|\^/| 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(arctan(c(x))); > end; exact_soln_y := proc(x) return arctan(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_1D0, #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_tmp4, > 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_1D0, 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_tmp4, 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_1D0, #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_tmp4, > 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_1D0, 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_tmp4, 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_1D0, #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_tmp4, > 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_1D0, 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_tmp4, 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_1D0, #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_tmp4, > 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_1D0, 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_tmp4, 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_1D0, #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_tmp4, > 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)*22*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_1D0, 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_tmp4, 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)*22*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_1D0, #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_tmp4, > 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_1D0, 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_tmp4, 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_1D0, #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_tmp4, > 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_1D0, 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_tmp4, 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_1D0, #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_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > # before write maple main top matter > # before generate constants assign > # before generate globals assign > #END OUTFILE1 > #BEGIN OUTFILE2 > #END OUTFILE2 > #BEGIN ATOMHDR1 > #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_x[1] * array_x[1]; > #emit pre add FULL - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_1D0[1]; > #emit pre div CONST FULL $eq_no = 1 i = 1 > array_tmp3[1] := array_const_1D0[1] / array_tmp2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp4[1] := array_const_0D0[1] + array_tmp3[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_tmp4[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1)); > if (2 <= ATS_MAX_TERMS) then # if number 3 > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(1); > array_y_higher[2,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_x[1] * array_x[2] + array_x[2] * array_x[1]; > #emit pre add FULL CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre div CONST FULL $eq_no = 1 i = 2 > array_tmp3[2] := neg(ats(2,array_tmp2,array_tmp3,2)) / array_tmp2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp4[2] := array_tmp3[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_tmp4[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 mult LINEAR - LINEAR $eq_no = 1 i = 3 > array_tmp1[3] := array_x[2] * array_x[2]; > #emit pre add FULL CONST $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre div CONST FULL $eq_no = 1 i = 3 > array_tmp3[3] := neg(ats(3,array_tmp2,array_tmp3,2)) / array_tmp2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp4[3] := array_tmp3[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_tmp4[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 add FULL CONST $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre div CONST FULL $eq_no = 1 i = 4 > array_tmp3[4] := neg(ats(4,array_tmp2,array_tmp3,2)) / array_tmp2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp4[4] := array_tmp3[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_tmp4[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 add FULL CONST $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre div CONST FULL $eq_no = 1 i = 5 > array_tmp3[5] := neg(ats(5,array_tmp2,array_tmp3,2)) / array_tmp2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp4[5] := array_tmp3[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_tmp4[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 mult LINEAR - LINEAR $eq_no = 1 i = 1 > #emit FULL - NOT FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit div CONST FULL $eq_no = 1 i = 1 > array_tmp3[kkk] := neg(ats(kkk,array_tmp2,array_tmp3,2)) / array_tmp2[1]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp4[kkk] := array_tmp3[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_tmp4[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_1D0, 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_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; array_tmp1[1] := array_x[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_1D0[1]; array_tmp3[1] := array_const_1D0[1]/array_tmp2[1]; array_tmp4[1] := array_const_0D0[1] + array_tmp3[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp4[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_x[1]*array_x[2] + array_x[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := neg(ats(2, array_tmp2, array_tmp3, 2))/array_tmp2[1]; array_tmp4[2] := array_tmp3[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp4[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_x[2]*array_x[2]; array_tmp2[3] := array_tmp1[3]; array_tmp3[3] := neg(ats(3, array_tmp2, array_tmp3, 2))/array_tmp2[1]; array_tmp4[3] := array_tmp3[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp4[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_y[4] := temporary; array_y_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y_higher[2, 3] := c(temporary) end if end if; kkk := 4; array_tmp2[4] := array_tmp1[4]; array_tmp3[4] := neg(ats(4, array_tmp2, array_tmp3, 2))/array_tmp2[1]; array_tmp4[4] := array_tmp3[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp4[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_y[5] := temporary; array_y_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y_higher[2, 4] := c(temporary) end if end if; kkk := 5; array_tmp2[5] := array_tmp1[5]; array_tmp3[5] := neg(ats(5, array_tmp2, array_tmp3, 2))/array_tmp2[1]; array_tmp4[5] := array_tmp3[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp4[5])*expt(glob_h, c(1))*c(factorial_3(4, 5)); if 6 <= ATS_MAX_TERMS then array_y[6] := temporary; array_y_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y_higher[2, 5] := c(temporary) end if end if; kkk := 6; while kkk <= ATS_MAX_TERMS do array_tmp2[kkk] := array_tmp1[kkk]; array_tmp3[kkk] := neg(ats(kkk, array_tmp2, array_tmp3, 2))/array_tmp2[1]; array_tmp4[kkk] := array_tmp3[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_tmp4[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_1D0, > #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_tmp4, > 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 := 20; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=20; > #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..(20),[]); > array_norms:= Array(0..(20),[]); > array_fact_1:= Array(0..(20),[]); > 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..(20),[]); > array_x:= Array(0..(20),[]); > array_tmp0:= Array(0..(20),[]); > array_tmp1:= Array(0..(20),[]); > array_tmp2:= Array(0..(20),[]); > array_tmp3:= Array(0..(20),[]); > array_tmp4:= Array(0..(20),[]); > array_m1:= Array(0..(20),[]); > array_y_higher := Array(0..(2) ,(0..20+ 1),[]); > array_y_higher_work := Array(0..(2) ,(0..20+ 1),[]); > array_y_higher_work2 := Array(0..(2) ,(0..20+ 1),[]); > array_y_set_initial := Array(0..(2) ,(0..20+ 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..(20) ,(0..20+ 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 <= 20) do # do number 1 > array_y_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_norms[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) 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 <= 20) do # do number 1 > array_y[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_x[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) 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 <= 20) 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 <= 20) 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 <= 20) 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 <= 20) 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 <=20) do # do number 1 > term := 1; > while (term <= 20) 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_tmp4); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_const_1D0); > array_const_1D0[1] := c(1.0); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_h := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 1000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_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; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 20; > 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/sing2_backpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=20;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := c(-1.5);"); > omniout_str(ALWAYS,"x_end := c(-2.0);"); > 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 := 2;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(0.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(1.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(1.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);"); > 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(arctan(c(x)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := glob__0; > glob_smallish_float := glob__0; > glob_large_float := c(1.0e100); > glob_larger_float := c( 1.1e100); > glob_almost_1 := c( 0.99); > # before second block > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN BLOCK 2 > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := c(-1.5); > x_end := c(-2.0); > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_type_given_pole := 2; > array_given_rad_poles[1,1] := c(0.0); > array_given_rad_poles[1,2] := c(1.0); > array_given_ord_poles[1,1] := c(1.0); > array_given_ord_poles[1,2] := c(0.0); > #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 ) = 1.0 / ( x * x + 1.0 ) ; "); > 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,"2016-08-26T17:08:40-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sing2_back") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; ") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_h_reason(html_log_file) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_float(html_log_file,glob_desired_digits_correct) > ; > if (array_est_digits[1] <> -16) then # if number 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,"sing2_back diffeq.mxt") > ; > logitem_str(html_log_file,"sing2_back 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_1D0, 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_tmp4, 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 := 20; Digits := 32; max_terms := 20; glob_html_log := true; array_y_init := Array(0 .. 20, []); array_norms := Array(0 .. 20, []); array_fact_1 := Array(0 .. 20, []); 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 .. 20, []); array_x := Array(0 .. 20, []); array_tmp0 := Array(0 .. 20, []); array_tmp1 := Array(0 .. 20, []); array_tmp2 := Array(0 .. 20, []); array_tmp3 := Array(0 .. 20, []); array_tmp4 := Array(0 .. 20, []); array_m1 := Array(0 .. 20, []); array_y_higher := Array(0 .. 2, 0 .. 21, []); array_y_higher_work := Array(0 .. 2, 0 .. 21, []); array_y_higher_work2 := Array(0 .. 2, 0 .. 21, []); array_y_set_initial := Array(0 .. 2, 0 .. 21, []); 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 .. 20, 0 .. 21, []); term := 1; while term <= 20 do array_y_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_norms[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 20 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 <= 20 do array_y[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_x[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 20 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 <= 20 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 <= 20 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 <= 20 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 <= 20 do term := 1; while term <= 20 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_tmp4); zero_ats_ar(array_m1); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_const_1D0); array_const_1D0[1] := c(1.0); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_h := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 1000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_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; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 20; 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/sing2_backpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; ") ; omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=20;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := c(-1.5);"); omniout_str(ALWAYS, "x_end := c(-2.0);"); 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 := 2;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(0.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(1.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(1.