > fi;# end if 3; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr((left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := clock_sec1 - glob_orig_start_sec; glob_clock_sec := clock_sec1 - glob_clock_start_sec; left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1; expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, clock_sec1 - glob_orig_start_sec); opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec; glob_optimal_expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec) ; glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(total_clock_sec); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(glob_clock_sec); if c(percent_done) < glob__100 then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(expect_sec); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(glob_optimal_expect_sec); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(glob_total_exp_sec) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(left_sec); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc # End Function number 9 # Begin Function number 10 > check_for_pole := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no; > #TOP CHECK FOR POLE > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,1] := glob_larger_float; > array_ord_test_poles[1,1] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 3 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 3; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 4 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 5 > if (rad_c < array_rad_test_poles[1,1]) then # if number 6 > array_rad_test_poles[1,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,1] := rad_c; > array_ord_test_poles[1,1] := tmp_ord; > fi;# end if 6; > fi;# end if 5; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,2] := glob_larger_float; > array_ord_test_poles[1,2] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 5 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 5; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 6 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 7 > found_sing := 0; > fi;# end if 7; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 7 > if (rad_c < array_rad_test_poles[1,2]) then # if number 8 > array_rad_test_poles[1,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 9 > glob_min_pole_est := rad_c; > fi;# end if 9; > array_ord_test_poles[1,2] := tmp_ord; > fi;# end if 8; > fi;# end if 7; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,3] := glob_larger_float; > array_ord_test_poles[1,3] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 7 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 7; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 8 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 9 > found_sing := 0; > fi;# end if 9; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 9 > if (rad_c < array_rad_test_poles[1,3]) then # if number 10 > array_rad_test_poles[1,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 11 > glob_min_pole_est := rad_c; > fi;# end if 11; > array_ord_test_poles[1,3] := tmp_ord; > fi;# end if 10; > fi;# end if 9; > #BOTTOM general radius test1 > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 10; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 9; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 9 > display_poles(); > fi;# end if 9 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad, last_no; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 1] := glob_larger_float; array_ord_test_poles[1, 1] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 1] then array_rad_test_poles[1, 1] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 1] := rad_c; array_ord_test_poles[1, 1] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 2] := glob_larger_float; array_ord_test_poles[1, 2] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do tmp_rad := comp_rad_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 2] then array_rad_test_poles[1, 2] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 2] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 2] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 3] := glob_larger_float; array_ord_test_poles[1, 3] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 3] then array_rad_test_poles[1, 3] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_six_terms( array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 3] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 3] := tmp_ord end if end if; if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc # End Function number 10 # Begin Function number 11 > atomall := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_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 exp 1 $eq_no = 1 > array_tmp1[1] := exp(array_x[1]); > #emit pre div CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_2D0[1] / array_tmp1[1]; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1)); > if (2 <= ATS_MAX_TERMS) then # if number 3 > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(1); > array_y_higher[2,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre exp ID_LINEAR iii = 2 $eq_no = 1 > array_tmp1[2] := array_tmp1[1] * array_x[2] / c(1); > #emit pre div CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := neg(ats(2,array_tmp1,array_tmp2,2)) / array_tmp1[1]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp3[2] := array_tmp2[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y_higher[2,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre exp ID_LINEAR iii = 3 $eq_no = 1 > array_tmp1[3] := array_tmp1[2] * array_x[2] / c(2); > #emit pre div CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := neg(ats(3,array_tmp1,array_tmp2,2)) / array_tmp1[1]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp3[3] := array_tmp2[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y_higher[2,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre exp ID_LINEAR iii = 4 $eq_no = 1 > array_tmp1[4] := array_tmp1[3] * array_x[2] / c(3); > #emit pre div CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := neg(ats(4,array_tmp1,array_tmp2,2)) / array_tmp1[1]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp3[4] := array_tmp2[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y_higher[2,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre exp ID_LINEAR iii = 5 $eq_no = 1 > array_tmp1[5] := array_tmp1[4] * array_x[2] / c(4); > #emit pre div CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := neg(ats(5,array_tmp1,array_tmp2,2)) / array_tmp1[1]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp3[5] := array_tmp2[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y_higher[2,5] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= ATS_MAX_TERMS) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit exp LINEAR $eq_no = 1 > array_tmp1[kkk] := array_tmp1[kkk - 1] * array_x[2] / c(kkk - 1); > #emit div CONST FULL $eq_no = 1 i = 1 > array_tmp2[kkk] := neg(ats(kkk,array_tmp1,array_tmp2,2)) / array_tmp1[1]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp3[kkk] := array_tmp2[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := c(array_tmp3[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_y[kkk + order_d] := c(temporary); > array_y_higher[1,kkk + order_d] := c(temporary); > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := c(temporary) / c(glob_h) * c(adj2); > else > temporary := c(temporary); > fi;# end if 4; > array_y_higher[adj3,term] := c(temporary); > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_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] := exp(array_x[1]); array_tmp2[1] := array_const_2D0[1]/array_tmp1[1]; array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp3[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_y[2] := temporary; array_y_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_y_higher[2, 1] := c(temporary) end if end if; kkk := 2; array_tmp1[2] := array_tmp1[1]*array_x[2]/c(1); array_tmp2[2] := neg(ats(2, array_tmp1, array_tmp2, 2))/array_tmp1[1]; array_tmp3[2] := array_tmp2[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp3[2])*expt(glob_h, c(1))*c(factorial_3(1, 2)); if 3 <= ATS_MAX_TERMS then array_y[3] := temporary; array_y_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y_higher[2, 2] := c(temporary) end if end if; kkk := 3; array_tmp1[3] := array_tmp1[2]*array_x[2]/c(2); array_tmp2[3] := neg(ats(3, array_tmp1, array_tmp2, 2))/array_tmp1[1]; array_tmp3[3] := array_tmp2[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp3[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_y[4] := temporary; array_y_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y_higher[2, 3] := c(temporary) end if end if; kkk := 4; array_tmp1[4] := array_tmp1[3]*array_x[2]/c(3); array_tmp2[4] := neg(ats(4, array_tmp1, array_tmp2, 2))/array_tmp1[1]; array_tmp3[4] := array_tmp2[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp3[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_y[5] := temporary; array_y_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y_higher[2, 4] := c(temporary) end if end if; kkk := 5; array_tmp1[5] := array_tmp1[4]*array_x[2]/c(4); array_tmp2[5] := neg(ats(5, array_tmp1, array_tmp2, 2))/array_tmp1[1]; array_tmp3[5] := array_tmp2[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp3[5])*expt(glob_h, c(1))*c(factorial_3(4, 5)); if 6 <= ATS_MAX_TERMS then array_y[6] := temporary; array_y_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y_higher[2, 5] := c(temporary) end if end if; kkk := 6; while kkk <= ATS_MAX_TERMS do array_tmp1[kkk] := array_tmp1[kkk - 1]*array_x[2]/c(kkk - 1); array_tmp2[kkk] := neg(ats(kkk, array_tmp1, array_tmp2, 2))/array_tmp1[1]; array_tmp3[kkk] := array_tmp2[kkk]; order_d := 1; if kkk + order_d <= ATS_MAX_TERMS then if not array_y_set_initial[1, kkk + order_d] then temporary := c(array_tmp3[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_y[kkk + order_d] := c(temporary); array_y_higher[1, kkk + order_d] := c(temporary); term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1 do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := c(temporary)*c(adj2)/c(glob_h) else temporary := c(temporary) end if; array_y_higher[adj3, term] := c(temporary) end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc # End Function number 12 #END OUTFILE5 # Begin Function number 12 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it; > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 30; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_y_init:= Array(0..(30),[]); > array_norms:= Array(0..(30),[]); > array_fact_1:= Array(0..(30),[]); > array_1st_rel_error:= Array(0..(2),[]); > array_last_rel_error:= Array(0..(2),[]); > array_est_rel_error:= Array(0..(2),[]); > array_max_est_error:= Array(0..(2),[]); > array_type_pole:= Array(0..(2),[]); > array_type_real_pole:= Array(0..(2),[]); > array_type_complex_pole:= Array(0..(2),[]); > array_est_digits:= Array(0..(2),[]); > array_y:= Array(0..(30),[]); > array_x:= Array(0..(30),[]); > array_tmp0:= Array(0..(30),[]); > array_tmp1:= Array(0..(30),[]); > array_tmp2:= Array(0..(30),[]); > array_tmp3:= Array(0..(30),[]); > array_m1:= Array(0..(30),[]); > array_y_higher := Array(0..(2) ,(0..30+ 1),[]); > array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]); > array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]); > array_y_set_initial := Array(0..(2) ,(0..30+ 1),[]); > array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]); > array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_fact_2 := Array(0..(30) ,(0..30+ 1),[]); > # before generate constants > # before generate globals definition > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > # before generate const definition > # before arrays initialized > term := 1; > while (term <= 30) do # do number 1 > array_y_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_norms[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_fact_1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_max_est_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_digits[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_y[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_x[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher_work[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher_work2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_set_initial[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_rad_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_ord_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=30) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_fact_2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > # before symbols initialized > #BEGIN SYMBOLS INITIALIZATED > zero_ats_ar(array_y); > zero_ats_ar(array_x); > zero_ats_ar(array_tmp0); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_tmp3); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_const_2D0); > array_const_2D0[1] := c(2.0); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_h := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 1000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 30; > glob_iolevel := INFO; > # set default block > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := (0.0); > glob_max_minutes := (15.0); > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/div_c_exppostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = 2.0 / exp ( x ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := c(1.