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);"); 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(arctan(c(x)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := glob__0; glob_smallish_float := glob__0; glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := c(-1.5); x_end := c(-2.0); array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_type_given_pole := 2; array_given_rad_poles[1, 1] := c(0.); array_given_rad_poles[1, 2] := c(1.0); array_given_ord_poles[1, 1] := c(1.0); array_given_ord_poles[1, 2] := c(0.); 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 ) = 1.0 / ( x * \ x + 1.0 ) ; "); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2016-08-26T17:08:40-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sing2_back"); logitem_str(html_log_file, "diff ( y , x , 1 ) = 1.\ 0 / ( x * x + 1.0 ) ; "); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_h_reason(html_log_file); logitem_integer(html_log_file, Digits); logitem_float(html_log_file, glob_desired_digits_correct); if array_est_digits[1] <> -16 then logitem_integer(html_log_file, array_est_digits[1]) else logitem_str(html_log_file, "Unknown") end if; if glob_min_good_digits <> -16 then logitem_integer(html_log_file, glob_min_good_digits) else logitem_str(html_log_file, "Unknown") end if; if glob_good_digits <> -16 then logitem_integer(html_log_file, glob_good_digits) else logitem_str(html_log_file, "Unknown") end if; logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); logitem_integer(html_log_file, ATS_MAX_TERMS); if glob_type_given_pole = 0 then logitem_str(html_log_file, "Not Given"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 4 then logitem_str(html_log_file, "No Solution"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 5 then logitem_str(html_log_file, "Some Pole"); logitem_str(html_log_file, "????") elif glob_type_given_pole = 3 then logitem_str(html_log_file, "No Pole"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 1 then logitem_str(html_log_file, "Real Sing"); logitem_float(html_log_file, glob_least_given_sing) elif glob_type_given_pole = 2 then logitem_str(html_log_file, "Complex Sing"); logitem_float(html_log_file, glob_least_given_sing) end if; if glob_least_ratio_sing < glob_large_float then logitem_float(html_log_file, glob_least_ratio_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_3_sing < glob_large_float then logitem_float(html_log_file, glob_least_3_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_6_sing < glob_large_float then logitem_float(html_log_file, glob_least_6_sing) else logitem_str(html_log_file, "NONE") end if; logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, glob_clock_sec); if c(glob_percent_done) < glob__100 then logitem_time(html_log_file, glob_total_exp_sec); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 308.maple.seems.ok "); logitem_str(html_log_file, "sing2_back diffeq.mxt"); logitem_str(html_log_file, "sing2_back 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/sing2_backpostode.ode################# diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=20; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := c(-1.5); x_end := c(-2.0); array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_type_given_pole := 2; array_given_rad_poles[1,1] := c(0.0); array_given_rad_poles[1,2] := c(1.0); array_given_ord_poles[1,1] := c(1.0); array_given_ord_poles[1,2] := c(0.0); #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(arctan(c(x))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -1.501 y[1] (closed_form) = -0.98310127359900396476034773737684 y[1] (numeric) = -0.98310127359900396476034773737684 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.502 y[1] (closed_form) = -0.98340854026177727563391104913087 y[1] (numeric) = -0.98340854026177727563391104913087 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.503 y[1] (closed_form) = -0.9837155235700465720273252455123 y[1] (numeric) = -0.9837155235700465720273252455123 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.504 y[1] (closed_form) = -0.98402222385780658567937768037798 y[1] (numeric) = -0.98402222385780658567937768037798 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.505 y[1] (closed_form) = -0.98432864145864946425894653704764 y[1] (numeric) = -0.98432864145864946425894653704764 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] = -1.506 memory used=4.4MB, alloc=40.3MB, time=0.09 y[1] (closed_form) = -0.9846347767057650282660065385424 y[1] (numeric) = -0.98463477670576502826600653854241 absolute error = 1e-32 relative error = 1.0156049975663479005392035556027e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.507 y[1] (closed_form) = -0.98494062993194102921194323609649 y[1] (numeric) = -0.9849406299319410292119432360965 absolute error = 1e-32 relative error = 1.0152896221461587656659697438830e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.508 y[1] (closed_form) = -0.98524620146956340906975142451197 y[1] (numeric) = -0.98524620146956340906975142451198 absolute error = 1e-32 relative error = 1.0149747327200351259048605356962e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.509 y[1] (closed_form) = -0.98555149165061656098473757267363 y[1] (numeric) = -0.98555149165061656098473757267364 absolute error = 1e-32 relative error = 1.0146603282241345487276712183737e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.51 y[1] (closed_form) = -0.98585650080668359123639033173802 y[1] (numeric) = -0.98585650080668359123639033173803 absolute error = 1e-32 relative error = 1.0143464075976000535183737410635e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.511 y[1] (closed_form) = -0.98616122926894658244212719255684 y[1] (numeric) = -0.98616122926894658244212719255685 absolute error = 1e-32 relative error = 1.0140329697825499265225548265063e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.512 y[1] (closed_form) = -0.98646567736818685799366920818855 y[1] (numeric) = -0.98646567736818685799366920818855 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] = -1.513 y[1] (closed_form) = -0.98676984543478524771683937729389 y[1] (numeric) = -0.98676984543478524771683937729389 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] = -1.514 y[1] (closed_form) = -0.98707373379872235474562380020178 y[1] (numeric) = -0.98707373379872235474562380020179 absolute error = 1e-32 relative error = 1.0130955426719048784320153085668e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.515 y[1] (closed_form) = -0.98737734278957882360137807187295 y[1] (numeric) = -0.98737734278957882360137807187296 absolute error = 1e-32 relative error = 1.0127840255831262335345418482739e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.516 y[1] (closed_form) = -0.98768067273653560946810456528295 y[1] (numeric) = -0.98768067273653560946810456528296 absolute error = 1e-32 relative error = 1.0124729860606987681761494415628e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.517 y[1] (closed_form) = -0.98798372396837424865476928529662 y[1] (numeric) = -0.98798372396837424865476928529663 absolute error = 1e-32 relative error = 1.0121624230643807621195390458299e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.518 y[1] (closed_form) = -0.9882864968134771302356698373165 y[1] (numeric) = -0.9882864968134771302356698373165 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] = -1.519 y[1] (closed_form) = -0.98858899159982776885990875726318 y[1] (numeric) = -0.98858899159982776885990875726318 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] = -1.52 y[1] (closed_form) = -0.9888912086550110787210689901915 y[1] (numeric) = -0.98889120865501107872106899019151 absolute error = 1e-32 relative error = 1.0112335828731837608199914232457e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.521 y[1] (closed_form) = -0.98919314830621364867823068446841 y[1] (numeric) = -0.98919314830621364867823068446842 absolute error = 1e-32 relative error = 1.0109249156368408175054508491175e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.522 y[1] (closed_form) = -0.98949481088022401851951068734359 y[1] (numeric) = -0.9894948108802240185195106873436 absolute error = 1e-32 relative error = 1.0106167197687786656931726859718e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.523 y[1] (closed_form) = -0.98979619670343295635934818633987 y[1] (numeric) = -0.98979619670343295635934818633987 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] = -1.524 y[1] (closed_form) = -0.99009730610183373716080183958421 y[1] (numeric) = -0.99009730610183373716080183958421 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] = -1.525 y[1] (closed_form) = -0.99039813940102242237416547740178 y[1] (numeric) = -0.99039813940102242237416547740177 absolute error = 1e-32 relative error = 1.0096949501589175393516249432437e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.526 y[1] (closed_form) = -0.99069869692619814068325103761255 y[1] (numeric) = -0.99069869692619814068325103761254 absolute error = 1e-32 relative error = 1.0093886295628132411230180264630e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.527 y[1] (closed_form) = -0.99099897900216336985072881841382 y[1] (numeric) = -0.99099897900216336985072881841381 absolute error = 1e-32 relative error = 1.0090827752485676180975535439494e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.528 y[1] (closed_form) = -0.9912989859533242196539563959113 y[1] (numeric) = -0.99129898595332421965395639591129 absolute error = 1e-32 relative error = 1.0087773862073591102177024628328e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.529 y[1] (closed_form) = -0.99159871810369071590276865868826 y[1] (numeric) = -0.99159871810369071590276865868826 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] = -1.53 y[1] (closed_form) = -0.99189817577687708553074235968741 y[1] (numeric) = -0.9918981757768770855307423596874 absolute error = 1e-32 relative error = 1.0081679999227515289002876770172e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.531 y[1] (closed_form) = -0.99219735929610204275148937653489 y[1] (numeric) = -0.99219735929610204275148937653488 absolute error = 1e-32 relative error = 1.0078640006756653850196823697524e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.532 y[1] (closed_form) = -0.99249626898418907627157350567385 y[1] (numeric) = -0.99249626898418907627157350567384 absolute error = 1e-32 relative error = 1.0075604626942234496474832341855e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.533 y[1] (closed_form) = -0.99279490516356673755168609370703 y[1] (numeric) = -0.99279490516356673755168609370702 absolute error = 1e-32 relative error = 1.0072573849835039148024289807873e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.534 y[1] (closed_form) = -0.99309326815626893010775613158899 y[1] (numeric) = -0.99309326815626893010775613158898 absolute error = 1e-32 relative error = 1.0069547665513369042031581283280e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.535 y[1] (closed_form) = -0.99339135828393519984371060417091 y[1] (numeric) = -0.9933913582839351998437106041709 absolute error = 1e-32 relative error = 1.0066526064082952199653306655054e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.536 y[1] (closed_form) = -0.99368917586781102640764089949904 y[1] (numeric) = -0.99368917586781102640764089949903 absolute error = 1e-32 relative error = 1.0063509035676851259335398545291e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.537 y[1] (closed_form) = -0.99398672122874811556317093961612 y[1] (numeric) = -0.99398672122874811556317093961611 absolute error = 1e-32 relative error = 1.0060496570455371674807906947054e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.538 y[1] (closed_form) = -0.99428399468720469256786239782779 y[1] (numeric) = -0.99428399468720469256786239782777 absolute error = 2e-32 relative error = 2.0114977317211940552183768576798e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.539 y[1] (closed_form) = -0.99458099656324579655053191688854 y[1] (numeric) = -0.99458099656324579655053191688852 absolute error = 2e-32 relative error = 2.0108970580686328383726845935783e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.54 y[1] (closed_form) = -0.99487772717654357587939463874932 y[1] (numeric) = -0.9948777271765435758793946387493 absolute error = 2e-32 relative error = 2.0102972911816880263056931026699e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.541 y[1] (closed_form) = -0.9951741868463775845129875998069 y[1] (numeric) = -0.99517418684637758451298759980688 absolute error = 2e-32 relative error = 2.0096984291140328050741051682160e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.542 y[1] (closed_form) = -0.99547037589163507932586563642001 y[1] (numeric) = -0.99547037589163507932586563641999 absolute error = 2e-32 relative error = 2.0091004699246982042283857913480e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.543 y[1] (closed_form) = -0.99576629463081131840110138422489 y[1] (numeric) = -0.99576629463081131840110138422487 absolute error = 2e-32 relative error = 2.0085034116780551670955192320692e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.544 y[1] (closed_form) = -0.99606194338200986028165974190967 y[1] (numeric) = -0.99606194338200986028165974190965 absolute error = 2e-32 relative error = 2.0079072524437966917037547427228e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.545 y[1] (closed_form) = -0.9963573224629428641727558060101 y[1] (numeric) = -0.99635732246294286417275580601008 absolute error = 2e-32 relative error = 2.0073119902969200420284850624773e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.546 y[1] (closed_form) = -0.99665243219093139108734376838494 y[1] (numeric) = -0.99665243219093139108734376838492 absolute error = 2e-32 relative error = 