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"x_end := c(5.0) ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_type_given_pole := 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)/exp(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(1.0); > x_end := c(5.0) ; > array_y_init[0 + 1] := exact_soln_y(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 := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 10 > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 10; > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > atomall(); > if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > glob_h := glob_check_sign * float_abs(glob_min_h); > glob_h_reason := 1; > found_h := true; > fi;# end if 10; > if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL"); > glob_h_reason := 2; > glob_h := glob_display_interval; > found_h := true; > fi;# end if 10; > if (glob_look_poles) then # if number 10 > check_for_pole(); > fi;# end if 10; > if ( not found_h) then # if number 10 > est_answer := est_size_answer(); > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (estimated_step_error < est_needed_step_err) then # if number 11 > omniout_str(ALWAYS,"Double H and LOOP"); > glob_h := glob_h*glob__2; > else > omniout_str(ALWAYS,"Found H for OPTIMAL"); > found_h := true; > glob_h_reason := 3; > glob_h := glob_h/glob__2; > fi;# end if 11; > fi;# end if 10; > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 10 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 10; > if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MAX H"); > glob_h := glob_check_sign * float_abs(glob_max_h); > glob_h_reason := 1; > found_h := true; > fi;# end if 10; > else > found_h := true; > glob_h := glob_h * glob_check_sign; > fi;# end if 9; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 9 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 9; > #BEGIN SOLUTION CODE > if (found_h) then # if number 9 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := c(x_start); > array_x[2] := c(glob_h); > glob_next_display := c(x_start); > glob_min_pole_est := glob_larger_float; > glob_least_given_sing := glob_larger_float; > glob_least_ratio_sing := glob_larger_float; > glob_least_3_sing := glob_larger_float; > glob_least_6_sing := glob_larger_float; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 10 > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 10; > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_iter < glob_max_iter) and (glob_check_sign * array_x[1] < glob_check_sign * x_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 10 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 10; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > track_estimated_error(); > atomall(); > track_estimated_error(); > display_alot(current_iter); > if (glob_look_poles) then # if number 10 > check_for_pole(); > fi;# end if 10; > if (reached_interval()) then # if number 10 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 10; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := ATS_MAX_TERMS; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 10 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 10; > if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 10; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = 2.0 / exp ( 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,"2016-08-26T16:29:03-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"div_c_exp") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = 2.0 / exp ( 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,"div_c_exp diffeq.mxt") > ; > logitem_str(html_log_file,"div_c_exp maple results") > ; > logitem_str(html_log_file,"OK") > ; > logend(html_log_file) > ; > ; > fi;# end if 15; > if (glob_html_log) then # if number 15 > fclose(html_log_file); > fi;# end if 15 > ; > ;; > fi;# end if 14 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, found_h, repeat_it; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 30; Digits := 32; max_terms := 30; glob_html_log := true; array_y_init := Array(0 .. 30, []); array_norms := Array(0 .. 30, []); array_fact_1 := Array(0 .. 30, []); array_1st_rel_error := Array(0 .. 2, []); array_last_rel_error := Array(0 .. 2, []); array_est_rel_error := Array(0 .. 2, []); array_max_est_error := Array(0 .. 2, []); array_type_pole := Array(0 .. 2, []); array_type_real_pole := Array(0 .. 2, []); array_type_complex_pole := Array(0 .. 2, []); array_est_digits := Array(0 .. 2, []); array_y := Array(0 .. 30, []); array_x := Array(0 .. 30, []); array_tmp0 := Array(0 .. 30, []); array_tmp1 := Array(0 .. 30, []); array_tmp2 := Array(0 .. 30, []); array_tmp3 := Array(0 .. 30, []); array_m1 := Array(0 .. 30, []); array_y_higher := Array(0 .. 2, 0 .. 31, []); array_y_higher_work := Array(0 .. 2, 0 .. 31, []); array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []); array_y_set_initial := Array(0 .. 2, 0 .. 31, []); array_given_rad_poles := Array(0 .. 2, 0 .. 4, []); array_given_ord_poles := Array(0 .. 2, 0 .. 4, []); array_rad_test_poles := Array(0 .. 2, 0 .. 5, []); array_ord_test_poles := Array(0 .. 2, 0 .. 5, []); array_fact_2 := Array(0 .. 30, 0 .. 31, []); term := 1; while term <= 30 do array_y_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 30 do array_fact_1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_real_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do ; term := 1; while term <= 30 do array_y[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_x[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher_work[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_rad_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_ord_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 30 do term := 1; while term <= 30 do array_fact_2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; zero_ats_ar(array_y); zero_ats_ar(array_x); zero_ats_ar(array_tmp0); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2); zero_ats_ar(array_tmp3); zero_ats_ar(array_m1); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_const_2D0); array_const_2D0[1] := c(2.0); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_h := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 1000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 30; glob_iolevel := INFO; glob_orig_start_sec := elapsed_time_seconds(); glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/div_c_exppostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = 2.0 / exp ( x ) ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := c(1.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "x_end := c(5.0) ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_type_given_pole := 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)/exp(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(1.0); x_end := c(5.0); array_y_init[1] := exact_soln_y(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 := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y_higher[r_order, term_no] := array_y_init[it]*expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); glob_h := float_abs(glob_min_h)*glob_check_sign; glob_h_reason := 1; found_h := true end if; if glob_check_sign*glob_display_interval <= glob_check_sign*glob_h then omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL"); glob_h_reason := 2; glob_h := glob_display_interval; found_h := true end if; if glob_look_poles then check_for_pole() end if; if not found_h then est_answer := est_size_answer(); est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if estimated_step_error < est_needed_step_err then omniout_str(ALWAYS, "Double H and LOOP"); glob_h := glob_h*glob__2 else omniout_str(ALWAYS, "Found H for OPTIMAL"); found_h := true; glob_h_reason := 3; glob_h := glob_h/glob__2 end if end if; opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then omniout_str(ALWAYS, "SETTING H FOR MAX H"); glob_h := float_abs(glob_max_h)*glob_check_sign; glob_h_reason := 1; found_h := true end if else found_h := true; glob_h := glob_check_sign*glob_h end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); glob_min_pole_est := glob_larger_float; glob_least_given_sing := glob_larger_float; glob_least_ratio_sing := glob_larger_float; glob_least_3_sing := glob_larger_float; glob_least_6_sing := glob_larger_float; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and glob_clock_sec - glob_orig_start_sec < glob_max_sec do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); track_estimated_error(); atomall(); track_estimated_error(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); term_no := ATS_MAX_TERMS; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = 2.0 / exp ( 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, "2016-08-26T16:29:03-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "div_c_exp"); logitem_str(html_log_file, "diff ( y , x , 1 ) = 2.0 / exp ( 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, "div_c_exp diffeq.mxt"); logitem_str(html_log_file, "div_c_exp 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/div_c_exppostode.ode################# diff ( y , x , 1 ) = 2.0 / exp ( x ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := c(1.0); x_end := c(5.0) ; array_y_init[0 + 1] := exact_soln_y(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)/exp(c(x))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = -0.73575888234288464319104754032291 y[1] (numeric) = -0.73575888234288464319104754032291 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 32 h = 0.001 memory used=4.5MB, alloc=40.3MB, time=0.09 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = -0.72843795914304663951409259127469 y[1] (numeric) = -0.72843795914304663951409259127468 absolute error = 1e-32 relative error = 1.3728005075084582469948881583302e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (closed_form) = -0.72118988034615659656268326930804 y[1] (numeric) = -0.72118988034615659656268326930801 absolute error = 3e-32 relative error = 4.1597921459464468751987996657181e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (closed_form) = -0.71401392113829473953486123130269 y[1] (numeric) = -0.71401392113829473953486123130267 absolute error = 2e-32 relative error = 2.8010658346990791093697628196836e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (closed_form) = -0.70690936391756029630511653061792 y[1] (numeric) = -0.70690936391756029630511653061788 absolute error = 4e-32 relative error = 5.6584340287031190390389720143626e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 memory used=23.8MB, alloc=40.3MB, time=0.33 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (closed_form) = -0.69987549822231070934359774715362 y[1] (numeric) = -0.69987549822231070934359774715362 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] = 1.06 y[1] (closed_form) = -0.69291162066011487940701669618026 y[1] (numeric) = -0.69291162066011487940701669618025 absolute error = 1e-32 relative error = 1.4431854946339791231206876424608e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (closed_form) = -0.68601703483741333626641097879752 y[1] (numeric) = -0.68601703483741333626641097879749 absolute error = 3e-32 relative error = 4.3730692499654950108168061594632e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (closed_form) = -0.67919105128987830243022043049529 y[1] (numeric) = -0.67919105128987830243022043049529 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] = 1.09 y[1] (closed_form) = -0.67243298741346668581101630178611 y[1] (numeric) = -0.67243298741346668581101630178609 absolute error = 2e-32 relative error = 2.9742740725630653163119065891359e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (closed_form) = -0.66574216739615910657769381286262 y[1] (numeric) = -0.66574216739615910657769381286262 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] = 1.11 y[1] (closed_form) = -0.65911792215037813203892896763225 y[1] (numeric) = -0.65911792215037813203892896763224 absolute error = 1e-32 relative error = 1.5171791972178377913293332296919e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (closed_form) = -0.65255958924607896132506964748516 y[1] (numeric) = -0.65255958924607896132506964748513 absolute error = 3e-32 relative error = 4.5972813049395030674529346378482e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (closed_form) = -0.64606651284450586888117122528068 y[1] (numeric) = -0.64606651284450586888117122528066 absolute error = 2e-32 relative error = 3.0956565001247114903930123270235e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 memory used=67.8MB, alloc=52.3MB, time=0.86 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (closed_form) = -0.63963804363260778236032285534765 y[1] (numeric) = -0.63963804363260778236032285534762 absolute error = 3e-32 relative error = 4.6901525477792336341973343617693e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (closed_form) = -0.63327353875810643642039990485905 y[1] (numeric) = -0.63327353875810643642039990485902 absolute error = 3e-32 relative error = 4.7372893645346514408760509420102e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (closed_form) = -0.62697236176521060918551214962199 y[1] (numeric) = -0.62697236176521060918551214962198 absolute error = 1e-32 relative error = 1.5949666380580923363238956180109e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (closed_form) = -0.62073388253097001274222223091491 y[1] (numeric) = -0.6207338825309700127422222309149 absolute error = 1e-32 relative error = 1.6109963192642499637752786362050e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (closed_form) = -0.61455747720226247300654539383636 y[1] (numeric) = -0.61455747720226247300654539383635 absolute error = 1e-32 relative error = 1.6271871014448354239410142814865e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (closed_form) = -0.60844252813340809762720634865897 y[1] (numeric) = -0.60844252813340809762720634865894 absolute error = 3e-32 relative error = 4.9306218110746774164762468054117e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (closed_form) = -0.60238842382440419328995521416645 y[1] (numeric) = -0.60238842382440419328995521416641 absolute error = 4e-32 relative error = 6.6402338454730949790615348592032e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (closed_form) = -0.59639455885977475586320190075193 y[1] (numeric) = -0.59639455885977475586320190075189 absolute error = 4e-32 relative error = 6.7069693050980473620071788547514e-30 % 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) = -0.59046033384802841828302456864059 y[1] (numeric) = -0.59046033384802841828302456864054 absolute error = 5e-32 relative error = 8.4679693340533365847178629701582e-30 % 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) = -0.58458515536171880192188878381439 y[1] (numeric) = -0.58458515536171880192188878381434 absolute error = 5e-32 relative error = 8.5530738407241839344753808786304e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=111.9MB, alloc=52.3MB, time=1.38 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (closed_form) = -0.57876843587810127742626436986212 y[1] (numeric) = -0.57876843587810127742626436986209 absolute error = 3e-32 relative error = 5.1834201971440133970864232411830e-30 % 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) = -0.57300959372038020064977085329567 y[1] (numeric) = -0.57300959372038020064977085329564 absolute error = 3e-32 relative error = 5.2355144361927620641958190445084e-30 % 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) = -0.56730805299954074835648401695181 y[1] (numeric) = -0.56730805299954074835648401695179 absolute error = 2e-32 relative error = 3.5254214873653821649737080556228e-30 % 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) = -0.56166324355675953682950026030951 y[1] (numeric) = -0.56166324355675953682950026030948 absolute error = 3e-32 relative error = 5.3412788435332807865392070843279e-30 % 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) = -0.55607460090638826439862831202818 y[1] (numeric) = -0.55607460090638826439862831202812 absolute error = 6e-32 relative error = 1.0789919176707844387106155221722e-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) = -0.55054156617950467620394727427232 y[1] (numeric) = -0.55054156617950467620394727427226 absolute error = 6e-32 relative error = 1.0898359667258427271547045107534e-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) = -0.5450635860680252062446663351267 y[1] (numeric) = -0.54506358606802520624466633512662 absolute error = 8e-32 relative error = 