2.0067176233177090292400565785294e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.547 y[1] (closed_form) = -0.99694727288290570592692260273558 y[1] (numeric) = -0.99694727288290570592692260273555 absolute error = 3e-32 relative error = 3.0091862243875745439539329787192e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.548 y[1] (closed_form) = -0.99724184485540558048988255126777 y[1] (numeric) = -0.99724184485540558048988255126775 absolute error = 2e-32 relative error = 2.0055315672097460699414486869408e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.549 y[1] (closed_form) = -0.99753614842458059739965445777235 y[1] (numeric) = -0.99753614842458059739965445777233 absolute error = 2e-32 relative error = 2.0049398742678359866643891290517e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.55 y[1] (closed_form) = -0.9978301839061904549449618794427 y[1] (numeric) = -0.99783018390619045494496187944269 absolute error = 1e-32 relative error = 1.0021745344336201570957514174432e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.551 y[1] (closed_form) = -0.99812395161560527282451364706925 y[1] (numeric) = -0.99812395161560527282451364706923 absolute error = 2e-32 relative error = 2.0037591491144122463150941120963e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.552 y[1] (closed_form) = -0.99841745186780589878851213227124 y[1] (numeric) = -0.99841745186780589878851213227122 absolute error = 2e-32 relative error = 2.0031701131209866638806943773121e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.553 y[1] (closed_form) = -0.99871068497738421616938992156386 y[1] (numeric) = -0.99871068497738421616938992156384 absolute error = 2e-32 relative error = 2.0025819590037628972477737693479e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.554 y[1] (closed_form) = -0.99900365125854345229422489073047 y[1] (numeric) = -0.99900365125854345229422489073045 absolute error = 2e-32 relative error = 2.0019946848846875562572133080829e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.555 y[1] (closed_form) = -0.99929635102509848777132081959536 y[1] (numeric) = -0.99929635102509848777132081959534 absolute error = 2e-32 relative error = 2.0014082888908374274008063406578e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.556 y[1] (closed_form) = -0.99958878459047616664347768728934 y[1] (numeric) = -0.99958878459047616664347768728933 absolute error = 1e-32 relative error = 1.0004113845772012189448098980883e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.557 y[1] (closed_form) = -0.99988095226771560740051264188759 y[1] (numeric) = -0.99988095226771560740051264188757 absolute error = 2e-32 relative error = 2.0002381238126686863195985685500e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.558 y[1] (closed_form) = -1.0001728543694685148436293462945 y[1] (numeric) = -1.0001728543694685148436293462945 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] = -1.559 y[1] (closed_form) = -1.0004644912079994927942699648733 y[1] (numeric) = -1.0004644912079994927942699648733 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] = -1.56 y[1] (closed_form) = -1.0007558630951863576401204729864 y[1] (numeric) = -1.0007558630951863576401204729863 absolute error = 1e-31 relative error = 9.9924470780231195695041504208782e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.561 y[1] (closed_form) = -1.0010469703425204527109762447437 y[1] (numeric) = -1.0010469703425204527109762447437 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] = -1.562 y[1] (closed_form) = -1.0013378132611069634772110032747 y[1] (numeric) = -1.0013378132611069634772110032746 absolute error = 1e-31 relative error = 9.9866397409206984795123833259935e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.563 y[1] (closed_form) = -1.0016283921616652335636282031507 y[1] (numeric) = -1.0016283921616652335636282031506 absolute error = 1e-31 relative error = 9.9837425518844277414517124878672e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.564 y[1] (closed_form) = -1.001918707354529081571509756627 y[1] (numeric) = -1.0019187073545290815715097566269 absolute error = 1e-31 relative error = 9.9808496703330827548601767358754e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.565 y[1] (closed_form) = -1.0022087591496471187017127145426 y[1] (numeric) = -1.0022087591496471187017127145424 absolute error = 2e-31 relative error = 1.9955922174307851709345529703947e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.566 y[1] (closed_form) = -1.0024985478565830671717000694497 y[1] (numeric) = -1.0024985478565830671717000694495 absolute error = 2e-31 relative error = 1.9950153586517902704066465140728e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.567 y[1] (closed_form) = -1.0027880737845160794194272632517 y[1] (numeric) = -1.0027880737845160794194272632515 absolute error = 2e-31 relative error = 1.9944393559169607872432465925644e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.568 y[1] (closed_form) = -1.0030773372422410580870412547239 y[1] (numeric) = -1.0030773372422410580870412547236 absolute error = 3e-31 relative error = 2.9907963111278092180339826162946e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.569 y[1] (closed_form) = -1.0033663385381689767773841342047 y[1] (numeric) = -1.0033663385381689767773841342044 absolute error = 3e-31 relative error = 2.9899348670305000923592591927199e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.57 y[1] (closed_form) = -1.0036550779803272015763282638849 y[1] (numeric) = -1.0036550779803272015763282638847 absolute error = 2e-31 relative error = 1.9927164659243644153112744467419e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.571 y[1] (closed_form) = -1.0039435558763598133340047729067 y[1] (numeric) = -1.0039435558763598133340047729065 absolute error = 2e-31 relative error = 1.9921438693375198474508749766600e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.572 y[1] (closed_form) = -1.004231772533527930698021947339 y[1] (numeric) = -1.0042317725335279306980219473388 absolute error = 2e-31 relative error = 1.9915721198048697547926563574943e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.573 y[1] (closed_form) = -1.0045197282587100338918046264291 y[1] (numeric) = -1.0045197282587100338918046264289 absolute error = 2e-31 relative error = 1.9910012155429843464938403992728e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.574 y[1] (closed_form) = -1.0048074233584022892312201487656 y[1] (numeric) = -1.0048074233584022892312201487654 absolute error = 2e-31 relative error = 1.9904311547732514288682017670631e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.575 y[1] (closed_form) = -1.0050948581387188743726906855402 y[1] (numeric) = -1.00509485813871887437269068554 absolute error = 2e-31 relative error = 1.9898619357218605849435159616717e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.576 y[1] (closed_form) = -1.0053820329053923042860259533815 y[1] (numeric) = -1.0053820329053923042860259533813 absolute error = 2e-31 relative error = 1.9892935566197874151690296312179e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.577 y[1] (closed_form) = -1.0056689479637737579452443166746 y[1] (numeric) = -1.0056689479637737579452443166745 absolute error = 1e-31 relative error = 9.9436300785138891950029597712342e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.578 y[1] (closed_form) = -1.0059556036188334057306841692848 y[1] (numeric) = -1.0059556036188334057306841692846 absolute error = 2e-31 relative error = 1.9881593112113324570924626842326e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.579 y[1] (closed_form) = -1.0062420001751607375357412285954 y[1] (numeric) = -1.0062420001751607375357412285952 absolute error = 2e-31 relative error = 1.9875934413906909738261814870047e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.58 y[1] (closed_form) = -1.0065281379369648915716009811645 y[1] (numeric) = -1.0065281379369648915716009811643 absolute error = 2e-31 relative error = 1.9870284044908166799082444859662e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.581 y[1] (closed_form) = -1.0068140172080749838633689895111 y[1] (numeric) = -1.0068140172080749838633689895109 absolute error = 2e-31 relative error = 1.9864641987663809947696875038172e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.582 y[1] (closed_form) = -1.0070996382919404384310351039872 y[1] (numeric) = -1.007099638291940438431035103987 absolute error = 2e-31 relative error = 1.9859008224767480685020214023166e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.583 y[1] (closed_form) = -1.0073850014916313181487408227815 y[1] (numeric) = -1.0073850014916313181487408227814 absolute error = 1e-31 relative error = 9.9266913694297972153265161079853e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.584 y[1] (closed_form) = -1.0076701071098386562758521072564 y[1] (numeric) = -1.0076701071098386562758521072563 absolute error = 1e-31 relative error = 9.9238827563135938625272877774428e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.585 y[1] (closed_form) = -1.0079549554488747886533728894521 y[1] (numeric) = -1.007954955448874788653372889452 absolute error = 1e-31 relative error = 9.9210782644018830095964290836528e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.586 y[1] (closed_form) = -1.0082395468106736865592673041213 y[1] (numeric) = -1.0082395468106736865592673041212 absolute error = 1e-31 relative error = 9.9182778850845760245345839649560e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.587 y[1] (closed_form) = -1.0085238814967912902162913394908 y[1] (numeric) = -1.0085238814967912902162913394907 absolute error = 1e-31 relative error = 9.9154816097746673962638010907097e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.588 y[1] (closed_form) = -1.008807959808405842945967129505 y[1] (numeric) = -1.0088079598084058429459671295049 absolute error = 1e-31 relative error = 9.9126894299081595028866301487158e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.589 y[1] (closed_form) = -1.0090917820463182259623655059993 y[1] (numeric) = -1.0090917820463182259623655059992 absolute error = 1e-31 relative error = 9.9099013369439876685178279969791e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.59 y[1] (closed_form) = -1.0093753485109522937993946924935 y[1] (numeric) = -1.0093753485109522937993946924935 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] = -1.591 y[1] (closed_form) = -1.0096586595023552103653251525016 y[1] (numeric) = -1.0096586595023552103653251525016 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] = -1.592 y[1] (closed_form) = -1.0099417153201977856183126048325 y[1] (numeric) = -1.0099417153201977856183126048324 absolute error = 1e-31 relative error = 9.9015614943972701784384100812268e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.593 y[1] (closed_form) = -1.0102245162637748128567130867272 y[1] (numeric) = -1.0102245162637748128567130867271 absolute error = 1e-31 relative error = 9.8987896640878477837764750418765e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.594 y[1] (closed_form) = -1.0105070626320054066180156832441 y[1] (numeric) = -1.010507062632005406618015683244 absolute error = 1e-31 relative error = 9.8960218783168292879219808824331e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.595 y[1] (closed_form) = -1.0107893547234333411802501484831 y[1] (numeric) = -1.0107893547234333411802501484829 absolute error = 2e-31 relative error = 1.9786516257358379769423144315890e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.596 y[1] (closed_form) = -1.0110713928362273896597581214427 y[1] (numeric) = -1.0110713928362273896597581214426 absolute error = 1e-31 relative error = 9.8904984067923210855263332625312e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.597 y[1] (closed_form) = -1.011353177268181663699247986941 y[1] (numeric) = -1.0113531772681816636992479869408 absolute error = 2e-31 relative error = 1.9775485408591916078653517785836e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.598 y[1] (closed_form) = -1.0116347083167159537400846505073 y[1] (numeric) = -1.0116347083167159537400846505071 absolute error = 2e-31 relative error = 1.9769982025704214260019990384210e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.599 y[1] (closed_form) = -1.0119159862788760698727965858925 y[1] (numeric) = -1.0119159862788760698727965858923 absolute error = 2e-31 relative error = 1.9764486648289947699740695019256e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (closed_form) = -1.0121970114513341832598134752381 y[1] (numeric) = -1.0121970114513341832598134752379 absolute error = 2e-31 relative error = 1.9758999259761781895900260792693e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.601 y[1] (closed_form) = -1.0124777841303891681244785954202 y[1] (numeric) = -1.01247778413038916812447859542 absolute error = 2e-31 relative error = 1.9753519843576493704147962259709e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.602 y[1] (closed_form) = -1.0127583046119669443004108100369 y[1] (numeric) = -1.0127583046119669443004108100368 absolute error = 1e-31 relative error = 9.8740241916174143633657699528886e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.603 y[1] (closed_form) = -1.0130385731916208203353216053524 y[1] (numeric) = -1.0130385731916208203353216053522 absolute error = 2e-31 relative error = 1.9742584862281359244106437022219e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.604 y[1] (closed_form) = -1.0133185901645318371434230606528 y[1] (numeric) = -1.0133185901645318371434230606526 absolute error = 2e-31 relative error = 1.9737129264304342686742565813469e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.605 