1.4677186670476976881829959664046e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (closed_form) = -0.53964011276937370793091808153778 y[1] (numeric) = -0.53964011276937370793091808153769 absolute error = 9e-32 relative error = 1.6677781704945894106558462555010e-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) = -0.5342706039317007399654310472076 y[1] (numeric) = -0.53427060393170073996543104720751 absolute error = 9e-32 relative error = 1.6845396197673881558511251234217e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=156.0MB, alloc=52.3MB, time=1.90 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (closed_form) = -0.52895452259964792943801891542745 y[1] (numeric) = -0.52895452259964792943801891542736 absolute error = 9e-32 relative error = 1.7014695244059513356198900037149e-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) = -0.52369133716065198852399931102871 y[1] (numeric) = -0.52369133716065198852399931102861 absolute error = 1.0e-31 relative error = 1.9095217526831678968590932800393e-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) = -0.51848052129178301514346522142309 y[1] (numeric) = -0.51848052129178301514346522142299 absolute error = 1.0e-31 relative error = 1.9287127653484871690694194549651e-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) = -0.51332155390711176136717341008552 y[1] (numeric) = -0.51332155390711176136717341008542 absolute error = 1.0e-31 relative error = 1.9480966508976072853320848856501e-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) = -0.50821391910560060625202965545668 y[1] (numeric) = -0.50821391910560060625202965545658 absolute error = 1.0e-31 relative error = 1.9676753477352364494605386111894e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (closed_form) = -0.50315710611951302216003002973818 y[1] (numeric) = -0.50315710611951302216003002973809 absolute error = 9e-32 relative error = 1.7887057323726366535091255014228e-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) = -0.49815060926333637546429785699966 y[1] (numeric) = -0.49815060926333637546429785699954 absolute error = 1.2e-31 relative error = 2.4089100317965211268207395153139e-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) = -0.49319392788321295387972247966754 y[1] (numeric) = -0.49319392788321295387972247966743 absolute error = 1.1e-31 relative error = 2.2303599817645710229732598923757e-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) = -0.48828656630687416347879194624471 y[1] (numeric) = -0.48828656630687416347879194624461 absolute error = 1.0e-31 relative error = 2.0479777020355881670203686398563e-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) = -0.48342803379407288877059956197097 y[1] (numeric) = -0.48342803379407288877059956197085 absolute error = 1.2e-31 relative error = 2.4822722641508356477345804854116e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=200.0MB, alloc=52.3MB, time=2.42 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (closed_form) = -0.4786178444875090590377256987904 y[1] (numeric) = -0.47861784448750905903772569879026 absolute error = 1.4e-31 relative error = 2.9250894343462723096062742350470e-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) = -0.4738555173642435134467330551028 y[1] (numeric) = -0.47385551736424351344673305510267 absolute error = 1.3e-31 relative error = 2.7434522810477593366876638040391e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (closed_form) = -0.46914057618759530627829783412195 y[1] (numeric) = -0.46914057618759530627829783412183 absolute error = 1.2e-31 relative error = 2.5578687091012904330331664053486e-29 % 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) = -0.4644725494595176419674141413649 y[1] (numeric) = -0.46447254945951764196741414136478 absolute error = 1.2e-31 relative error = 2.5835757170071236624935939335696e-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) = -0.45985097037344767750748876862291 y[1] (numeric) = -0.45985097037344767750748876862279 absolute error = 1.2e-31 relative error = 2.6095410846376445451049031519172e-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) = -0.45527537676762547715927481158951 y[1] (numeric) = -0.45527537676762547715927481158938 absolute error = 1.3e-31 relative error = 2.8554146925971918457269619681562e-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) = -0.45074531107887745132121401376173 y[1] (numeric) = -0.45074531107887745132121401376162 absolute error = 1.1e-31 relative error = 2.4404025354520155347899257197077e-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) = -0.44626032029685965786656094152802 y[1] (numeric) = -0.44626032029685965786656094152791 absolute error = 1.1e-31 relative error = 2.4649289886859356524311305030656e-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) = -0.44181995591875639023929199353893 y[1] (numeric) = -0.44181995591875639023929199353882 absolute error = 1.1e-31 relative error = 2.4897019368728387012463868590964e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=244.1MB, alloc=52.3MB, time=2.94 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (closed_form) = -0.43742377390442952212985753283752 y[1] (numeric) = -0.43742377390442952212985753283741 absolute error = 1.1e-31 relative error = 2.5147238573281875638435300328918e-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) = -0.43307133463201412362786904627373 y[1] (numeric) = -0.43307133463201412362786904627361 absolute error = 1.2e-31 relative error = 2.7709060933798684854477118246528e-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) = -0.42876220285395590837633282336661 y[1] (numeric) = -0.4287622028539559083763328233665 absolute error = 1.1e-31 relative error = 2.5655246490434692465363627214341e-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) = -0.42449594765348611543550999515945 y[1] (numeric) = -0.42449594765348611543550999515933 absolute error = 1.2e-31 relative error = 2.8268821095544447952835838875507e-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) = -0.42027214240152947330831826638783 y[1] (numeric) = -0.4202721424015294733083182663877 absolute error = 1.3e-31 relative error = 3.0932338093396051402245580778698e-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) = -0.41609036471404093688776773145513 y[1] (numeric) = -0.416090364714040936887767731455 absolute error = 1.3e-31 relative error = 3.1243213259538658128537408434014e-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) = -0.41195019640976693096457268007686 y[1] (numeric) = -0.41195019640976693096457268007672 absolute error = 1.4e-31 relative error = 3.3984690678662033215355814449680e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.59 y[1] (closed_form) = -0.40785122346842687638409107270102 y[1] (numeric) = -0.40785122346842687638409107270088 absolute error = 1.4e-31 relative error = 3.4326242498286355386324007394226e-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) = -0.4037930359893108169703585352867 y[1] (numeric) = -0.40379303598931081697035853528656 absolute error = 1.4e-31 relative error = 3.4671226970765803625580004494968e-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) = -0.39977522815028900694540718427019 y[1] (numeric) = -0.39977522815028900694540718427003 absolute error = 1.6e-31 relative error = 4.0022489822668701596159067562513e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=288.1MB, alloc=52.3MB, time=3.45 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (closed_form) = -0.39579739816722935976845242258825 y[1] (numeric) = -0.39579739816722935976845242258809 absolute error = 1.6e-31 relative error = 4.0424722532510937659248743399240e-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) = -0.39185914825381870010601272007459 y[1] (numeric) = -0.39185914825381870010601272007444 absolute error = 1.5e-31 relative error = 3.8279060389025443016524908263419e-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) = -0.38796008458178380102467698857468 y[1] (numeric) = -0.38796008458178380102467698857454 absolute error = 1.4e-31 relative error = 3.6086186585642767320668588127085e-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) = -0.38409981724150822847708958234667 y[1] (numeric) = -0.38409981724150822847708958234654 absolute error = 1.3e-31 relative error = 3.3845368876669016794772496102630e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (closed_form) = -0.38027796020304105473278211658868 y[1] (numeric) = -0.38027796020304105473278211658854 absolute error = 1.4e-31 relative error = 3.6815175911128291139543293308576e-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) = -0.37649413127749354159270234015759 y[1] (numeric) = -0.37649413127749354159270234015745 absolute error = 1.4e-31 relative error = 3.7185174580268169468433113321819e-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) = -0.37274795207881993302359197748017 y[1] (numeric) = -0.37274795207881993302359197748002 absolute error = 1.5e-31 relative error = 4.0241669783414810775174264501924e-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) = -0.3690390479859785352596275318049 y[1] (numeric) = -0.36903904798597853525962753180475 absolute error = 1.5e-31 relative error = 4.0646105288484046631661444046899e-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) = -0.36536704810546930044780167551788 y[1] (numeric) = -0.36536704810546930044780167551771 absolute error = 1.7e-31 relative error = 4.6528552829681197966722332635577e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=332.2MB, alloc=52.3MB, time=3.97 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (closed_form) = -0.36173158523424416756419098130371 y[1] (numeric) = -0.36173158523424416756419098130353 absolute error = 1.8e-31 relative error = 4.9760653298616036502909671163148e-29 % 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) = -0.35813229582298645160429346866125 y[1] (numeric) = -0.35813229582298645160429346866109 absolute error = 1.6e-31 relative error = 4.4676227714208432061169483784155e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.73 y[1] (closed_form) = -0.35456881993975560895575438851885 y[1] (numeric) = -0.35456881993975560895575438851869 absolute error = 1.6e-31 relative error = 4.5125231267426566381208773742464e-29 % 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) = -0.35104080123399374339972138868441 y[1] (numeric) = -0.35104080123399374339972138868425 absolute error = 1.6e-31 relative error = 4.5578747381375928095496790690881e-29 % 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) = -0.34754788690089025336143451733274 y[1] (numeric) = -0.34754788690089025336143451733258 absolute error = 1.6e-31 relative error = 4.6036821408045843494931997638742e-29 % 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) = -0.34408972764610105684507989725189 y[1] (numeric) = -0.34408972764610105684507989725172 absolute error = 1.7e-31 relative error = 4.9405717852422003523982895307823e-29 % 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) = -0.34066597765081886594599981232611 y[1] (numeric) = -0.34066597765081886594599981232593 absolute error = 1.8e-31 relative error = 5.2837680252443409865046285242457e-29 % 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) = -0.33727629453719101793860222566362 y[1] (numeric) = -0.33727629453719101793860222566341 absolute error = 2.1e-31 relative error = 6.2263492395207032071475251611492e-29 % 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) = -0.33392033933408140469425995016587 y[1] (numeric) = -0.33392033933408140469425995016567 absolute error = 2.0e-31 relative error = 5.9894524663831133289584667268155e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop memory used=376.3MB, alloc=52.3MB, time=4.49 x[1] = 1.8 y[1] (closed_form) = -0.33059777644317307659360944086443 y[1] (numeric) = -0.33059777644317307659360944086423 absolute error = 2.0e-31 relative error = 6.0496474644129460837310239530277e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.81 y[1] (closed_form) = -0.32730827360540813116539251467187 y[1] (numeric) = -0.32730827360540813116539251467168 absolute error = 1.9e-31 relative error = 5.8049250606190793334925888796950e-29 % 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) = -0.3240515018677615304127380290285 y[1] (numeric) = -0.32405150186776153041273802902832 absolute error = 1.8e-31 relative error = 5.5546726048951978143573944813097e-29 % 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) = -0.32082713555034552418092756975611 y[1] (numeric) = -0.32082713555034552418092756975592 absolute error = 1.9e-31 relative error = 5.9221923255984814385112320814742e-29 % 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) = -0.31763485221384138998156885278391 y[1] (numeric) = -0.31763485221384138998156885278372 absolute error = 1.9e-31 relative error = 5.9817113479753239763514138481736e-29 % 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) = -0.31447433262725523242001894980624 y[1] (numeric) = -0.31447433262725523242001894980604 absolute error = 2.0e-31 relative error = 6.3598195226018317043472218706368e-29 % 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) = -0.31134526073599461777912982348316 y[1] (numeric) = -0.31134526073599461777912982348297 absolute error = 1.9e-31 relative error = 6.1025499328576773408670470782642e-29 % 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) = -0.30824732363026285139617165354796 y[1] (numeric) = -0.30824732363026285139617165354776 absolute error = 2.0e-31 relative error = 6.4882963992867111150290313243490e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (closed_form) = -0.30518021151376773723433345617434 y[1] (numeric) = -0.30518021151376773723433345617415 absolute error = 1.9e-31 relative error = 6.2258296190815911199365372342538e-29 % 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) = -0.3021436176727416904986820260546 y[1] (numeric) = -0.30214361767274169049868202605439 absolute error = 2.1e-31 relative error = 6.9503371150952312179909511215980e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=420.5MB, alloc=52.3MB, time=5.01 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (closed_form) = -0.29913723844527010528202413820747 y[1] (numeric) = -0.29913723844527010528202413820725 absolute error = 2.2e-31 relative error = 7.3544838865071963576797838004621e-29 % 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) = -0.29616077319092491005187681690838 y[1] (numeric) = -0.29616077319092491005187681690816 absolute error = 2.2e-31 relative error = 7.4283976783844153507287237107371e-29 % 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) = -0.29321392426070027430878891399001 y[1] (numeric) = -0.29321392426070027430878891398978 absolute error = 2.3e-31 relative error = 7.8441022396843623101885886578832e-29 % 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) = -0.29029639696724745996162616737418 y[1] (numeric) = -0.29029639696724745996162616737394 absolute error = 2.4e-31 relative error = 8.2674122898975516807348230807925e-29 % 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) = -0.28740789955540584088015289513921 y[1] (numeric) = -0.28740789955540584088015289513897 