y[1] (closed_form) = -1.0135983558255091122005929693204 y[1] (numeric) = -1.0135983558255091122005929693203 absolute error = 1e-31 relative error = 9.8658407864677903223812695475112e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.606 y[1] (closed_form) = -1.0138778704689901842764935268911 y[1] (numeric) = -1.013877870468990184276493526891 absolute error = 1e-31 relative error = 9.8631208859251392065285307720563e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.607 y[1] (closed_form) = -1.0141571343890413586978700768424 y[1] (numeric) = -1.0141571343890413586978700768423 absolute error = 1e-31 relative error = 9.8604049223834525347674332765327e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.608 y[1] (closed_form) = -1.0144361478793580531372863542673 y[1] (numeric) = -1.0144361478793580531372863542671 absolute error = 2e-31 relative error = 1.9715385775447054084176211713667e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.609 y[1] (closed_form) = -1.0147149112332651439215824923232 y[1] (numeric) = -1.014714911233265143921582492323 absolute error = 2e-31 relative error = 1.9709969547695304456570508232268e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.61 y[1] (closed_form) = -1.0149934247437173128543717568226 y[1] (numeric) = -1.0149934247437173128543717568224 absolute error = 2e-31 relative error = 1.9704561145359082379630157539480e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.611 y[1] (closed_form) = -1.015271688703299394546921550942 y[1] (numeric) = -1.0152716887032993945469215509418 absolute error = 2e-31 relative error = 1.9699160552328523427184102412606e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.612 y[1] (closed_form) = -1.015549703404226724251793685188 y[1] (numeric) = -1.0155497034042267242517936851878 absolute error = 2e-31 relative error = 1.9693767752536335263165970467481e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.613 y[1] (closed_form) = -1.0158274691383454861936482378634 y[1] (numeric) = -1.0158274691383454861936482378632 absolute error = 2e-31 relative error = 1.9688382729957660870122995291303e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.614 y[1] (closed_form) = -1.0161049861971330623916445387347 y[1] (numeric) = -1.0161049861971330623916445387345 absolute error = 2e-31 relative error = 1.9683005468609942294783145168151e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.615 y[1] (closed_form) = -1.0163822548716983819679018938144 y[1] (numeric) = -1.0163822548716983819679018938142 absolute error = 2e-31 relative error = 1.9677635952552784908429071680757e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.616 y[1] (closed_form) = -1.016659275452782270936511632536 y[1] (numeric) = -1.0166592754527822709365116325358 absolute error = 2e-31 relative error = 1.9672274165887822179838610839669e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.617 y[1] (closed_form) = -1.0169360482307578024676209005257 y[1] (numeric) = -1.0169360482307578024676209005254 absolute error = 3e-31 relative error = 2.9500380139137871437843942262857e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.618 y[1] (closed_form) = -1.0172125734956306476211373420518 y[1] (numeric) = -1.0172125734956306476211373420516 absolute error = 2e-31 relative error = 1.9661573717350347266321996807807e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.619 y[1] (closed_form) = -1.0174888515370394265446324164765 y[1] (numeric) = -1.0174888515370394265446324164762 absolute error = 3e-31 relative error = 2.9484352535835048891474651394292e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.62 y[1] (closed_form) = -1.0177648826442560601300495730236 y[1] (numeric) = -1.0177648826442560601300495730234 absolute error = 2e-31 relative error = 1.9650903996646040704248800094666e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.621 y[1] (closed_form) = -1.0180406671061861221238518683366 y[1] (numeric) = -1.0180406671061861221238518683364 absolute error = 2e-31 relative error = 1.9645580619928134930879272594581e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.622 y[1] (closed_form) = -1.018316205211369191685271852 y[1] (numeric) = -1.0183162052113691916852718519997 absolute error = 3e-31 relative error = 2.9460397317130958975901869036881e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.623 y[1] (closed_form) = -1.0185914972479792063873546668637 y[1] (numeric) = -1.0185914972479792063873546668635 absolute error = 2e-31 relative error = 1.9634956755515640247208153631386e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.624 y[1] (closed_form) = -1.0188665435038248156555133140183 y[1] (numeric) = -1.018866543503824815655513314018 memory used=37.1MB, alloc=40.3MB, time=0.52 absolute error = 3e-31 relative error = 2.9444484354969282859046589788524e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.625 y[1] (closed_form) = -1.0191413442663497346383429170231 y[1] (numeric) = -1.0191413442663497346383429170228 absolute error = 3e-31 relative error = 2.9436544958929253351456167073972e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.626 y[1] (closed_form) = -1.0194158998226330985054685868957 y[1] (numeric) = -1.0194158998226330985054685868954 absolute error = 3e-31 relative error = 2.9428616921925254058438186787245e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.627 y[1] (closed_form) = -1.0196902104593898171672291388033 y[1] (numeric) = -1.019690210459389817167229138803 absolute error = 3e-31 relative error = 2.9420700220790027889587574966974e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.628 y[1] (closed_form) = -1.0199642764629709304110264437729 y[1] (numeric) = -1.0199642764629709304110264437726 absolute error = 3e-31 relative error = 2.9412794832416984583141692345269e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.629 y[1] (closed_form) = -1.0202380981193639634491976144342 y[1] (numeric) = -1.0202380981193639634491976144339 absolute error = 3e-31 relative error = 2.9404900733760007562066346540415e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.63 y[1] (closed_form) = -1.0205116757141932828732945232312 y[1] (numeric) = -1.020511675714193282873294523231 absolute error = 2e-31 relative error = 1.9598011934555507675764509282270e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.631 y[1] (closed_form) = -1.0207850095327204530096823350723 y[1] (numeric) = -1.0207850095327204530096823350721 absolute error = 2e-31 relative error = 1.9592764209140667126308369757500e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.632 y[1] (closed_form) = -1.0210580998598445926713958044295 y[1] (numeric) = -1.0210580998598445926713958044293 absolute error = 2e-31 relative error = 1.9587523964351585281760648568171e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.633 y[1] (closed_form) = -1.0213309469801027323012190398388 y[1] (numeric) = -1.0213309469801027323012190398385 absolute error = 3e-31 relative error = 2.9373436777476254359297959247823e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.634 y[1] (closed_form) = -1.0216035511776701715009812769787 y[1] (numeric) = -1.0216035511776701715009812769784 absolute error = 3e-31 relative error = 2.9365598783811009901091554311984e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.635 y[1] (closed_form) = -1.0218759127363608369420879254161 y[1] (numeric) = -1.0218759127363608369420879254158 absolute error = 3e-31 relative error = 2.9357771942844354355827290059646e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.636 y[1] (closed_form) = -1.0221480319396276406523327640814 y[1] (numeric) = -1.0221480319396276406523327640811 absolute error = 3e-31 relative error = 2.9349956231948139293070104440877e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.637 y[1] (closed_form) = -1.0224199090705628386740636569746 y[1] (numeric) = -1.0224199090705628386740636569742 absolute error = 4e-31 relative error = 3.9122868838070894135642903667542e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.638 y[1] (closed_form) = -1.022691544411898390088800543882 y[1] (numeric) = -1.0226915444118983900888005438816 absolute error = 4e-31 relative error = 3.9112477480198695662161152183968e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.639 y[1] (closed_form) = -1.0229629382460063164034307314038 y[1] (numeric) = -1.0229629382460063164034307314034 absolute error = 4e-31 relative error = 3.9102100872378463627927445843385e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.64 y[1] (closed_form) = -1.0232340908548990612931326677265 y[1] (numeric) = -1.023234090854899061293132667726 absolute error = 5e-31 relative error = 4.8864673730940332819661931569450e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.641 y[1] (closed_form) = -1.0235050025202298506962054307213 y[1] (numeric) = -1.0235050025202298506962054307208 absolute error = 5e-31 relative error = 4.8851739734424733892712655592292e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.642 y[1] (closed_form) = -1.0237756735232930532560070934894 y[1] (numeric) = -1.0237756735232930532560070934889 absolute error = 5e-31 relative error = 4.8838824063797599767954636528409e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.643 y[1] (closed_form) = -1.0240461041450245411052309547881 y[1] (numeric) = -1.0240461041450245411052309547875 absolute error = 6e-31 relative error = 5.8591112018431985428149941102425e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.644 y[1] (closed_form) = -1.0243162946660020509877743342532 y[1] (numeric) = -1.0243162946660020509877743342526 absolute error = 6e-31 relative error = 5.8575657062610869937352233128663e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.645 y[1] (closed_form) = -1.0245862453664455457134802343583 y[1] (numeric) = -1.0245862453664455457134802343577 absolute error = 6e-31 relative error = 5.8560223964885324780135003647156e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.646 y[1] (closed_form) = -1.0248559565262175759410576630018 y[1] (numeric) = -1.0248559565262175759410576630013 absolute error = 5e-31 relative error = 4.8787343900967915295825162404301e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.647 y[1] (closed_form) = -1.0251254284248236422845117928801 y[1] (numeric) = -1.0251254284248236422845117928796 absolute error = 5e-31 relative error = 4.8774519306216478963057071131223e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.648 y[1] (closed_form) = -1.025394661341412557738440406758 y[1] (numeric) = -1.0253946613414125577384404067574 absolute error = 6e-31 relative error = 5.8514055379914413938122377877707e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.649 y[1] (closed_form) = -1.0256636555547768104175782417792 y[1] (numeric) = -1.0256636555547768104175782417786 absolute error = 6e-31 relative error = 5.8498709274773193220925944018235e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.65 y[1] (closed_form) = -1.0259324113433529266059959014387 y[1] (numeric) = -1.0259324113433529266059959014381 absolute error = 6e-31 relative error = 5.8483384808397050113481824659516e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.651 y[1] (closed_form) = -1.0262009289852218341113849511525 y[1] (numeric) = -1.0262009289852218341113849511519 absolute error = 6e-31 relative error = 5.8468081937259726466353609559315e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.652 y[1] (closed_form) = -1.0264692087581092259198856528828 y[1] (numeric) = -1.0264692087581092259198856528822 absolute error = 6e-31 relative error = 5.8452800617947413938089092945662e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.653 y[1] (closed_form) = -1.0267372509393859241469385263886 y[1] (numeric) = -1.026737250939385924146938526388 absolute error = 6e-31 relative error = 5.8437540807158400772927127893318e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.654 y[1] (closed_form) = -1.0270050558060682442796655497461 y[1] (numeric) = -1.0270050558060682442796655497455 absolute error = 6e-31 relative error = 5.8422302461702719883807880573529e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.655 y[1] (closed_form) = -1.0272726236348183597063113302 y[1] (numeric) = -1.0272726236348183597063113301994 absolute error = 6e-31 relative error = 5.8407085538501798235133217256992e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.656 y[1] (closed_form) = -1.0275399547019446665282989885398 y[1] (numeric) = -1.0275399547019446665282989885392 absolute error = 6e-31 relative error = 5.8391889994588107519750743080505e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.657 y[1] (closed_form) = -1.0278070492834021486504798064199 y[1] (numeric) = -1.0278070492834021486504798064193 absolute error = 6e-31 relative error = 5.8376715787104816124661652932972e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.658 y[1] (closed_form) = -1.0280739076547927431451798867289 y[1] (numeric) = -1.0280739076547927431451798867283 absolute error = 6e-31 relative error = 5.8361562873305442379979052245236e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.659 y[1] (closed_form) = -1.0283405300913657058856711726431 y[1] (numeric) = -1.0283405300913657058856711726425 absolute error = 6e-31 relative error = 5.8346431210553509085689759842852e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.66 y[1] (closed_form) = -1.0286069168680179774447181617342 y[1] (numeric) = -1.0286069168680179774447181617336 absolute error = 6e-31 relative error = 5.8331320756322199310798817199252e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.661 y[1] (closed_form) = -1.0288730682592945492538755378225 y[1] (numeric) = -1.0288730682592945492538755378219 absolute error = 6e-31 relative error = 