absolute error = 2.4e-31 relative error = 8.3505011647647265213582417510513e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (closed_form) = -0.28454814317302714370230801772766 y[1] (numeric) = -0.28454814317302714370230801772741 absolute error = 2.5e-31 relative error = 8.7858594757366166678636024169556e-29 % 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) = -0.28171684184208999229594292219192 y[1] (numeric) = -0.28171684184208999229594292219168 absolute error = 2.4e-31 relative error = 8.5191924781879592057297225664985e-29 % 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) = -0.27891371243010186730539604907824 y[1] (numeric) = -0.278913712430101867305396049078 absolute error = 2.4e-31 relative error = 8.6048117860159359358534009246771e-29 % 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) = -0.27613847462178562095502707959073 y[1] (numeric) = -0.27613847462178562095502707959049 absolute error = 2.4e-31 relative error = 8.6912915821932146502149217037737e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=464.5MB, alloc=52.3MB, time=5.52 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (closed_form) = -0.27339085089104771573759642680838 y[1] (numeric) = -0.27339085089104771573759642680812 absolute error = 2.6e-31 relative error = 9.5101938910024364648657220835680e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = -0.27067056647322538378799898994497 y[1] (numeric) = -0.27067056647322538378799898994474 absolute error = 2.3e-31 relative error = 8.4974145137702477613149915796612e-29 % 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) = -0.26797734933760993163516210074751 y[1] (numeric) = -0.26797734933760993163516210074728 absolute error = 2.3e-31 relative error = 8.5828149494170734247022295054701e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (closed_form) = -0.2653109301602434426396855294633 y[1] (numeric) = -0.26531093016024344263968552946307 absolute error = 2.3e-31 relative error = 8.6690736737112104278080429786192e-29 % 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) = -0.2626710422969861567647978241762 y[1] (numeric) = -0.26267104229698615676479782417597 absolute error = 2.3e-31 relative error = 8.7561993125969706941858521045567e-29 % 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) = -0.2600574217568518343961621541422 y[1] (numeric) = -0.26005742175685183439616215414198 absolute error = 2.2e-31 relative error = 8.4596701187668978391694287176327e-29 % 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) = -0.25746980717560843772469303348974 y[1] (numeric) = -0.25746980717560843772469303348951 absolute error = 2.3e-31 relative error = 8.9330862722527875886813637670309e-29 % 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) = -0.25490793978964148973852270144483 y[1] (numeric) = -0.2549079397896414897385227014446 absolute error = 2.3e-31 relative error = 9.0228652818662160895552397271991e-29 % 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) = -0.25237156341007749713823574894352 y[1] (numeric) = -0.25237156341007749713823574894328 absolute error = 2.4e-31 relative error = 9.5097877414193850544201872652156e-29 % 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) = -0.24986042439716484949609962897764 y[1] (numeric) = -0.24986042439716484949609962897739 absolute error = 2.5e-31 relative error = 1.0005586142870440680299979909837e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=508.7MB, alloc=52.3MB, time=6.04 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (closed_form) = -0.24737427163490963272785765185998 y[1] (numeric) = -0.24737427163490963272785765185973 absolute error = 2.5e-31 relative error = 1.0106143955381325218716800895552e-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) = -0.24491285650596382043729475214525 y[1] (numeric) = -0.24491285650596382043729475214501 absolute error = 2.4e-31 relative error = 9.7994038950811800881396728925745e-29 % 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) = -0.24247593286676333193178390681564 y[1] (numeric) = -0.24247593286676333193178390681541 absolute error = 2.3e-31 relative error = 9.4854774773206601667733867165789e-29 % 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) = -0.24006325702291347069389640532458 y[1] (numeric) = -0.24006325702291347069389640532434 absolute error = 2.4e-31 relative error = 9.9973649852252303250007793393364e-29 % 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) = -0.23767458770481928183241092954488 y[1] (numeric) = -0.23767458770481928183241092954463 absolute error = 2.5e-31 relative error = 1.0518583514300161680965592443436e-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) = -0.23530968604355839152815844137813 y[1] (numeric) = -0.23530968604355839152815844137787 absolute error = 2.6e-31 relative error = 1.1049268917551960093939185782390e-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) = -0.23296831554699391573854142836567 y[1] (numeric) = -0.23296831554699391573854142836541 absolute error = 2.6e-31 relative error = 1.1160315916331262026111983896122e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (closed_form) = -0.23065024207612504943169198345969 y[1] (numeric) = -0.23065024207612504943169198345942 absolute error = 2.7e-31 relative error = 1.1706035838925664093223131687804e-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) = -0.22835523382167297138948422676448 y[1] (numeric) = -0.2283552338216729713894842267642 absolute error = 2.8e-31 relative error = 1.2261597657037168135139395376261e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=552.7MB, alloc=52.3MB, time=6.57 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (closed_form) = -0.2260830612808997231503695594535 y[1] (numeric) = -0.22608306128089972315036955945322 absolute error = 2.8e-31 relative error = 1.2384828762209235257261010382875e-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) = -0.22383349723465774396061136811429 y[1] (numeric) = -0.22383349723465774396061136811401 absolute error = 2.8e-31 relative error = 1.2509298360578248340446264203398e-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) = -0.22160631672466776666828885169988 y[1] (numeric) = -0.2216063167246677666682888516996 absolute error = 2.8e-31 relative error = 1.2635018899207769297060488033644e-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) = -0.21940129703102280233072422159711 y[1] (numeric) = -0.21940129703102280233072422159682 absolute error = 2.9e-31 relative error = 1.3217788769908443849089296341665e-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) = -0.21721821764991596391504727554914 y[1] (numeric) = -0.21721821764991596391504727554886 absolute error = 2.8e-31 relative error = 1.2890263212235151342309001640711e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (closed_form) = -0.21505686027158990185570719310607 y[1] (numeric) = -0.21505686027158990185570719310579 absolute error = 2.8e-31 relative error = 1.3019812511277019472350548032446e-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) = -0.2129170087585056463941117721627 y[1] (numeric) = -0.21291700875850564639411177216242 absolute error = 2.8e-31 relative error = 1.3150663802419895229947292839419e-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) = -0.2107984491237286735664353784814 y[1] (numeric) = -0.21079844912372867356643537848112 absolute error = 2.8e-31 relative error = 1.3282830170901936008770516662316e-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) = -0.20870096950953003342818271727923 y[1] (numeric) = -0.20870096950953003342818271727895 absolute error = 2.8e-31 relative error = 1.3416324833470129020429259399415e-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) = -0.20662436016620040061049843066899 y[1] (numeric) = -0.20662436016620040061049843066871 absolute error = 2.8e-31 relative error = 1.3551161139701977007184017078550e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=596.9MB, alloc=52.3MB, time=7.09 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (closed_form) = -0.20456841343107492859562313519417 y[1] (numeric) = -0.20456841343107492859562313519389 absolute error = 2.8e-31 relative error = 1.3687352573340467116905969084545e-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) = -0.20253292370776681017944409869335 y[1] (numeric) = -0.20253292370776681017944409869306 absolute error = 2.9e-31 relative error = 1.4318659637701115596791770528258e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (closed_form) = -0.20051768744560746745988138759597 y[1] (numeric) = -0.20051768744560746745988138759568 absolute error = 2.9e-31 relative error = 1.4462564559481345072938541977518e-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) = -0.19852250311929131535297509114374 y[1] (numeric) = -0.19852250311929131535297509114345 absolute error = 2.9e-31 relative error = 1.4607915749769699990355910170042e-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) = -0.19654717120872306309606247764772 y[1] (numeric) = -0.19654717120872306309606247764744 absolute error = 2.8e-31 relative error = 1.4245944028502668836051896046145e-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) = -0.19459149417906553845140142910307 y[1] (numeric) = -0.19459149417906553845140142910281 absolute error = 2.6e-31 relative error = 1.3361323992956482079209580356936e-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) = -0.19265527646098603937603364791825 y[1] (numeric) = -0.19265527646098603937603364791799 absolute error = 2.6e-31 relative error = 1.3495607531551398234516820977154e-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) = -0.1907383244310992377765931935996 y[1] (numeric) = -0.19073832443109923777659319359933 absolute error = 2.7e-31 relative error = 1.4155519128382225343567755177797e-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) = -0.18884044639260467962313819571542 y[1] (numeric) = -0.18884044639260467962313819571514 absolute error = 2.8e-31 relative error = 1.4827332033407292722440592169944e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=641.0MB, alloc=52.3MB, time=7.62 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (closed_form) = -0.18696145255611694515588165595398 y[1] (numeric) = -0.18696145255611694515588165595371 absolute error = 2.7e-31 relative error = 1.4441479583549920710207064971543e-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) = -0.18510115502068655218486709261196 y[1] (numeric) = -0.18510115502068655218486709261168 absolute error = 2.8e-31 relative error = 1.5126864009503762082273406461002e-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) = -0.18325936775500970455710302844059 y[1] (numeric) = -0.18325936775500970455710302844032 absolute error = 2.7e-31 relative error = 1.4733216823106664551616055323560e-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) = -0.18143590657882500675034444015938 y[1] (numeric) = -0.18143590657882500675034444015911 absolute error = 2.7e-31 relative error = 1.4881288113866162230521218689052e-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) = -0.17963058914449528424947775826781 y[1] (numeric) = -0.17963058914449528424947775826754 absolute error = 2.7e-31 relative error = 1.5030847545838161290856479436467e-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) = -0.17784323491877266787219852147351 y[1] (numeric) = -0.17784323491877266787219852147324 absolute error = 2.7e-31 relative error = 1.5181910075090492207948145427467e-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) = -0.17607366516474511853721843978805 y[1] (numeric) = -0.17607366516474511853721843978777 absolute error = 2.8e-31 relative error = 1.5902434912002038893163399614863e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (closed_form) = -0.1743217029239625871124340741545 y[1] (numeric) = -0.17432170292396258711243407415423 absolute error = 2.7e-31 relative error = 1.5488605002773025075645754157787e-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) = -0.17258717299874102194414703303231 y[1] (numeric) = -0.17258717299874102194414703303203 absolute error = 2.8e-31 relative error = 1.6223685406912744691126988670312e-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) = -0.17086990193464245445334189841079 y[1] (numeric) = -0.17086990193464245445334189841052 absolute error = 2.7e-31 relative error = 1.5801495578974154073127050217092e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=685.1MB, alloc=52.3MB, time=8.14 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (closed_form) = -0.16916971800312941079298153170792 y[1] (numeric) = -0.16916971800312941079298153170766 absolute error = 2.6e-31 relative error = 1.5369180907140269154967259290836e-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) = -0.16748645118439191499303078395017 y[1] (numeric) = -0.16748645118439191499303078394991 absolute error = 2.6e-31 relative error = 1.5523643743203834455367761996215e-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) = -0.1658199331503453662792122341894 y[1] (numeric) = -0.16581993315034536627921223418913 absolute error = 2.7e-31 relative error = 1.6282722762600368932931489122066e-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) = -0.16416999724779759033905734893432 y[1] (numeric) = -0.16416999724779759033905734893403 absolute error = 2.9e-31 relative error = 1.7664616243020036485201755129194e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (closed_form) = -0.16253647848178338122635216367639 y[1] (numeric) = -0.16253647848178338122635216367609 absolute error = 3.0e-31 relative error = 1.8457395090765617454441627741077e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (closed_form) = -0.16091921349906486734428000303859 y[1] (numeric) = -0.16091921349906486734428000303828 absolute error = 3.1e-31 relative error = 1.9264324828545192331788087821054e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (closed_form) = -0.15931804057179605153010981297284 y[1] (numeric) = -0.15931804057179605153010981297251 absolute error = 3.3e-31 relative error = 2.0713285125502581823252838280124e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (closed_form) = -0.15773279958134989168182564520009 y[1] (numeric) = -0.15773279958134989168182564519977 absolute error = 3.2e-31 relative error = 2.0287473553334201894631054489830e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (closed_form) = -0.15616333200230630462128247910557 y[1] (numeric) = -0.15616333200230630462128247910526 absolute error = 3.1e-31 relative error = 1.9851010863127699669658943316767e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=729.2MB, alloc=52.3MB, time=8.66 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (closed_form) = -0.15460948088659949198093132207952 y[1] (numeric) = -0.15460948088659949198093132207921 absolute error = 3.1e-31 relative error = 2.0050516839091768218262744328810e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (closed_form) = -0.15307109084782300283349165501697 y[1] (numeric) = -0.15307109084782300283349165501665 absolute error = 3.2e-31 relative error = 2.0905319105495293597155520782475e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (closed_form) = -0.15154800804569096355775503214886 y[1] (numeric) = -0.15154800804569096355775503214854 absolute error = 3.2e-31 relative error = 2.1115421055453372016929623260559e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (closed_form) = -0.15004008017065392105055739728929 y[1] (numeric) = -0.15004008017065392105055739728898 absolute error = 3.1e-31 relative error = 2.0661145984953449933309239773734e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (closed_form) = -0.14854715642866776085642114033995 y[1] (numeric) = -0.14854715642866776085642114033963 absolute error = 3.2e-31 relative error = 2.1541980856002704636401320532135e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (closed_form) = -0.14706908752611417709398724772342 y[1] (numeric) = -0.1470690875261141770939872477231 absolute error = 3.2e-31 relative error = 2.1758481362929481454709090411882e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (closed_form) = -0.14560572565487118621366387301155 y[1] (numeric) = -0.14560572565487118621366387301124 absolute error = 3.1e-31 relative error = 2.1290371556870783230689456010562e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (closed_form) = -0.14415692447753219162542581259969 y[1] (numeric) = -0.14415692447753219162542581259937 absolute error = 3.2e-31 relative error = 2.2198031843407849102318934106801e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (closed_form) = -0.14272253911277212109091017917259 y[1] (numeric) = -0.14272253911277212109091017917228 absolute error = 3.1e-31 relative error = 2.1720465591987100398413474586178e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop memory used=773.3MB, alloc=52.3MB, time=9.18 x[1] = 2.65 y[1] (closed_form) = -0.14130242612085917348135255637331 y[1] (numeric) = -0.14130242612085917348135255637299 absolute error = 3.2e-31 relative error = 2.2646461832601284146634623692636e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (closed_form) = -0.13989644348931072606396584367654 y[1] (numeric) = -0.13989644348931072606396584367622 absolute error = 3.2e-31 relative error = 2.2874062557884161799375592817761e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (closed_form) = -0.13850445061869196789553697891176 y[1] (numeric) = -0.13850445061869196789553697891144 absolute error = 3.2e-31 relative error = 2.3103950708484610205709424528951e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (closed_form) = -0.13712630830855583917474638648806 y[1] (numeric) = -0.13712630830855583917474638648774 absolute error = 3.2e-31 relative error = 2.3336149273409263507889795646483e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (closed_form) = -0.13576187874352287053542862700309 y[1] (numeric) = -0.13576187874352287053542862700279 absolute error = 3.0e-31 relative error = 2.2097513880663856519076219455086e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (closed_form) = -0.13441102547949953025310340171193 y[1] (numeric) = -0.13441102547949953025310340171163 absolute error = 3.0e-31 relative error = 2.2319597587309251167803489529203e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (closed_form) = -0.13307361343003370118801281601234 y[1] (numeric) = -0.13307361343003370118801281601204 absolute error = 3.0e-31 relative error = 2.2543913272313103396731481974885e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (closed_form) = -0.13174950885280592300098873189073 y[1] (numeric) = -0.13174950885280592300098873189043 absolute error = 3.0e-31 relative error = 2.2770483367430843951686537471095e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (closed_form) = -0.13043857933625504875511446038598 y[1] (numeric) = -0.13043857933625504875511446038568 absolute error = 3.0e-31 relative error = 2.2999330529860793648684767840416e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (closed_form) = -0.12914069378633697845769563692426 y[1] (numeric) = -0.12914069378633697845769563692395 absolute error = 3.1e-31 relative error = 2.4004826899326898823311034951793e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=817.4MB, alloc=52.3MB, time=9.70 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (closed_form) = -0.1278557224134151454048600511159 y[1] (numeric) = -0.12785572241341514540486005111558 absolute error = 3.2e-31 relative error = 2.5028211014701074576340316873851e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (closed_form) = -0.12658353671928144436649625986908 y[1] (numeric) = -0.12658353671928144436649625986874 absolute error = 3.4e-31 relative error = 2.6859733012042675469260736316065e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (closed_form) = -0.12532400948430630369353354844936 y[1] (numeric) = -0.12532400948430630369353354844903 absolute error = 3.3e-31 relative error = 2.6331746116160147483679053831070e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (closed_form) = -0.12407701475471661634406565854311 y[1] (numeric) = -0.12407701475471661634406565854278 absolute error = 3.3e-31 relative error = 2.6596384564245450286925317175126e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (closed_form) = -0.12284242783000025761081913621326 y[1] (numeric) = -0.12284242783000025761081913621294 absolute error = 3.2e-31 relative error = 2.6049631682861483944451962899630e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (closed_form) = -0.12162012525043592999124277636788 y[1] (numeric) = -0.12162012525043592999124277636756 absolute error = 3.2e-31 relative error = 2.6311434833755279794396825617480e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (closed_form) = -0.12040998478474708817431334210487 y[1] (numeric) = -0.12040998478474708817431334210456 absolute error = 3.1e-31 relative error = 2.5745373239119384955986481306985e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (closed_form) = -0.11921188541787870952626780936569 y[1] (numeric) = -0.11921188541787870952626780936537 absolute error = 3.2e-31 relative error = 2.6842961075423797433771520167190e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (closed_form) = -0.11802570733889568774212465157395 y[1] (numeric) = -0.11802570733889568774212465157363 absolute error = 3.2e-31 relative error = 2.7112737319265626086153473122359e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=861.5MB, alloc=52.3MB, time=10.29 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (closed_form) = -0.11685133192900163949227461081453 y[1] (numeric) = -0.1168513319290016394922746108142 absolute error = 3.3e-31 relative error = 2.8241013136290698267382826631828e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (closed_form) = -0.1156886417496769259348212535548 y[1] (numeric) = -0.11568864174967692593482125355448 absolute error = 3.2e-31 relative error = 2.7660450944908222801668849205514e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (closed_form) = -0.11453752053093470288593752994038 y[1] (numeric) = -0.11453752053093470288593752994005 absolute error = 3.3e-31 relative error = 2.8811519445356984188124362612449e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (closed_form) = -0.11339785315969382524346871484118 y[1] (numeric) = -0.11339785315969382524346871484085 absolute error = 3.3e-31 relative error = 2.9101080029731578880385397508125e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (closed_form) = -0.11226952566826744294453481233074 y[1] (numeric) = -0.11226952566826744294453481233041 absolute error = 3.3e-31 relative error = 2.9393550746360127591788553354033e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (closed_form) = -0.11115242522296613730713531516097 y[1] (numeric) = -0.11115242522296613730713531516064 absolute error = 3.3e-31 relative error = 2.9688960842558019586815535776000e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (closed_form) = -0.11004644011281445805989306166835 y[1] (numeric) = -0.11004644011281445805989306166803 absolute error = 3.2e-31 relative error = 2.9078632591108897508282010518605e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (closed_form) = -0.10895145973837973270423724734572 y[1] (numeric) = -0.1089514597383797327042372473454 absolute error = 3.2e-31 relative error = 2.9370877707228676664602070110965e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (closed_form) = -0.10786737460071203108065245281805 y[1] (numeric) = -0.10786737460071203108065245281773 absolute error = 3.2e-31 relative error = 2.9666059935594991697196251805445e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (closed_form) = -0.10679407629039417912623358620798 y[1] (numeric) = -0.10679407629039417912623358620767 absolute error = 3.1e-31 relative error = 2.9027827269843019458830639344394e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=905.8MB, alloc=52.3MB, time=10.82 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (closed_form) = -0.10573145747670072681579747643322 y[1] (numeric) = -0.1057314574767007268157974764329 absolute error = 3.2e-31 relative error = 3.0265354099608063694604721313068e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (closed_form) = -0.10467941189686478617431100509864 y[1] (numeric) = -0.10467941189686478617431100509832 absolute error = 3.2e-31 relative error = 3.0569525965170635434671960477701e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (closed_form) = -0.10363783434545166603549268832574 y[1] (numeric) = -0.10363783434545166603549268832543 absolute error = 3.1e-31 relative error = 2.9911856221029276183360992642769e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (closed_form) = -0.10260662066383824090120823479189 y[1] (numeric) = -0.10260662066383824090120823479156 absolute error = 3.3e-31 relative error = 3.2161667333451343908529559677371e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (closed_form) = -0.10158566772979700182977879769406 y[1] (numeric) = -0.10158566772979700182977879769372 absolute error = 3.4e-31 relative error = 3.3469288296096079657896770572952e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (closed_form) = -0.10057487344718374774961076493595 y[1] (numeric) = -0.10057487344718374774961076493562 absolute error = 3.3e-31 relative error = 3.2811376111081799345890220510380e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3 y[1] (closed_form) = -0.099574136735727885958684831300122 y[1] (numeric) = -0.099574136735727885958684831299798 absolute error = 3.24e-31 relative error = 3.2538569815564021740304218040423e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (closed_form) = -0.098583357520924320831446190234969 y[1] (numeric) = -0.098583357520924320831446190234643 absolute error = 3.26e-31 relative error = 3.3068461878142716880577881929101e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (closed_form) = -0.097602436724025919913543080119995 y[1] (numeric) = -0.097602436724025919913543080119666 absolute error = 3.29e-31 relative error = 3.3708174820497387144956601129644e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=949.9MB, alloc=52.3MB, time=11.33 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (closed_form) = -0.096631276252135556642683519477524 y[1] (numeric) = -0.096631276252135556642683519477196 absolute error = 3.28e-31 relative error = 3.3943461446598784991541949332050e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (closed_form) = -0.095669778988396738891625658216285 y[1] (numeric) = -0.095669778988396738891625658215954 absolute error = 3.31e-31 relative error = 3.4598177554078510916533728963618e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (closed_form) = -0.094717848782281842387981540479467 y[1] (numeric) = -0.09471784878228184238798154047914 absolute error = 3.27e-31 relative error = 3.4523588130853900641321144326832e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (closed_form) = -0.093775390439976977826083093679625 y[1] (numeric) = -0.093775390439976977826083093679295 absolute error = 3.30e-31 relative error = 3.5190469317344387066514051808769e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (closed_form) = -0.092842309714862530149608892870319 y[1] (numeric) = -0.092842309714862530149608892869992 absolute error = 3.27e-31 relative error = 3.5221010873628951348578815668306e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (closed_form) = -0.091918513298088418050967052756972 y[1] (numeric) = -0.091918513298088418050967052756643 absolute error = 3.29e-31 relative error = 3.5792571941744193054015608687875e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (closed_form) = -0.091003908809243131205530209038912 y[1] (numeric) = -0.091003908809243131205530209038582 absolute error = 3.30e-31 relative error = 3.6262178660009644825796243506120e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (closed_form) = -0.090098404787115612136670184356672 y[1] (numeric) = -0.090098404787115612136670184356341 absolute error = 3.31e-31 relative error = 3.6737609370785903284990297600980e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (closed_form) = -0.089201910680549058892080384870443 y[1] (numeric) = -0.089201910680549058892080384870115 absolute error = 3.28e-31 relative error = 3.6770512817224004589801095913198e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (closed_form) = -0.088314336839385733904031703200168 y[1] (numeric) = -0.088314336839385733904031703199839 absolute error = 3.29e-31 relative error = 3.7253294513023525929501529094831e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=994.0MB, alloc=52.3MB, time=11.85 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (closed_form) = -0.087435594505501873506901935547708 y[1] (numeric) = -0.087435594505501873506901935547376 absolute error = 3.32e-31 relative error = 3.7970806040451745635586964032973e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (closed_form) = -0.086565595803931801595459532304399 y[1] (numeric) = -0.086565595803931801595459532304069 absolute error = 3.30e-31 relative error = 3.8121380316891601594555489557025e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (closed_form) = -0.085704253734080359827870913912309 y[1] (numeric) = -0.085704253734080359827870913911979 absolute error = 3.30e-31 relative error = 3.8504506558555477643577144480947e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.16 y[1] (closed_form) = -0.08485148216102277560912865346997 y[1] (numeric) = -0.084851482161022775609128653469636 absolute error = 3.34e-31 relative error = 3.9362895201543767481116840427606e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (closed_form) = -0.084007195806891097834448734719998 y[1] (numeric) = -0.084007195806891097834448734719668 absolute error = 3.30e-31 relative error = 3.9282349188107306024108172063683e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (closed_form) = -0.083171310242346339029033231003973 y[1] (numeric) = -0.08317131024234633902903323100364 absolute error = 3.33e-31 relative error = 4.0037844664187385325794132174604e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (closed_form) = -0.082343741878135471091305809546969 