5.8316231468194013459461999259718e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.662 y[1] (closed_form) = -1.0291389845393888300192357255379 y[1] (numeric) = -1.0291389845393888300192357255373 absolute error = 6e-31 relative error = 5.8301163303860427598737552340514e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.663 y[1] (closed_form) = -1.0294046659821430123893490511472 y[1] (numeric) = -1.0294046659821430123893490511466 absolute error = 6e-31 relative error = 5.8286116221121553042614175282429e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.664 y[1] (closed_form) = -1.0296701128610484398710627684934 y[1] (numeric) = -1.0296701128610484398710627684928 absolute error = 6e-31 relative error = 5.8271090177885797186997911888878e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.665 y[1] (closed_form) = -1.0299353254492459739890486812413 y[1] (numeric) = -1.0299353254492459739890486812407 absolute error = 6e-31 relative error = 5.8256085132169525590366136534791e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.666 y[1] (closed_form) = -1.0302003040195263616848124624 y[1] (numeric) = -1.0302003040195263616848124623995 absolute error = 5e-31 relative error = 4.8534250868413937745685159598058e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.667 y[1] (closed_form) = -1.0304650488443306029510010396658 y[1] (numeric) = -1.0304650488443306029510010396652 absolute error = 6e-31 relative error = 5.8226137865898669382309475054841e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.668 y[1] (closed_form) = -1.0307295601957503186968475808608 y[1] (numeric) = -1.0307295601957503186968475808602 absolute error = 6e-31 relative error = 5.8211195561913582760768883624261e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.669 y[1] (closed_form) = -1.0309938383455281188406166780065 y[1] (numeric) = -1.0309938383455281188406166780059 absolute error = 6e-31 relative error = 5.8196274088586309175048482407590e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.67 y[1] (closed_form) = -1.0312578835650579706249352917186 y[1] (numeric) = -1.031257883565057970624935291718 absolute error = 6e-31 relative error = 5.8181373404467979437399113726815e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.671 y[1] (closed_form) = -1.0315216961253855671509178800198 y[1] (numeric) = -1.0315216961253855671509178800191 absolute error = 7e-31 relative error = 6.7860909046251627684483415760003e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.672 y[1] (closed_form) = -1.0317852762972086961270168976902 y[1] (numeric) = -1.0317852762972086961270168976895 absolute error = 7e-31 relative error = 6.7843573278357482633180789215599e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.673 y[1] (closed_form) = -1.0320486243508776088285525142806 y[1] (numeric) = -1.0320486243508776088285525142799 absolute error = 7e-31 relative error = 6.7826261620209556625426058135853e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.674 y[1] (closed_form) = -1.0323117405563953892638979612579 y[1] (numeric) = -1.0323117405563953892638979612572 absolute error = 7e-31 relative error = 6.7808974023942999526831584289193e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.675 y[1] (closed_form) = -1.0325746251834183235433193818035 y[1] (numeric) = -1.0325746251834183235433193818028 absolute error = 7e-31 relative error = 6.7791710441815048593343211878944e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.676 y[1] (closed_form) = -1.0328372785012562694464914208908 y[1] (numeric) = -1.0328372785012562694464914208901 absolute error = 7e-31 relative error = 6.7774470826204649818949108479010e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.677 y[1] (closed_form) = -1.0330997007788730261847320588002 y[1] (numeric) = -1.0330997007788730261847320587995 absolute error = 7e-31 relative error = 6.7757255129612080664845880109801e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.678 y[1] (closed_form) = -1.0333618922848867043540223585378 y[1] (numeric) = -1.033361892284886704354022358537 absolute error = 8e-31 relative error = 7.7417215205324084759155327089157e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.679 y[1] (closed_form) = -1.0336238532875700960748988670659 y[1] (numeric) = -1.0336238532875700960748988670652 absolute error = 7e-31 relative error = 6.7722895304085944397157490564181e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.68 y[1] (closed_form) = -1.0338855840548510453153283821921 y[1] (numeric) = -1.0338855840548510453153283821914 absolute error = 7e-31 relative error = 6.7705751080756213329076747582604e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.681 y[1] (closed_form) = -1.0341470848543128183926966717421 y[1] (numeric) = -1.0341470848543128183926966717414 absolute error = 7e-31 relative error = 6.7688630587651239008397739730989e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.682 y[1] (closed_form) = -1.034408355953194474651064509632 y[1] (numeric) = -1.0344083559531944746510645096313 absolute error = 7e-31 relative error = 6.7671533777872345116324203706343e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.683 y[1] (closed_form) = -1.0346693976183912373098660749934 y[1] (numeric) = -1.0346693976183912373098660749926 absolute error = 8e-31 relative error = 7.7319383548159944987352582000105e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.684 y[1] (closed_form) = -1.034930210116454864480246345955 y[1] (numeric) = -1.0349302101164548644802463459542 absolute error = 8e-31 relative error = 7.7299898310049380835028842974328e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.685 y[1] (closed_form) = -1.0351907937135940203452556094 y[1] (numeric) = -1.0351907937135940203452556093992 absolute error = 8e-31 relative error = 7.7280439978616714901181196049292e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.686 y[1] (closed_form) = -1.0354511486756746465001406023373 y[1] (numeric) = -1.0354511486756746465001406023366 absolute error = 7e-31 relative error = 6.7603382438204712356794081887588e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.687 y[1] (closed_form) = -1.0357112752682203334489930998183 y[1] (numeric) = -1.0357112752682203334489930998176 absolute error = 7e-31 relative error = 6.7586403345731610730982651991830e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.688 y[1] (closed_form) = -1.0359711737564126922540379689265 y[1] (numeric) = -1.0359711737564126922540379689258 absolute error = 7e-31 relative error = 6.7569447657680733731319198084786e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.689 y[1] (closed_form) = -1.0362308444050917263338638186339 y[1] (numeric) = -1.0362308444050917263338638186332 absolute error = 7e-31 relative error = 6.7552515327979404314656769942663e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.69 y[1] (closed_form) = -1.0364902874787562034069203915875 y[1] (numeric) = -1.0364902874787562034069203915868 absolute error = 7e-31 relative error = 6.7535606310671495494601254348885e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.691 y[1] (closed_form) = -1.0367495032415640275766277665203 y[1] (numeric) = -1.0367495032415640275766277665196 absolute error = 7e-31 relative error = 6.7518720559917071814333503771844e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.692 y[1] (closed_form) = -1.0370084919573326115544632693128 y[1] (numeric) = -1.0370084919573326115544632693121 absolute error = 7e-31 relative error = 6.7501858029992032116706275548249e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.693 y[1] (closed_form) = -1.0372672538895392490174127271123 y[1] (numeric) = -1.0372672538895392490174127271116 absolute error = 7e-31 relative error = 6.7485018675287753606214018388441e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.694 y[1] (closed_form) = -1.0375257893013214870961933436928 y[1] (numeric) = -1.0375257893013214870961933436921 absolute error = 7e-31 relative error = 6.7468202450310737197459034022100e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.695 y[1] (closed_form) = -1.037784098455477498990676025748 y[1] (numeric) = -1.0377840984554774989906760257473 absolute error = 7e-31 relative error = 6.7451409309682254144762898073551e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.696 y[1] (closed_form) = -1.0380421816144664567089554494038 y[1] (numeric) = -1.0380421816144664567089554494031 absolute error = 7e-31 relative error = 6.7434639208137993947597246585187e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.697 y[1] (closed_form) = -1.038300039040408903926536524248 y[1] (numeric) = -1.0383000390404089039265365242473 absolute error = 7e-31 relative error = 6.7417892100527713526533123780750e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.698 y[1] (closed_form) = -1.038557670995087128962126188953 y[1] (numeric) = -1.0385576709950871289621261889522 absolute error = 8e-31 relative error = 7.7029906219217014473637763950644e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.699 y[1] (closed_form) = -1.0388150777399455378665396584461 y[1] (numeric) = -1.0388150777399455378665396584453 absolute error = 8e-31 relative error = 7.7010819070944412237296847526919e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (closed_form) = -1.0390722595360910276212503379073 y[1] (numeric) = -1.0390722595360910276212503379065 absolute error = 8e-31 relative error = 7.6991758047430856596457476662046e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.701 y[1] (closed_form) = -1.0393292166442933594431326239748 y[1] (numeric) = -1.039329216644293359443132623974 absolute error = 8e-31 relative error = 7.6972723097593540226204367943251e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.702 y[1] (closed_form) = -1.0395859493249855321919667287672 y[1] (numeric) = -1.0395859493249855321919667287664 absolute error = 8e-31 relative error = 7.6953714170478035430006282420110e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.703 y[1] (closed_form) = -1.0398424578382641558772944880061 y[1] (numeric) = -1.0398424578382641558772944880053 absolute error = 8e-31 relative error = 7.6934731215257901784438578874278e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.704 y[1] (closed_form) = -1.0400987424438898252612348509983 y[1] (numeric) = -1.0400987424438898252612348509974 absolute error = 9e-31 relative error = 8.6530245953888582093599651057326e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.705 y[1] (closed_form) = -1.0403548034012874935538873978328 y[1] (numeric) = -1.0403548034012874935538873978319 absolute error = 9e-31 relative error = 8.6508948395065025646410906194064e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.706 y[1] (closed_form) = -1.0406106409695468461979717882109 y[1] (numeric) = -1.04061064096954684619797178821 absolute error = 9e-31 relative error = 8.6487679883944049172457318367933e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.707 y[1] (closed_form) = -1.0408662554074226747393705171791 y[1] (numeric) = -1.0408662554074226747393705171782 absolute error = 9e-31 relative error = 8.6466440363917467563342684713637e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.708 y[1] (closed_form) = -1.0411216469733352507802617360203 y[1] (numeric) = -1.0411216469733352507802617360194 absolute error = 9e-31 relative error = 8.6445229778518898064259398430795e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.709 y[1] (closed_form) = -1.0413768159253707000115481919974 y[1] (numeric) = -1.0413768159253707000115481919964 absolute error = 1.0e-30 relative error = 9.6026720079359253662998380548771e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.71 y[1] (closed_form) = -1.0416317625212813763213075488757 y[1] (numeric) = -1.0416317625212813763213075488748 absolute error = 9e-31 relative error = 8.6402895186446685828944022342828e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.711 y[1] (closed_form) = -1.0418864870184862359760084715006 y[1] (numeric) = -1.0418864870184862359760084714997 absolute error = 9e-31 relative error = 8.6381771067545409287969596581956e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.712 y[1] (closed_form) = -1.0421409896740712118712558925046 y[1] (numeric) = -1.0421409896740712118712558925037 absolute error = 9e-31 relative error = 8.6360675658816021006387471000434e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.713 y[1] (closed_form) = -1.0423952707447895878488478277957 y[1] (numeric) = -1.0423952707447895878488478277948 absolute error = 9e-31 relative error = 8.6339608904494701198126771603298e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.714 y[1] (closed_form) = -1.0426493304870623730769449701572 y[1] (numeric) = -1.0426493304870623730769449701562 absolute error = 1.0e-30 relative error = 9.5909523054396515173944119685222e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.715 y[1] (closed_form) = -1.0429031691569786764901730673983 y[1] (numeric) = -1.0429031691569786764901730673973 absolute error = 1.0e-30 relative error = 9.5886179040796369965269530555733e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.716 y[1] (closed_form) = -1.0431567870102960812864967833629 y[1] (numeric) = -1.0431567870102960812864967833619 absolute error = 1.0e-30 relative error = 9.5862866680474359155275506951969e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.717 y[1] (closed_form) = -1.0434101843024410194777223470474 y[1] (numeric) = -1.0434101843024410194777223470464 absolute error = 1.0e-30 relative error = 9.5839585912086687022814937407696e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.718 y[1] (closed_form) = -1.0436633612885091464905048174304 y[1] (numeric) = -1.0436633612885091464905048174294 absolute error = 