y[1] (numeric) = -0.082343741878135471091305809546637 absolute error = 3.32e-31 relative error = 4.0318789555536962303149783171646e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (closed_form) = -0.081524407956732430332158524288851 y[1] (numeric) = -0.081524407956732430332158524288517 absolute error = 3.34e-31 relative error = 4.0969325429172612234745640425700e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (closed_form) = -0.080713226544062295903747969588037 y[1] (numeric) = -0.080713226544062295903747969587702 absolute error = 3.35e-31 relative error = 4.1504969426184390679357252640163e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1038.1MB, alloc=52.3MB, time=12.38 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (closed_form) = -0.079910116521307814028787133448768 y[1] (numeric) = -0.079910116521307814028787133448434 absolute error = 3.34e-31 relative error = 4.1796960702834141586759996185392e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.23 y[1] (closed_form) = -0.079114997576797448675927960221868 y[1] (numeric) = -0.079114997576797448675927960221531 absolute error = 3.37e-31 relative error = 4.2596221996072474469435336716519e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.24 y[1] (closed_form) = -0.078327790197974147479542180731511 y[1] (numeric) = -0.078327790197974147479542180731176 absolute error = 3.35e-31 relative error = 4.2768983926813802208932426919292e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (closed_form) = -0.077548415663444019773799670535193 y[1] (numeric) = -0.077548415663444019773799670534857 absolute error = 3.36e-31 relative error = 4.3327771060884344309654580884553e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (closed_form) = -0.076776796035104131602221620427345 y[1] (numeric) = -0.076776796035104131602221620427011 absolute error = 3.34e-31 relative error = 4.3502727028005630051993403451002e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (closed_form) = -0.076012854150348630475649281811054 y[1] (numeric) = -0.076012854150348630475649281810718 absolute error = 3.36e-31 relative error = 4.4203050096686699266898177427370e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.28 y[1] (closed_form) = -0.075256513614352420484609166127661 y[1] (numeric) = -0.075256513614352420484609166127326 absolute error = 3.35e-31 relative error = 4.4514419272288881808842125298084e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (closed_form) = -0.07450769879243161612715564269026 y[1] (numeric) = -0.074507698792431616127155642689925 absolute error = 3.35e-31 relative error = 4.4961796623630095746030340322043e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (closed_form) = -0.073766334802480010891207409483032 y[1] (numeric) = -0.073766334802480010891207409482695 absolute error = 3.37e-31 relative error = 4.5684796581308540314188957005739e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (closed_form) = -0.073032347507480804231933106715629 y[1] (numeric) = -0.073032347507480804231933106715294 absolute error = 3.35e-31 relative error = 4.5870085165437888639349299612541e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1082.3MB, alloc=52.3MB, time=12.90 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (closed_form) = -0.072305663508092838110643563374324 y[1] (numeric) = -0.072305663508092838110643563373989 absolute error = 3.35e-31 relative error = 4.6331087185515558015970769167829e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.33 y[1] (closed_form) = -0.071586210135310601712666409183133 y[1] (numeric) = -0.071586210135310601712666409182798 absolute error = 3.35e-31 relative error = 4.6796722352921146967351022179300e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (closed_form) = -0.070873915443197270338558156312127 y[1] (numeric) = -0.070873915443197270338558156311793 absolute error = 3.34e-31 relative error = 4.7125941598032383587357045544722e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (closed_form) = -0.070168708201690051766487050931066 y[1] (numeric) = -0.07016870820169005176648705093073 absolute error = 3.36e-31 relative error = 4.7884592521529027661670380279408e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (closed_form) = -0.069470517889477120614427368210285 y[1] (numeric) = -0.069470517889477120614427368209948 absolute error = 3.37e-31 relative error = 4.8509786631523912012514157617768e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (closed_form) = -0.068779274686945428389665462380541 y[1] (numeric) = -0.068779274686945428389665462380205 absolute error = 3.36e-31 relative error = 4.8851925457099083936435066550098e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (closed_form) = -0.068094909469198684000745677908606 y[1] (numeric) = -0.068094909469198684000745677908267 absolute error = 3.39e-31 relative error = 4.9783457037025594280769645569515e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (closed_form) = -0.067417353799144806524088947411793 y[1] (numeric) = -0.067417353799144806524088947411455 absolute error = 3.38e-31 relative error = 5.0135459336923359304807669912467e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (closed_form) = -0.066746539920652158964800262941896 y[1] (numeric) = -0.066746539920652158964800262941558 absolute error = 3.38e-31 relative error = 5.0639329080100952558395052627004e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1126.4MB, alloc=52.3MB, time=13.42 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (closed_form) = -0.066082400751773878629337943842434 y[1] (numeric) = -0.066082400751773878629337943842097 absolute error = 3.37e-31 relative error = 5.0996936577089137065653582024741e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.42 y[1] (closed_form) = -0.065424869878039626537435557928615 y[1] (numeric) = -0.065424869878039626537435557928277 absolute error = 3.38e-31 relative error = 5.1662311385574855410855297496435e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (closed_form) = -0.064773881545814085042627460724618 y[1] (numeric) = -0.064773881545814085042627460724281 absolute error = 3.37e-31 relative error = 5.2027143033205815287628949017919e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (closed_form) = -0.064129370655721539505605401547277 y[1] (numeric) = -0.064129370655721539505605401546942 absolute error = 3.35e-31 relative error = 5.2238154931918349222987322730940e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.45 y[1] (closed_form) = -0.06349127275613588647309399855947 y[1] (numeric) = -0.063491272756135886473093998559134 absolute error = 3.36e-31 relative error = 5.2920659078696525953825785894459e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.46 y[1] (closed_form) = -0.062859524036735417357637959073097 y[1] (numeric) = -0.062859524036735417357637959072761 absolute error = 3.36e-31 relative error = 5.3452520544641721260486619322790e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.47 y[1] (closed_form) = -0.062234061322121733091297992320118 y[1] (numeric) = -0.062234061322121733091297992319781 absolute error = 3.37e-31 relative error = 5.4150411019409062102211720850897e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (closed_form) = -0.061614822065502151639403195435717 y[1] (numeric) = -0.061614822065502151639403195435379 absolute error = 3.38e-31 relative error = 5.4856930308209817314403139486888e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (closed_form) = -0.061001744342434976609846609938077 y[1] (numeric) = -0.061001744342434976609846609937737 absolute error = 3.40e-31 relative error = 5.5736111100594207584363662361522e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.5 y[1] (closed_form) = -0.060394766844637001479572584727239 y[1] (numeric) = -0.0603947668446370014795725847269 absolute error = 3.39e-31 relative error = 5.6130691069983471807357257648909e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1170.5MB, alloc=52.3MB, time=13.94 TOP MAIN SOLVE Loop x[1] = 3.51 y[1] (closed_form) = -0.059793828873852630183518163993323 y[1] (numeric) = -0.059793828873852630183518163992983 absolute error = 3.40e-31 relative error = 5.6862055232706350181478160237895e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.52 y[1] (closed_form) = -0.059198870335784000972958310966756 y[1] (numeric) = -0.059198870335784000972958310966415 absolute error = 3.41e-31 relative error = 5.7602450530863489368965169599966e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (closed_form) = -0.058609831734081506550582555054073 y[1] (numeric) = -0.058609831734081506550582555053732 absolute error = 3.41e-31 relative error = 5.8181364783156192462177451514844e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (closed_form) = -0.05802665416439410952930865344351 y[1] (numeric) = -0.058026654164394109529308653443168 absolute error = 3.42e-31 relative error = 5.8938431816366130373373181205633e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (closed_form) = -0.057449279308478858241421061568647 y[1] (numeric) = -0.057449279308478858241421061568306 absolute error = 3.41e-31 relative error = 5.9356706316361446530207545494507e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.56 y[1] (closed_form) = -0.056877649428369013844706373088932 y[1] (numeric) = -0.056877649428369013844706373088591 absolute error = 3.41e-31 relative error = 5.9953251132406772572946627935802e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (closed_form) = -0.056311707360600205533436432653193 y[1] (numeric) = -0.056311707360600205533436432652852 absolute error = 3.41e-31 relative error = 6.0555791323526548440388070802763e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (closed_form) = -0.055751396510494036464908666394755 y[1] (numeric) = -0.055751396510494036464908666394414 absolute error = 3.41e-31 relative error = 6.1164387144242004609777506700317e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (closed_form) = -0.055196660846498568757372606584414 y[1] (numeric) = -0.055196660846498568757372606584073 absolute error = 3.41e-31 relative error = 6.1779099454642377501208386643529e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1214.6MB, alloc=52.3MB, time=14.45 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (closed_form) = -0.054647444894585121603126124871106 y[1] (numeric) = -0.054647444894585121603126124870766 absolute error = 3.40e-31 relative error = 6.2216998554252579179411102028612e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (closed_form) = -0.054103693732700822171923333263377 y[1] (numeric) = -0.054103693732700822171923333263037 absolute error = 3.40e-31 relative error = 6.2842289785198260074760062690714e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.62 y[1] (closed_form) = -0.053565352985276354555161603984964 y[1] (numeric) = -0.053565352985276354555161603984623 absolute error = 3.41e-31 relative error = 6.3660553136601478444576198756851e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (closed_form) = -0.053032368817788357521165235770362 y[1] (numeric) = -0.053032368817788357521165235770022 absolute error = 3.40e-31 relative error = 6.4111788249208973469460232252782e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (closed_form) = -0.052504687931375927316809944658597 y[1] (numeric) = -0.052504687931375927316809944658258 absolute error = 3.39e-31 relative error = 6.4565663249551330876884432613075e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (closed_form) = -0.051982257557510687161282079114776 y[1] (numeric) = -0.051982257557510687161282079114439 absolute error = 3.37e-31 relative error = 6.4829812292619129642735156504697e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (closed_form) = -0.051465025452719890434480311840354 y[1] (numeric) = -0.051465025452719890434480311840018 absolute error = 3.36e-31 relative error = 6.5287056023838541807723546518650e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (closed_form) = -0.050952939893362029865981219773543 y[1] (numeric) = -0.050952939893362029865981219773206 absolute error = 3.37e-31 relative error = 6.6139461374613082321571210071014e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.68 y[1] (closed_form) = -0.050445949670454430281133975316452 y[1] (numeric) = -0.050445949670454430281133975316117 absolute error = 3.35e-31 relative error = 6.6407710071559097395474166227363e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1258.6MB, alloc=52.3MB, time=14.96 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (closed_form) = -0.049944004084552307659248404512019 y[1] (numeric) = -0.049944004084552307659248404511683 absolute error = 3.36e-31 relative error = 6.7275342888241689837922475910279e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (closed_form) = -0.049447052940678782405514765966805 y[1] (numeric) = -0.04944705294067878240551476596647 absolute error = 3.35e-31 relative error = 6.7749234803112879135897766975391e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (closed_form) = -0.048955046543305339833757439474213 y[1] (numeric) = -0.048955046543305339833757439473879 absolute error = 3.34e-31 relative error = 6.8225856900073745849531601528489e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (closed_form) = -0.048467935691382235901887836166041 y[1] (numeric) = -0.048467935691382235901887836165708 absolute error = 3.33e-31 relative error = 6.8705216190836973183539760793506e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (closed_form) = -0.047985671673418351236488733125186 y[1] (numeric) = -0.047985671673418351236488733124851 absolute error = 3.35e-31 relative error = 6.9812506174749066155880051962944e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.74 y[1] (closed_form) = -0.047508206262610001427832355579656 y[1] (numeric) = -0.047508206262610001427832355579321 absolute error = 3.35e-31 relative error = 7.0514133526369808490719755185811e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (closed_form) = -0.047035491712018216472302370200866 y[1] (numeric) = -0.04703549171201821647230237020053 absolute error = 3.36e-31 relative error = 7.1435417760105475533270530004294e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (closed_form) = -0.046567480749794007086145084511088 y[1] (numeric) = -0.046567480749794007086145084510752 absolute error = 3.36e-31 relative error = 7.2153355644321881852575498786667e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (closed_form) = -0.046104126574451140413202269518292 y[1] (numeric) = -0.046104126574451140413202269517956 absolute error = 3.36e-31 relative error = 7.2878508924230717156679764837675e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (closed_form) = -0.045645382850185952400257012152537 y[1] (numeric) = -0.045645382850185952400257012152203 absolute error = 3.34e-31 relative error = 7.3172789698408529048455102653508e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1302.7MB, alloc=52.3MB, time=15.48 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (closed_form) = -0.045191203702243728817329962734743 y[1] (numeric) = -0.045191203702243728817329962734409 absolute error = 3.34e-31 