1.0e-30 relative error = 9.5816336674442392815023589292596e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.719 y[1] (closed_form) = -1.0439163182232657158147542296939 y[1] (numeric) = -1.0439163182232657158147542296928 absolute error = 1.1e-30 relative error = 1.0537243079715317642053847310091e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.72 y[1] (closed_form) = -1.0441690553611459536963532426421 y[1] (numeric) = -1.044169055361145953696353242641 absolute error = 1.1e-30 relative error = 1.0534692580211964241002577780581e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.721 y[1] (closed_form) = -1.0444215729562554338711171776211 y[1] (numeric) = -1.04442157295625543387111717762 absolute error = 1.1e-30 relative error = 1.0532145528997727947708964707052e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.722 y[1] (closed_form) = -1.0446738712623704523369455264271 y[1] (numeric) = -1.0446738712623704523369455264261 absolute error = 1.0e-30 relative error = 9.5723653812803117050287233485355e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.723 y[1] (closed_form) = -1.0449259505329384021611321098912 y[1] (numeric) = -1.0449259505329384021611321098902 absolute error = 1.0e-30 relative error = 9.5700561316328200831984887329475e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.724 y[1] (closed_form) = -1.0451778110210781483198190903494 y[1] (numeric) = -1.0451778110210781483198190903483 absolute error = 1.1e-30 relative error = 1.0524524998529807576526655637259e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.725 y[1] (closed_form) = -1.0454294529795804025665979803791 y[1] (numeric) = -1.045429452979580402566597980378 absolute error = 1.1e-30 relative error = 1.0521991673994720363192771087814e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.726 y[1] (closed_form) = -1.0456808766609080983272786473166 y[1] (numeric) = -1.0456808766609080983272786473155 absolute error = 1.1e-30 relative error = 1.0519461764592510851022434392873e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.727 y[1] (closed_form) = -1.0459320823171967656178650884773 y[1] (numeric) = -1.0459320823171967656178650884761 absolute error = 1.2e-30 relative error = 1.1473020287717682870413953957898e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.728 y[1] (closed_form) = -1.0461830702002549059827944460079 y[1] (numeric) = -1.0461830702002549059827944460068 absolute error = 1.1e-30 relative error = 1.0514412164875156487151503342649e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.729 y[1] (closed_form) = -1.0464338405615643674505133432104 y[1] (numeric) = -1.0464338405615643674505133432092 absolute error = 1.2e-30 relative error = 1.1467519048849041348955587742930e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.73 y[1] (closed_form) = -1.0466843936522807195034831563044 y[1] (numeric) = -1.0466843936522807195034831563032 absolute error = 1.2e-30 relative error = 1.1464773978455365179394934670042e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.731 y[1] (closed_form) = -1.0469347297232336280597232872656 y[1] (numeric) = -1.0469347297232336280597232872644 absolute error = 1.2e-30 relative error = 1.1462032597936936505289293761292e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.732 y[1] (closed_form) = -1.0471848490249272304630188748779 y[1] (numeric) = -1.0471848490249272304630188748767 absolute error = 1.2e-30 relative error = 1.1459294900201856830989130780254e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.733 y[1] (closed_form) = -1.0474347518075405104789366728037 y[1] (numeric) = -1.0474347518075405104789366728025 absolute error = 1.2e-30 relative error = 1.1456560878175754720691843853528e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.734 y[1] (closed_form) = -1.0476844383209276732938100356012 y[1] (numeric) = -1.0476844383209276732938100356 absolute error = 1.2e-30 relative error = 1.1453830524801733114388171002851e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.735 y[1] (closed_form) = -1.0479339088146185205138710865148 y[1] (numeric) = -1.0479339088146185205138710865136 absolute error = 1.2e-30 relative error = 1.1451103833040316830055258442015e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.736 y[1] (closed_form) = -1.0481831635378188251617251948455 y[1] (numeric) = -1.0481831635378188251617251948443 absolute error = 1.2e-30 relative error = 1.1448380795869400251338956766369e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.737 y[1] (closed_form) = -1.0484322027394107066673798660733 y[1] (numeric) = -1.0484322027394107066673798660721 absolute error = 1.2e-30 relative error = 1.1445661406284195199971401120796e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.738 y[1] (closed_form) = -1.048681026667953005851057044964 y[1] (numeric) = -1.0486810266679530058510570449628 absolute error = 1.2e-30 relative error = 1.1442945657297178992173402398693e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.739 y[1] (closed_form) = -1.0489296355716816598950346509516 y[1] (numeric) = -1.0489296355716816598950346509504 absolute error = 1.2e-30 relative error = 1.1440233541938042678294629602534e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.74 y[1] (closed_form) = -1.0491780296985100773017799064475 y[1] (numeric) = -1.0491780296985100773017799064463 absolute error = 1.2e-30 relative error = 1.1437525053253639464947998788342e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.741 y[1] (closed_form) = -1.0494262092960295128356536826984 y[1] (numeric) = -1.0494262092960295128356536826972 absolute error = 1.2e-30 relative error = 1.1434820184307933318898101623329e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.742 y[1] (closed_form) = -1.0496741746115094424454816746877 y[1] (numeric) = -1.0496741746115094424454816746865 absolute error = 1.2e-30 relative error = 1.1432118928181947751966906609218e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.743 y[1] (closed_form) = -1.0499219258918979381653047266663 y[1] (numeric) = -1.0499219258918979381653047266651 absolute error = 1.2e-30 relative error = 1.1429421277973714786223348563426e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.744 y[1] (closed_form) = -1.0501694633838220429906370634934 y[1] (numeric) = -1.0501694633838220429906370634922 absolute error = 1.2e-30 relative error = 1.1426727226798224098726787106318e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.745 y[1] (closed_form) = -1.0504167873335881457275775403811 y[1] (numeric) = -1.0504167873335881457275775403799 absolute error = 1.2e-30 relative error = 1.1424036767787372345097662773971e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.746 y[1] (closed_form) = -1.0506638979871823558121353051524 y[1] (numeric) = -1.0506638979871823558121353051512 absolute error = 1.2e-30 relative error = 1.1421349894089912661192010060941e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.747 y[1] (closed_form) = -1.0509107955902708780971474730531 y[1] (numeric) = -1.050910795590270878097147473052 absolute error = 1.1e-30 relative error = 1.0467111048965453980313150269618e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.748 y[1] (closed_form) = -1.0511574803882003876041825447895 y[1] (numeric) = -1.0511574803882003876041825447883 absolute error = 1.2e-30 relative error = 1.1415986875314162698170383844273e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.749 y[1] (closed_form) = -1.0514039526259984042378393540978 y[1] (numeric) = -1.0514039526259984042378393540966 absolute error = 1.2e-30 relative error = 1.1413310716617209086091580892417e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.75 y[1] (closed_form) = -1.0516502125483736674598673120863 y[1] (numeric) = -1.0516502125483736674598673120851 absolute error = 1.2e-30 relative error = 1.1410638115996221116412232880962e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.751 y[1] (closed_form) = -1.0518962603997165109205496221103 y[1] (numeric) = -1.0518962603997165109205496221091 absolute error = 1.2e-30 relative error = 1.1407969066683483034701272988026e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.752 y[1] (closed_form) = -1.0521420964240992370448069713523 y[1] (numeric) = -1.0521420964240992370448069713511 absolute error = 1.2e-30 relative error = 1.1405303561927836276899603564519e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.753 y[1] (closed_form) = -1.0523877208652764915704949638652 y[1] (numeric) = -1.052387720865276491570494963864 absolute error = 1.2e-30 relative error = 1.1402641594994630197744281559983e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.754 y[1] (closed_form) = -1.0526331339666856380363842448938 y[1] (numeric) = -1.0526331339666856380363842448926 absolute error = 1.2e-30 relative error = 1.1399983159165672971627709629272e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.755 y[1] (closed_form) = -1.0528783359714471322173278781071 y[1] (numeric) = -1.0528783359714471322173278781059 absolute error = 1.2e-30 relative error = 1.1397328247739182665197710950808e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.756 y[1] (closed_form) = -1.053123327122364896504136076245 y[1] (numeric) = -1.0531233271223648965041360762438 absolute error = 1.2e-30 relative error = 1.1394676854029738481007529890746e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.757 y[1] (closed_form) = -1.0533681076619266942256938518897 y[1] (numeric) = -1.0533681076619266942256938518885 absolute error = 1.2e-30 relative error = 1.1392028971368232171527948607892e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.758 y[1] (closed_form) = -1.0536126778323045039108725489141 y[1] (numeric) = -1.0536126778323045039108725489129 absolute error = 1.2e-30 relative error = 1.1389384593101819622836841602977e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.759 y[1] (closed_form) = -1.0538570378753548934878015369111 y[1] (numeric) = -1.0538570378753548934878015369099 absolute error = 1.2e-30 relative error = 1.1386743712593872607304606163541e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.76 y[1] (closed_form) = -1.0541011880326193944180816008678 y[1] (numeric) = -1.0541011880326193944180816008665 absolute error = 1.3e-30 relative error = 1.2332781850159258263313423960294e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.761 y[1] (closed_form) = -1.0543451285453248757635367367935 y[1] (numeric) = -1.0543451285453248757635367367923 absolute error = 1.2e-30 relative error = 1.1381472418387653390320055524683e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.762 y[1] (closed_form) = -1.0545888596543839181831161712323 y[1] (numeric) = -1.0545888596543839181831161712311 absolute error = 1.2e-30 relative error = 1.1378841991496772291634620316908e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.763 y[1] (closed_form) = -1.0548323816003951878575734588655 y[1] (numeric) = -1.0548323816003951878575734588643 absolute error = 1.2e-30 relative error = 1.1376215035979043609171503341428e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.764 y[1] (closed_form) = -1.0550756946236438103395644780314 y[1] (numeric) = -1.0550756946236438103395644780301 absolute error = 1.3e-30 relative error = 1.2321390840718050763295837082145e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.765 y[1] (closed_form) = -1.0553187989641017443268210392272 y[1] (numeric) = -1.0553187989641017443268210392259 absolute error = 1.3e-30 relative error = 1.2318552472258399090806495514683e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.766 y[1] (closed_form) = -1.0555616948614281553560716468066 y[1] (numeric) = -1.0555616948614281553560716468054 absolute error = 1.2e-30 relative error = 1.1368354932181708160146262519330e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.767 y[1] (closed_form) = -1.055804382554969789415395709414 y[1] (numeric) = -1.0558043825549697894153957094128 absolute error = 1.2e-30 relative error = 1.1365741796752986642279567410751e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.768 y[1] (closed_form) = -1.0560468622837613464727121804917 y[1] (numeric) = -1.0560468622837613464727121804905 absolute error = 1.2e-30 relative error = 1.1363132100074913470208715889938e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.769 y[1] (closed_form) = -1.0562891342865258539181182267354 y[1] (numeric) = -1.0562891342865258539181182267342 absolute error = 1.2e-30 relative error = 1.1360525835670402374863106655475e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.77 y[1] (closed_form) = -1.0565311988016750399178080699299 y[1] (numeric) = -1.0565311988016750399178080699286 absolute error = 1.3e-30 relative error = 1.2304416580167901816117083418069e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.771 y[1] (closed_form) = -1.0567730560673097066773166264532 y[1] (numeric) = -1.0567730560673097066773166264519 absolute error = 1.3e-30 relative error = 1.2301600542673168680609462834830e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.772 y[1] (closed_form) = -1.0570147063212201036118469791709 y[1] (numeric) = -1.0570147063212201036118469791696 absolute error = 1.3e-30 relative error = 1.2298788202526088581481295451807e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.773 y[1] (closed_form) = -1.057256149800886300421455058718 y[1] (numeric) = -1.0572561498008863004214550587167 absolute error = 1.3e-30 relative error = 1.2295979552777534544202629982869e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.774 y[1] (closed_form) = -1.0574973867434785600688791855726 y[1] (numeric) = -1.0574973867434785600688791855713 absolute error = 1.3e-30 relative error = 1.2293174586495184263043862600676e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.775 y[1] (closed_form) = -1.057738417385857711657816331125 y[1] (numeric) = -1.0577384173858577116578163311238 absolute error = 1.2e-30 relative error = 1.1344959966243203690479042336732e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.776 y[1] (closed_form) = -1.0579792419645755232094610954174 y[1] (numeric) = -1.0579792419645755232094610954161 absolute error = 1.3e-30 relative error = 1.2287575676683532642855639484393e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.777 y[1] (closed_form) = -1.0582198607158750743351374716394 y[1] (numeric) = -1.0582198607158750743351374716381 absolute error = 1.3e-30 relative error = 1.2284781719373165963312006729232e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.778 y[1] (closed_form) = -1.0584602738756911288028674730938 y[1] (numeric) = -1.0584602738756911288028674730925 absolute error = 1.3e-30 relative error = 1.2281991417966774338495691938642e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.779 y[1] (closed_form) = -1.0587004816796505069957346374499 y[1] (numeric) = -1.0587004816796505069957346374486 absolute error = 1.3e-30 relative error = 1.2279204765615320671177730766535e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.78 y[1] (closed_form) = -1.0589404843630724582599142959644 y[1] (numeric) = -1.0589404843630724582599142959631 absolute error = 1.3e-30 relative error = 1.2276421755486278466429945627031e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.781 y[1] (closed_form) = -1.0591802821609690331402563022281 y[1] (numeric) = -1.0591802821609690331402563022268 absolute error = 1.3e-30 relative error = 1.2273642380763583411250864356140e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.782 y[1] (closed_form) = -1.0594198753080454555013196561638 y[1] (numeric) = -1.0594198753080454555013196561625 absolute error = 1.3e-30 relative error = 1.2270866634647585121181570465233e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.783 y[1] (closed_form) = -1.0596592640387004945317721347226 y[1] (numeric) = -1.0596592640387004945317721347213 absolute error = 1.3e-30 relative error = 1.2268094510354999053249198616471e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.784 y[1] (closed_form) = -1.0598984485870268366300816512671 y[1] (numeric) = -1.0598984485870268366300816512657 absolute error = 1.4e-30 relative error = 1.3208812616589540014161744248589e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.785 y[1] (closed_form) = -1.0601374291868114571694396112554 y[1] (numeric) = -1.060137429186811457169439611254 absolute error = 1.4e-30 relative error = 1.3205835030972195506479804211304e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.786 y[1] (closed_form) = -1.0603762060715359921398700128174 y[1] (numeric) = -1.0603762060715359921398700128161 absolute error = 1.3e-30 relative error = 1.2259799800829351180114552273661e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.787 y[1] (closed_form) = -1.0606147794743771096654914573981 y[1] (numeric) = -1.0606147794743771096654914573968 absolute error = 1.3e-30 relative error = 1.2257042096323211612816813801389e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.788 y[1] (closed_form) = -1.0608531496282068813949125881078 y[1] (numeric) = -1.0608531496282068813949125881065 absolute error = 1.3e-30 relative error = 1.2254287979967877688214522607511e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.789 y[1] (closed_form) = -1.0610913167655931537627547620153 y[1] (numeric) = -1.061091316765593153762754762014 absolute error = 1.3e-30 relative error = 1.2251537445077259315710786745940e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.79 y[1] (closed_form) = -1.061329281118799919120308987613 y[1] (numeric) = -1.0613292811187999191203089876117 absolute error = 1.3e-30 relative error = 1.2248790484981300238961946845943e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.791 y[1] (closed_form) = -1.0615670429197876867333473203349 y[1] (numeric) = -1.0615670429197876867333473203336 absolute error = 1.3e-30 relative error = 1.2246047093025931255953635881365e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.792 y[1] (closed_form) = -1.061804602400213853645122007572 y[1] (numeric) = -1.0618046024002138536451220075707 absolute error = 1.3e-30 relative error = 1.2243307262573023599575942100505e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.793 y[1] (closed_form) = -1.0620419597914330754025987103692 y[1] (numeric) = -1.062041959791433075402598710368 absolute error = 1.2e-30 relative error = 1.1298988603384931518213349609925e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.794 y[1] (closed_form) = -1.0622791153244976366439831021563 y[1] (numeric) = -1.0622791153244976366439831021551 absolute error = 1.2e-30 relative error = 1.1296466085878308407394023429270e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.795 y[1] (closed_form) = -1.0625160692301578215456130557209 y[1] (numeric) = -1.0625160692301578215456130557197 absolute error = 1.2e-30 relative error = 1.1293946837617765759363710250592e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.796 y[1] (closed_form) = -1.0627528217388622841263014784297 y[1] (numeric) = -1.0627528217388622841263014784285 absolute error = 1.2e-30 relative error = 1.1291430852534229696711731850435e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.797 y[1] (closed_form) = -1.0629893730807584184072276426995 y[1] (numeric) = -1.0629893730807584184072276426983 absolute error = 1.2e-30 relative error = 1.1288918124573127624984062536998e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.798 y[1] (closed_form) = -1.0632257234856927284254875841644 y[1] (numeric) = -1.0632257234856927284254875841632 absolute error = 1.2e-30 relative error = 1.1286408647694346076102520513155e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.799 y[1] (closed_form) = -1.0634618731832111980994268041349 y[1] (numeric) = -1.0634618731832111980994268041338 absolute error = 1.1e-30 relative error = 1.0343577214549506304574826157275e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop memory used=85.7MB, alloc=44.3MB, time=1.14 x[1] = -1.8 y[1] (closed_form) = -1.0636978224025596609438911160525 y[1] (numeric) = -1.0636978224025596609438911160514 absolute error = 1.1e-30 relative error = 1.0341282804504056510603587166800e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.801 y[1] (closed_form) = -1.0639335713726841696335440179519 y[1] (numeric) = -1.0639335713726841696335440179507 absolute error = 1.2e-30 relative error = 1.1278899663366795523907842416577e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.802 y[1] (closed_form) = -1.0641691203222313654124114547175 y[1] (numeric) = -1.0641691203222313654124114547163 absolute error = 1.2e-30 relative error = 1.1276403130703876487463288400568e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.803 y[1] (closed_form) = -1.0644044694795488473478272553968 y[1] (numeric) = -1.0644044694795488473478272553956 absolute error = 1.2e-30 relative error = 1.1273909819138132105239175865596e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.804 y[1] (closed_form) = -1.0646396190726855414269648922663 y[1] (numeric) = -1.0646396190726855414269648922651 absolute error = 1.2e-30 relative error = 1.1271419722715326410188634923689e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.805 y[1] (closed_form) = -1.0648745693293920694941535099859 y[1] (numeric) = -1.0648745693293920694941535099847 absolute error = 1.2e-30 relative error = 1.1268932835495391469270362159918e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.806 y[1] (closed_form) = -1.0651093204771211180271884152658 y[1] (numeric) = -1.0651093204771211180271884152645 absolute error = 1.3e-30 relative error = 1.2205319914181751894412204725296e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.807 y[1] (closed_form) = -1.0653438727430278067508584002558 y[1] (numeric) = -1.0653438727430278067508584002546 absolute error = 1.2e-30 relative error = 1.1263968664974456311092044455682e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.808 y[1] (closed_form) = -1.0655782263539700570859243966009 y[1] (numeric) = -1.0655782263539700570859243965997 absolute error = 1.2e-30 relative error = 1.1261491369863791921116703299326e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.809 y[1] (closed_form) = -1.0658123815365089604317960220182 y[1] (numeric) = -1.065812381536508960431796022017 absolute error = 1.2e-30 relative error = 1.1259017260336588597175593081175e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.81 y[1] (closed_form) = -1.0660463385169091462811645876063 y[1] (numeric) = -1.0660463385169091462811645876051 absolute error = 1.2e-30 relative error = 1.1256546330523006070506268172978e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.811 y[1] (closed_form) = -1.0662800975211391501648630821168 y[1] (numeric) = -1.0662800975211391501648630821156 absolute error = 1.2e-30 relative error = 1.1254078574567128074005017442789e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.812 y[1] (closed_form) = -1.0665136587748717814252355393604 y[1] (numeric) = -1.0665136587748717814252355393592 absolute error = 1.2e-30 relative error = 1.1251613986626922152621228322583e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.813 y[1] (closed_form) = -1.0667470225034844908163100270173 y[1] (numeric) = -1.0667470225034844908163100270161 absolute error = 1.2e-30 relative error = 1.1249152560874199610161427405635e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.814 y[1] (closed_form) = -1.0669801889320597379290812696193 y[1] (numeric) = -1.066980188932059737929081269618 absolute error = 1.3e-30 relative error = 1.2183918815785790224634887178037e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.815 y[1] (closed_form) = -1.0672131582853853584402206356041 y[1] (numeric) = -1.0672131582853853584402206356028 absolute error = 1.3e-30 relative error = 1.2181259103744715078208034726732e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.816 y[1] (closed_form) = -1.0674459307879549311825428783578 y[1] (numeric) = -1.0674459307879549311825428783565 absolute error = 1.3e-30 relative error = 1.2178602798554686390499721120509e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.817 y[1] (closed_form) = -1.0676785066639681450355706242843 y[1] (numeric) = -1.067678506663968145035570624283 absolute error = 1.3e-30 relative error = 1.2175949893961391721470509679900e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.818 y[1] (closed_form) = -1.0679108861373311656345491474241 y[1] (numeric) = -1.0679108861373311656345491474228 absolute error = 1.3e-30 relative error = 1.2173300383725301278259935216776e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.819 y[1] (closed_form) = -1.0681430694316570018962754602112 y[1] (numeric) = -1.0681430694316570018962754602099 absolute error = 1.3e-30 relative error = 1.2170654261621625398865253540464e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.82 y[1] (closed_form) = -1.0683750567702658723601171838498 y[1] (numeric) = -1.0683750567702658723601171838485 absolute error = 1.3e-30 relative error = 1.2168011521440272179613534529675e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.821 y[1] (closed_form) = -1.068606848376185571342608039746 y[1] (numeric) = -1.0686068483761855713426080397447 absolute error = 1.3e-30 relative error = 1.2165372156985805245867972303321e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.822 y[1] (closed_form) = -1.068838444472151834904018125674 y[1] (numeric) = -1.0688384444721518349040181256727 absolute error = 1.3e-30 relative error = 1.2162736162077401665411746366238e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.823 y[1] (closed_form) = -1.0690698452806087066253084071283 y[1] (numeric) = -1.069069845280608706625308407127 absolute error = 1.3e-30 relative error = 1.2160103530548810003955215840690e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.824 y[1] (closed_form) = -1.0693010510237089031938900658457 y[1] (numeric) = -1.0693010510237089031938900658444 absolute error = 1.3e-30 relative error = 1.2157474256248308522214665087121e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.825 y[1] (closed_form) = -1.0695320619233141797966205039994 y[1] (numeric) = -1.0695320619233141797966205039981 absolute error = 1.3e-30 relative error = 1.2154848333038663514013243233856e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.826 y[1] (closed_form) = -1.0697628782009956953184789043136 y[1] (numeric) = -1.0697628782009956953184789043123 absolute error = 1.3e-30 relative error = 1.2152225754797087784857152440232e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.827 y[1] (closed_form) = -1.0699935000780343773453752935366 y[1] (numeric) = -1.0699935000780343773453752935353 absolute error = 1.3e-30 relative error = 1.2149606515415199270442540176164e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.828 y[1] (closed_form) = -1.0702239277754212869695580495882 y[1] (numeric) = -1.0702239277754212869695580495869 absolute error = 1.3e-30 relative error = 1.2146990608798979794550939477536e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.829 y[1] (closed_form) = -1.0704541615138579833960957314775 y[1] (numeric) = -1.0704541615138579833960957314762 absolute error = 1.3e-30 relative error = 1.2144378028868733965793478095406e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.83 y[1] (closed_form) = -1.0706842015137568883489199960067 y[1] (numeric) = -1.0706842015137568883489199960055 absolute error = 1.2e-30 relative error = 1.1207786556516044503999793318153e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.831 y[1] (closed_form) = -1.0709140479952416502749271965605 