relative error = 7.3908188460892225973472848369108e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (closed_form) = -0.044741543712331191557166645081646 y[1] (numeric) = -0.044741543712331191557166645081312 absolute error = 3.34e-31 relative error = 7.4650978103812374472721573977538e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (closed_form) = -0.044296357914074631458722837151075 y[1] (numeric) = -0.044296357914074631458722837150742 absolute error = 3.33e-31 relative error = 7.5175480712420666400664787093907e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (closed_form) = -0.043855601788523233464145468835525 y[1] (numeric) = -0.043855601788523233464145468835192 absolute error = 3.33e-31 relative error = 7.5931006854213147258605729221152e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.83 y[1] (closed_form) = -0.043419231259697144438017493467177 y[1] (numeric) = -0.043419231259697144438017493466845 absolute error = 3.32e-31 relative error = 7.6463813468796027025730850606891e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (closed_form) = -0.04298720269017983845193870167105 y[1] (numeric) = -0.042987202690179838451938701670717 absolute error = 3.33e-31 relative error = 7.7464914942249033083506805274516e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (closed_form) = -0.042559472876754338767297894474697 y[1] (numeric) = -0.042559472876754338767297894474363 absolute error = 3.34e-31 relative error = 7.8478415596737399044266895322741e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (closed_form) = -0.042135999046082860134798199089125 y[1] (numeric) = -0.042135999046082860134798199088792 absolute error = 3.33e-31 relative error = 7.9029810029141122723764485920793e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (closed_form) = -0.041716738850429439371365169807746 y[1] (numeric) = -0.041716738850429439371365169807413 absolute error = 3.33e-31 relative error = 7.9824072824564051471784968614820e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1346.8MB, alloc=52.3MB, time=16.00 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (closed_form) = -0.041301650363425126473930878432624 y[1] (numeric) = -0.041301650363425126473930878432289 absolute error = 3.35e-31 relative error = 8.1110560244503170812063084002377e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (closed_form) = -0.040890692075875312785676353468485 y[1] (numeric) = -0.040890692075875312785676353468152 absolute error = 3.33e-31 relative error = 8.1436626062013587966047536237765e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (closed_form) = -0.040483822891608776944055087487307 y[1] (numeric) = -0.040483822891608776944055087486974 absolute error = 3.33e-31 relative error = 8.2255077760707739509802875091132e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (closed_form) = -0.04008100212336803351173327510709 y[1] (numeric) = -0.040081002123368033511733275106756 absolute error = 3.34e-31 relative error = 8.3331249795591127752816586776409e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (closed_form) = -0.039682189488740573321885154718708 y[1] (numeric) = -0.039682189488740573321885154718373 absolute error = 3.35e-31 relative error = 8.4420745003259691315068002726052e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (closed_form) = -0.039287345106130588658487339147276 y[1] (numeric) = -0.039287345106130588658487339146942 absolute error = 3.34e-31 relative error = 8.5014652707566389725473038696385e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (closed_form) = -0.038896429490770780440773257808341 y[1] (numeric) = -0.038896429490770780440773257808007 absolute error = 3.34e-31 relative error = 8.5869064171879952286818787139615e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (closed_form) = -0.038509403550773848589242650711833 y[1] (numeric) = -0.038509403550773848589242650711499 absolute error = 3.34e-31 relative error = 8.6732062614168494845564037880910e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (closed_form) = -0.038126228583223270718972279600075 y[1] (numeric) = -0.038126228583223270718972279599739 absolute error = 3.36e-31 relative error = 8.8128307594486404524884942039095e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (closed_form) = -0.037746866270302978234839492009752 y[1] (numeric) = -0.037746866270302978234839492009415 absolute error = 3.37e-31 relative error = 8.9278934464854330436779003847479e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1391.0MB, alloc=52.3MB, time=16.51 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (closed_form) = -0.037371278675465542793042879942699 y[1] (numeric) = -0.03737127867546554279304287994236 absolute error = 3.39e-31 relative error = 9.0711373015597518193443623195462e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (closed_form) = -0.03699942823963848994437299661867 y[1] (numeric) = -0.036999428239638489944372996618333 absolute error = 3.37e-31 relative error = 9.1082488577205301038246297733667e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4 y[1] (closed_form) = -0.036631277777468360587436042546482 y[1] (numeric) = -0.036631277777468360587436042546146 absolute error = 3.36e-31 relative error = 9.1724892055682321651225238820807e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.01 y[1] (closed_form) = -0.036266790473602144634845884059948 y[1] (numeric) = -0.036266790473602144634845884059612 absolute error = 3.36e-31 relative error = 9.2646742546619208275359353058939e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (closed_form) = -0.035905929879005715032652207912938 y[1] (numeric) = -0.035905929879005715032652207912602 absolute error = 3.36e-31 relative error = 9.3577857789016632961692530724956e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.03 y[1] (closed_form) = -0.035548659907318893973338772871938 y[1] (numeric) = -0.035548659907318893973338772871603 absolute error = 3.35e-31 relative error = 9.4237026338939128219080101278523e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (closed_form) = -0.035194944831246786805975603183958 y[1] (numeric) = -0.035194944831246786805975603183622 absolute error = 3.36e-31 relative error = 9.5468255913187957628002762648703e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (closed_form) = -0.034844749278987022773908907373465 y[1] (numeric) = -0.034844749278987022773908907373129 absolute error = 3.36e-31 relative error = 9.6427727836349611761704495946023e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.06 y[1] (closed_form) = -0.034498038230692545301085182050658 y[1] (numeric) = -0.034498038230692545301085182050322 absolute error = 3.36e-31 relative error = 9.7396842612651608575484934250118e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1435.1MB, alloc=52.3MB, time=17.02 TOP MAIN SOLVE Loop x[1] = 4.07 y[1] (closed_form) = -0.034154777014969598103090448554437 y[1] (numeric) = -0.0341547770149695981030904485541 absolute error = 3.37e-31 relative error = 9.8668481967338638443076744094727e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (closed_form) = -0.033814931305410556918597371718443 y[1] (numeric) = -0.033814931305410556918597371718106 absolute error = 3.37e-31 relative error = 9.9660116697051614772807358633207e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (closed_form) = -0.033478467117161260141504088950542 y[1] (numeric) = -0.033478467117161260141504088950205 absolute error = 3.37e-31 relative error = 1.0066171752148467034571010439449e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (closed_form) = -0.033145350803522495083967396166902 y[1] (numeric) = -0.033145350803522495083967396166566 absolute error = 3.36e-31 relative error = 1.0137168316356810875577852910965e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (closed_form) = -0.032815549052585300016124489678115 y[1] (numeric) = -0.03281554905258530001612448967778 absolute error = 3.35e-31 relative error = 1.0208575192911720317206067412654e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (closed_form) = -0.032489028883899745509903311888252 y[1] (numeric) = -0.032489028883899745509903311887918 absolute error = 3.34e-31 relative error = 1.0280393458159562009398628323106e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (closed_form) = -0.032165757645176861962279857041206 y[1] (numeric) = -0.032165757645176861962279857040871 absolute error = 3.35e-31 relative error = 1.0414802091572434269185955620040e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (closed_form) = -0.031845703009023383487986359852932 y[1] (numeric) = -0.031845703009023383487986359852597 absolute error = 3.35e-31 relative error = 1.0519472592741280187921531229804e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (closed_form) = -0.031528832969708981653338582022219 y[1] (numeric) = -0.031528832969708981653338582021883 absolute error = 3.36e-31 relative error = 1.0656912050084718277643620536793e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (closed_form) = -0.031215115839965665771861598480226 y[1] (numeric) = -0.03121511583996566577186159847989 absolute error = 3.36e-31 relative error = 1.0764015796789353647135218303301e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1479.2MB, alloc=52.3MB, time=17.54 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (closed_form) = -0.030904520247819029699076470646538 y[1] (numeric) = -0.030904520247819029699076470646203 absolute error = 3.35e-31 relative error = 1.0839838227990009495198740326541e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (closed_form) = -0.030597015133451028248486648885946 y[1] (numeric) = -0.030597015133451028248486648885611 absolute error = 3.35e-31 relative error = 1.0948780413346661292678301325266e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (closed_form) = -0.030292569746093969503791341104983 y[1] (numeric) = -0.030292569746093969503791341104649 absolute error = 3.34e-31 relative error = 1.1025806090388456886670714939963e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (closed_form) = -0.029991153640955412423968720457457 y[1] (numeric) = -0.029991153640955412423968720457125 absolute error = 3.32e-31 relative error = 1.1069930952793573513073607952563e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (closed_form) = -0.029692736676173662228426886608675 y[1] (numeric) = -0.029692736676173662228426886608343 absolute error = 3.32e-31 relative error = 1.1181185608479352628829302373365e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (closed_form) = -0.029397289009803559109224000018468 y[1] (numeric) = -0.029397289009803559109224000018135 absolute error = 3.33e-31 relative error = 1.1327575134188375248064822558150e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (closed_form) = -0.029104781096832258846716960143819 y[1] (numeric) = -0.029104781096832258846716960143487 absolute error = 3.32e-31 relative error = 1.1407060540858512593769983759424e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (closed_form) = -0.028815183686224706904213334652431 y[1] (numeric) = -0.028815183686224706904213334652099 absolute error = 3.32e-31 relative error = 1.1521703405233361096698919562774e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (closed_form) = -0.028528467817998510546573891712003 y[1] (numeric) = -0.02852846781799851054657389171167 absolute error = 3.33e-31 relative error = 1.1672551155723528373938358019183e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1523.4MB, alloc=52.3MB, time=18.05 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (closed_form) = -0.028244604820327916467539980915243 y[1] (numeric) = -0.02824460482032791646753998091491 absolute error = 3.33e-31 relative error = 1.1789862245137048797264484807965e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (closed_form) = -0.027963566306676604321135135556967 y[1] (numeric) = -0.027963566306676604321135135556635 absolute error = 3.32e-31 relative error = 1.1872591512790391267176509515225e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (closed_form) = -0.027685324172959009434104689735196 y[1] (numeric) = -0.027685324172959009434104689734864 absolute error = 3.32e-31 relative error = 1.1991913041216010301030141937711e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.29 y[1] (closed_form) = -0.027409850594729890829299081946433 y[1] (numeric) = -0.027409850594729890829299081946101 absolute error = 3.32e-31 relative error = 1.2112433770939045114522928653678e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (closed_form) = -0.027137118024401863514461149051535 y[1] (numeric) = -0.027137118024401863514461149051204 absolute error = 3.31e-31 relative error = 1.2197315857283104388896602918743e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (closed_form) = -0.026867099188490616787327558519805 y[1] (numeric) = -0.026867099188490616787327558519474 absolute error = 3.31e-31 relative error = 1.2319900919627172137219218243903e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (closed_form) = -0.026599767084887543076579230029926 y[1] (numeric) = -0.026599767084887543076579230029595 absolute error = 3.31e-31 relative error = 1.2443717982329820924452975257146e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (closed_form) = -0.026335094980159504579252024594645 y[1] (numeric) = -0.026335094980159504579252024594312 absolute error = 3.33e-31 relative error = 1.2644723713769689569742234048850e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (closed_form) = -0.02607305640687546766902124030864 y[1] (numeric) = -0.026073056406875467669021240308308 absolute error = 3.32e-31 relative error = 1.2733451530157069183855101463826e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (closed_form) = -0.025813625160959737736572931083345 y[1] (numeric) = -0.025813625160959737736572931083012 absolute error = 3.33e-31 relative error = 1.2900164077055933577648142458067e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1567.5MB, alloc=52.3MB, time=18.57 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (closed_form) = -0.025556775299071529783340440515445 y[1] (numeric) = -0.025556775299071529783340440515112 absolute error = 3.33e-31 relative error = 1.3029812881443528330785433317521e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (closed_form) = -0.025302481136010612723481826091564 y[1] (numeric) = -0.025302481136010612723481826091231 absolute error = 3.33e-31 relative error = 1.3160764677977481031948045752583e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (closed_form) = -0.025050717242148767956366401183318 y[1] (numeric) = -0.025050717242148767956366401182984 absolute error = 3.34e-31 relative error = 1.3332951578649114195343253190371e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (closed_form) = -0.024801458440886805353287185162491 y[1] (numeric) = -0.024801458440886805353287185162157 absolute error = 3.34e-31 relative error = 1.3466949969739660063087167918353e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (closed_form) = -0.024554679806136882357878772473083 y[1] (numeric) = -0.024554679806136882357878772472751 absolute error = 3.32e-31 relative error = 1.3520844198384707495770534746546e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (closed_form) = -0.024310356659829874430052588037247 y[1] (numeric) = -0.024310356659829874430052588036915 absolute error = 3.32e-31 relative error = 1.3656730941697478128857478455390e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (closed_form) = -0.024068464569447547568416724299946 y[1] (numeric) = -0.024068464569447547568416724299613 absolute error = 3.33e-31 relative error = 1.3835531512164237447496725312607e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (closed_form) = -0.023828979345579286126376072142976 y[1] (numeric) = -0.023828979345579286126376072142642 absolute error = 3.34e-31 relative error = 1.4016546624014894793262694831670e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (closed_form) = -0.023591877039503131592658288741304 y[1] (numeric) = -0.023591877039503131592658288740971 absolute error = 3.33e-31 relative error = 1.4115027788692362198618494093800e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 memory used=1611.7MB, alloc=52.3MB, time=19.08 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (closed_form) = -0.023357133940790890438127847222936 y[1] (numeric) = -0.0233571339407908904381278472226 absolute error = 3.36e-31 relative error = 1.4385326592369696482921678156667e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (closed_form) = -0.0231247265749370715376770994238 y[1] (numeric) = -0.023124726574937071537677099423463 absolute error = 3.37e-31 relative error = 1.4573145282731502550699911383636e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (closed_form) = -0.022894631701011416058960648775872 y[1] (numeric) = -0.022894631701011416058960648775535 absolute error = 3.37e-31 relative error = 1.4719607827764809698222653653033e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.48 y[1] (closed_form) = -0.022666826309334785069005675152334 y[1] (numeric) = -0.022666826309334785069005675151996 absolute error = 3.38e-31 relative error = 1.4911659682185099810141687945867e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (closed_form) = -0.02244128761917817244552210591857 y[1] (numeric) = -0.022441287619178172445522105918232 absolute error = 3.38e-31 relative error = 1.5061524353493312418324624353527e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (closed_form) = -0.022217993076484612992286268573861 y[1] (numeric) = -0.022217993076484612992286268573524 absolute error = 3.37e-31 relative error = 1.5167886624137925583194454461629e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.51 y[1] (closed_form) = -0.021996920351613757947511147117173 y[1] (numeric) = -0.021996920351613757947511147116835 absolute error = 3.38e-31 relative error = 1.5365787328279494296537873782221e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.52 y[1] (closed_form) = -0.02177804733710889234087455248789 y[1] (numeric) = -0.021778047337108892340874552487551 absolute error = 3.39e-31 relative error = 1.5566133857297573898000579959443e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (closed_form) = -0.021561352145486170899080084826662 y[1] (numeric) = -0.021561352145486170899080084826322 absolute error = 3.40e-31 relative error = 1.5768955383958995804593910396058e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop memory used=1655.8MB, alloc=52.3MB, time=19.60 x[1] = 4.54 y[1] (closed_form) = -0.021346813107045851421699134099529 y[1] (numeric) = -0.021346813107045851421699134099189 absolute error = 3.40e-31 relative error = 1.5927436020310575177719279107891e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (closed_form) = -0.021134408767705306748807525018684 y[1] (numeric) = -0.021134408767705306748807525018343 absolute error = 3.41e-31 relative error = 1.6134825617694555240406242618014e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (closed_form) = -0.020924117886853598619807740544615 y[1] (numeric) = -0.020924117886853598619807740544275 absolute error = 3.40e-31 relative error = 1.6249191571111267466977214627687e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.57 y[1] (closed_form) = -0.020715919435227398879034745114834 y[1] (numeric) = -0.020715919435227398879034745114493 absolute error = 3.41e-31 relative error = 1.6460770716270013298160533252040e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (closed_form) = -0.020509792592808045618495896619257 y[1] (numeric) = -0.020509792592808045618495896618916 absolute error = 3.41e-31 relative error = 1.6626204212302707645734673987062e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (closed_form) = -0.02030571674673952396160676205756 y[1] (numeric) = -0.02030571674673952396160676205722 absolute error = 3.40e-31 relative error = 1.6744053127530875461852277366595e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (closed_form) = -0.0201036714892671632842661886631 y[1] (numeric) = -0.02010367148926716328426618866276 absolute error = 3.40e-31 relative error = 1.6912333659128747485027189092886e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.61 y[1] (closed_form) = -0.01990363661569684474127497995891 y[1] (numeric) = -0.019903636615696844741274979958569 absolute error = 3.41e-31 relative error = 1.7132547513004385423006234767761e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.62 y[1] (closed_form) = -0.019705592122374515017150152549829 y[1] (numeric) = -0.019705592122374515017150152549489 absolute error = 3.40e-31 relative error = 1.7253985462022754605495029198935e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (closed_form) = -0.019509518204685804251026110923004 y[1] (numeric) = -0.019509518204685804251026110922662 absolute error = 3.42e-31 relative error = 1.7529904962894383358210546644731e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 memory used=1700.0MB, alloc=52.3MB, time=20.13 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (closed_form) = -0.019315395255075548095768239755011 y[1] (numeric) = -0.019315395255075548095768239754668 absolute error = 3.43e-31 relative error = 1.7757855610532699286649772572305e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (closed_form) = -0.019123203861087015861854421299449 y[1] (numeric) = -0.019123203861087015861854421299106 absolute error = 3.43e-31 relative error = 1.7936325026475084086294165591792e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.66 y[1] (closed_form) = -0.018932924803420648667204884013348 y[1] (numeric) = -0.018932924803420648667204884013003 absolute error = 3.45e-31 relative error = 1.8222224172023763236647847097124e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.67 y[1] (closed_form) = -0.018744539054012113465157641806389 y[1] (numeric) = -0.018744539054012113465157641806044 absolute error = 3.45e-31 relative error = 1.8405360569597767997801752884110e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (closed_form) = -0.01855802777412948075439069447478 y[1] (numeric) = -0.018558027774129480754390694474433 absolute error = 3.47e-31 relative error = 1.8698107591137984624261026429699e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.69 y[1] (closed_form) = -0.018373372312489335686976291012424 y[1] (numeric) = -0.018373372312489335686976291012078 absolute error = 3.46e-31 relative error = 1.8831600106682964495567203115104e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (closed_form) = -0.018190554203391634184108148582775 y[1] (numeric) = -0.018190554203391634184108148582431 absolute error = 3.44e-31 relative error = 1.8910913661765241807313336478324e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (closed_form) = -0.018009555164873117543558908122057 y[1] (numeric) = -0.018009555164873117543558908121712 absolute error = 3.45e-31 relative error = 1.9156497583733108461273418573307e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (closed_form) = -0.017830357096879100878789746029528 y[1] (numeric) = -0.017830357096879100878789746029183 absolute error = 3.45e-31 relative error = 1.9349023585197087875672331273527e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 memory used=1744.1MB, alloc=52.3MB, time=20.75 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (closed_form) = -0.017652942079453452567032538193552 y[1] (numeric) = -0.01765294207945345256703253819321 absolute error = 3.42e-31 relative error = 1.9373541161620837266655401992646e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (closed_form) = -0.017477292370946583702781029082076 y[1] (numeric) = -0.017477292370946583702781029081732 absolute error = 3.44e-31 relative error = 1.9682682688987292677509539555353e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (closed_form) = -0.017303390406241268354143007914501 y[1] (numeric) = -0.017303390406241268354143007914157 absolute error = 3.44e-31 relative error = 1.9880496938676277198947253947483e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (closed_form) = -0.017131218794996117202600639084614 y[1] (numeric) = -0.017131218794996117202600639084272 absolute error = 3.42e-31 relative error = 1.9963553328727275439187266839797e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (closed_form) = -0.016960760319906528912079146021476 y[1] (numeric) = -0.016960760319906528912079146021134 absolute error = 3.42e-31 relative error = 2.0164190375274683960124503284303e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (closed_form) = -0.016791997934982945321011543333507 y[1] (numeric) = -0.016791997934982945321011543333165 absolute error = 3.42e-31 relative error = 2.0366843857663167940593274361203e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (closed_form) = -0.016624914763846238281483831586441 y[1] (numeric) = -0.016624914763846238281483831586098 absolute error = 3.43e-31 relative error = 2.0631684725741452426932502288221e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (closed_form) = -0.016459494098040057682724053532149 y[1] (numeric) = -0.016459494098040057682724053531805 absolute error = 3.44e-31 relative error = 2.0899791813222399490212276003235e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (closed_form) = -0.016295719395359971892331179358986 y[1] (numeric) = -0.016295719395359971892331179358642 absolute error = 3.44e-31 relative error = 2.1109838212969612293184205694077e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (closed_form) = -0.016133574278199233527895556245215 y[1] (numeric) = -0.016133574278199233527895556244871 absolute error = 3.44e-31 relative error = 2.1321995614129712540070989469706e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 memory used=1788.3MB, alloc=52.3MB, time=21.27 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (closed_form) = -0.01597304253191100513420955114174 y[1] (numeric) = -0.015973042531911005134209551141396 absolute error = 3.44e-31 relative error = 2.1536285232619614664524566250414e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (closed_form) = -0.015814108103186880987271291363368 y[1] (numeric) = -0.015814108103186880987271291363021 absolute error = 3.47e-31 relative error = 2.1942432525174915110833020785319e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (closed_form) = -0.015656755098451542875910667028563 y[1] (numeric) = -0.015656755098451542875910667028217 absolute error = 3.46e-31 relative error = 2.2099087443362992206957912303820e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (closed_form) = -0.015500967782273389325277966639986 y[1] (numeric) = -0.015500967782273389325277966639638 absolute error = 3.48e-31 relative error = 2.2450211166683808795287027147764e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (closed_form) = -0.015346730575790979323793014607349 y[1] (numeric) = -0.015346730575790979323793014607 absolute error = 3.49e-31 relative error = 2.2740999998432065990632878377534e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (closed_form) = -0.015194028055155133196616204361159 y[1] (numeric) = -0.01519402805515513319661620436081 absolute error = 3.49e-31 relative error = 2.2969550848077373788428173936425e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (closed_form) = -0.015042844949986534834430520561019 y[1] (numeric) = -0.01504284494998653483443052056067 absolute error = 3.49e-31 relative error = 2.3200398671948845501421971519827e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (closed_form) = -0.014893166141848681036472092840257 y[1] (numeric) = -0.014893166141848681036472092839907 absolute error = 3.50e-31 relative error = 2.3500711444863709847010259860511e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (closed_form) = -0.014744976662736025261471037686311 y[1] (numeric) = -0.01474497666273602526147103768596 absolute error = 3.51e-31 relative error = 2.3804717228685643258260759246985e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 memory used=1832.4MB, alloc=52.3MB, time=21.78 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (closed_form) = -0.014598261693577164599617798133888 y[1] (numeric) = -0.014598261693577164599617798133538 absolute error = 3.50e-31 relative error = 2.3975457307632073477338157064927e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.93 y[1] (closed_form) = -0.014453006562752920283004829557022 y[1] (numeric) = -0.014453006562752920283004829556672 absolute error = 3.50e-31 relative error = 2.4216414659493113860610183920018e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (closed_form) = -0.014309196744629163541359738704192 y[1] (numeric) = -0.014309196744629163541359738703841 absolute error = 3.51e-31 relative error = 2.4529678797780517848135299325848e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (closed_form) = -0.014166817858104240084432800094696 y[1] (numeric) = -0.014166817858104240084432800094345 absolute error = 3.51e-31 relative error = 2.4776206168219186698397966335478e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (closed_form) = -0.014025855665170847952276604894962 y[1] (numeric) = -0.014025855665170847952276604894612 absolute error = 3.50e-31 relative error = 2.4953914281973090220277763864890e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (closed_form) = -0.013886296069492224920004431120137 y[1] (numeric) = -0.013886296069492224920004431119784 absolute error = 3.53e-31 relative error = 2.5420745620967306737053726197700e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (closed_form) = -0.013748125114992503074581296546882 y[1] (numeric) = -0.013748125114992503074581296546529 absolute error = 3.53e-31 relative error = 2.5676228361862161651491668066944e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (closed_form) = -0.013611328984461089597930665007658 y[1] (numeric) = -0.013611328984461089597930665007305 absolute error = 3.53e-31 relative error = 2.5934278746990131073297150259502e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Finished! diff ( y , x , 1 ) = 2.0 / exp ( x ) ; Iterations = 4000 Total Elapsed Time = 22 Seconds Elapsed Time(since restart) = 22 Seconds Time to Timeout = 2 Minutes 37 Seconds Percent Done = 100 % > quit memory used=1870.8MB, alloc=52.3MB, time=22.21