y[1] (numeric) = -1.0709140479952416502749271965592 absolute error = 1.3e-30 relative error = 1.2139162824818749956383138504535e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.832 y[1] (closed_form) = -1.0711437011781475083446470371482 y[1] (numeric) = -1.0711437011781475083446470371469 absolute error = 1.3e-30 relative error = 1.2136560188610866920949325142078e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.833 y[1] (closed_form) = -1.0713731612820216562479973795565 y[1] (numeric) = -1.0713731612820216562479973795552 absolute error = 1.3e-30 relative error = 1.2133960854912586579951843783232e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.834 y[1] (closed_form) = -1.0716024285261236057836549731896 y[1] (numeric) = -1.0716024285261236057836549731883 absolute error = 1.3e-30 relative error = 1.2131364817715215739532365505973e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.835 y[1] (closed_form) = -1.0718315031294255502405824961646 y[1] (numeric) = -1.0718315031294255502405824961633 absolute error = 1.3e-30 relative error = 1.2128772071024140257020502338883e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.836 y[1] (closed_form) = -1.0720603853106127275702628626984 y[1] (numeric) = -1.0720603853106127275702628626971 absolute error = 1.3e-30 relative error = 1.2126182608858784894702817377044e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.837 y[1] (closed_form) = -1.0722890752880837833482022660042 y[1] (numeric) = -1.0722890752880837833482022660029 absolute error = 1.3e-30 relative error = 1.2123596425252573308206556336959e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.838 y[1] (closed_form) = -1.0725175732799511335232738880207 y[1] (numeric) = -1.0725175732799511335232738880193 absolute error = 1.4e-30 relative error = 1.3053399169195418028131443110131e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.839 y[1] (closed_form) = -1.0727458795040413269534846175545 y[1] (numeric) = -1.0727458795040413269534846175531 absolute error = 1.4e-30 relative error = 1.3050621090684187683450806650268e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.84 y[1] (closed_form) = -1.0729739941778954077267574770421 y[1] (numeric) = -1.0729739941778954077267574770407 absolute error = 1.4e-30 relative error = 1.3047846523742352717919367372552e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.841 y[1] (closed_form) = -1.0732019175187692772653327653487 y[1] (numeric) = -1.0732019175187692772653327653473 absolute error = 1.4e-30 relative error = 1.3045075462004244286776028255922e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.842 y[1] (closed_form) = -1.0734296497436340562124011800399 y[1] (numeric) = -1.0734296497436340562124011800385 absolute error = 1.4e-30 relative error = 1.3042307899119055984457027032584e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.843 y[1] (closed_form) = -1.0736571910691764460995923876043 y[1] (numeric) = -1.073657191069176446099592387603 absolute error = 1.3e-30 relative error = 1.2108147840982887212378714802348e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.844 y[1] (closed_form) = -1.073884541711799090793952664386 y[1] (numeric) = -1.0738845417117990907939526643847 absolute error = 1.3e-30 relative error = 1.2105584441394110729717872556686e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.845 y[1] (closed_form) = -1.0741117018876209377230553347201 y[1] (numeric) = -1.0741117018876209377230553347188 absolute error = 1.3e-30 relative error = 1.2103024273131070048177884446200e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.846 y[1] (closed_form) = -1.0743386718124775988768977861754 y[1] (numeric) = -1.0743386718124775988768977861741 absolute error = 1.3e-30 relative error = 1.2100467330351400297074244269686e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.847 y[1] (closed_form) = -1.0745654517019217115852488450957 y[1] (numeric) = -1.0745654517019217115852488450944 absolute error = 1.3e-30 relative error = 1.2097913607226342673662987159945e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.848 y[1] (closed_form) = -1.0747920417712232990691202490252 y[1] (numeric) = -1.0747920417712232990691202490238 absolute error = 1.4e-30 relative error = 1.3025775643936144792264396952036e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.849 y[1] (closed_form) = -1.0750184422353701307650458563007 y[1] (numeric) = -1.0750184422353701307650458562993 absolute error = 1.4e-30 relative error = 1.3023032396438429808716582247769e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.85 y[1] (closed_form) = -1.0752446533090680824208620873218 y[1] (numeric) = -1.0752446533090680824208620873204 absolute error = 1.4e-30 relative error = 1.3020292597517193265528208672030e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.851 y[1] (closed_form) = -1.0754706752067414959616928969641 y[1] (numeric) = -1.0754706752067414959616928969626 absolute error = 1.5e-30 relative error = 1.3947381686735900488719044211419e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.852 y[1] (closed_form) = -1.0756965081425335391248523335068 y[1] (numeric) = -1.0756965081425335391248523335053 absolute error = 1.5e-30 relative error = 1.3944453557724524734866374723127e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.853 y[1] (closed_form) = -1.0759221523303065648623874465032 y[1] (numeric) = -1.0759221523303065648623874465018 absolute error = 1.4e-30 relative error = 1.3012093830095265094341292846830e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.854 y[1] (closed_form) = -1.0761476079836424705099939644419 y[1] (numeric) = -1.0761476079836424705099939644404 absolute error = 1.5e-30 relative error = 1.3938608317965987800263523021779e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.855 y[1] (closed_form) = -1.0763728753158430567210467730395 y[1] (numeric) = -1.0763728753158430567210467730381 absolute error = 1.4e-30 relative error = 1.3006645114400473394855742149126e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.856 y[1] (closed_form) = -1.0765979545399303861644967867803 y[1] (numeric) = -1.0765979545399303861644967867788 absolute error = 1.5e-30 relative error = 1.3932777725190874682354813338574e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.857 y[1] (closed_form) = -1.0768228458686471419853953200687 y[1] (numeric) = -1.0768228458686471419853953200672 absolute error = 1.5e-30 relative error = 1.3929867904966169301615300232325e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.858 y[1] (closed_form) = -1.0770475495144569860268165303173 y[1] (numeric) = -1.0770475495144569860268165303158 absolute error = 1.5e-30 relative error = 1.3926961726770688046507706711353e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.859 y[1] (closed_form) = -1.0772720656895449168119579236318 y[1] (numeric) = -1.0772720656895449168119579236302 absolute error = 1.6e-30 relative error = 1.4852329796334829759205290302676e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.86 y[1] (closed_form) = -1.0774963946058176272852082847049 y[1] (numeric) = -1.0774963946058176272852082847033 absolute error = 1.6e-30 relative error = 1.4849237621675112628769070303755e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.861 y[1] (closed_form) = -1.0777205364749038623109817162831 y[1] (numeric) = -1.0777205364749038623109817162815 absolute error = 1.6e-30 relative error = 1.4846149310965255979660649237662e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.862 y[1] (closed_form) = -1.0779444915081547759291257503268 y[1] (numeric) = -1.0779444915081547759291257503252 absolute error = 1.6e-30 relative error = 1.4843064857276983572755170309824e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.863 y[1] (closed_form) = -1.0781682599166442883657207229581 y[1] (numeric) = -1.0781682599166442883657207229565 absolute error = 1.6e-30 relative error = 1.4839984253698024321462122879002e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.864 y[1] (closed_form) = -1.0783918419111694427980967886686 y[1] (numeric) = -1.078391841911169442798096788667 absolute error = 1.6e-30 relative error = 1.4836907493332067287454294922454e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.865 y[1] (closed_form) = -1.0786152377022507618729040862557 y[1] (numeric) = -1.0786152377022507618729040862541 absolute error = 1.6e-30 relative error = 1.4833834569298716825204050091492e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.866 y[1] (closed_form) = -1.07883844750013260397608065976 y[1] (numeric) = -1.0788384475001326039760806597584 absolute error = 1.6e-30 relative error = 1.4830765474733447874761369747427e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.867 y[1] (closed_form) = -1.0790614715147835192535717824957 y[1] (numeric) = -1.0790614715147835192535717824941 absolute error = 1.6e-30 relative error = 1.4827700202787561402210531860616e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.868 y[1] (closed_form) = -1.0792843099558966053816633312927 y[1] (numeric) = -1.0792843099558966053816633312911 absolute error = 1.6e-30 relative error = 1.4824638746628139987244718462296e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.869 y[1] (closed_form) = -1.0795069630328898630858008115048 y[1] (numeric) = -1.0795069630328898630858008115032 absolute error = 1.6e-30 relative error = 1.4821581099438003557300251522223e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.87 y[1] (closed_form) = -1.0797294309549065514067745413803 y[1] (numeric) = -1.0797294309549065514067745413787 absolute error = 1.6e-30 relative error = 1.4818527254415665267694553746682e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.871 y[1] (closed_form) = -1.0799517139308155427131603672314 y[1] (numeric) = -1.0799517139308155427131603672298 absolute error = 1.6e-30 relative error = 1.4815477204775287527214315912738e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.872 y[1] (closed_form) = -1.0801738121692116774589140986807 y[1] (numeric) = -1.0801738121692116774589140986791 absolute error = 1.6e-30 relative error = 1.4812430943746638168602726036612e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.873 y[1] (closed_form) = -1.0803957258784161186850266262912 y[1] (numeric) = -1.0803957258784161186850266262896 absolute error = 1.6e-30 relative error = 1.4809388464575046763396977977773e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.874 y[1] (closed_form) = -1.0806174552664767062641554123057 y[1] (numeric) = -1.0806174552664767062641554123041 absolute error = 1.6e-30 relative error = 1.4806349760521361080569628065910e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.875 y[1] (closed_form) = -1.0808390005411683108871567292172 y[1] (numeric) = -1.0808390005411683108871567292156 absolute error = 1.6e-30 relative error = 1.4803314824861903688429708065635e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.876 y[1] (closed_form) = -1.0810603619099931877904516606612 y[1] (numeric) = -1.0810603619099931877904516606596 absolute error = 1.6e-30 relative error = 1.4800283650888428699241831323101e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.877 y[1] (closed_form) = -1.0812815395801813302231674748537 y[1] (numeric) = -1.0812815395801813302231674748521 absolute error = 1.6e-30 relative error = 1.4797256231908078656023846329226e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.878 y[1] (closed_form) = -1.0815025337586908226530045326886 y[1] (numeric) = -1.081502533758690822653004532687 absolute error = 1.6e-30 relative error = 1.4794232561243341560985898244704e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.879 y[1] (closed_form) = -1.0817233446522081937097874008434 y[1] (numeric) = -1.0817233446522081937097874008418 absolute error = 1.6e-30 relative error = 1.4791212632232008045076054221314e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.88 y[1] (closed_form) = -1.0819439724671487688656673050121 y[1] (numeric) = -1.0819439724671487688656673050105 absolute error = 1.6e-30 relative error = 1.4788196438227128678099932680413e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.881 y[1] (closed_form) = -1.0821644174096570228509514798842 y[1] (numeric) = -1.0821644174096570228509514798827 absolute error = 1.5e-30 relative error = 1.3861109974309660705203796997697e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.882 y[1] (closed_form) = -1.0823846796856069318045433508962 y[1] (numeric) = -1.0823846796856069318045433508947 absolute error = 1.5e-30 relative error = 1.3858289276929668004645182827774e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.883 y[1] (closed_form) = -1.0826047595006023251579858182959 y[1] (numeric) = -1.0826047595006023251579858182943 absolute error = 1.6e-30 relative error = 1.4779170200009727681207723198626e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.884 y[1] (closed_form) = -1.0828246570599772372521082068612 y[1] (numeric) = -1.0828246570599772372521082068596 absolute error = 1.6e-30 relative error = 1.4776168879864883067042244070112e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.885 y[1] (closed_form) = -1.0830443725687962586852856948912 y[1] (numeric) = -1.0830443725687962586852856948896 absolute error = 1.6e-30 relative error = 1.4773171261719160161442729993185e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.886 y[1] (closed_form) = -1.0832639062318548873923282440222 y[1] (numeric) = -1.0832639062318548873923282440206 absolute error = 1.6e-30 relative error = 1.4770177339016280485484634856434e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.887 y[1] (closed_form) = -1.0834832582536798794530242172078 y[1] (numeric) = -1.0834832582536798794530242172062 absolute error = 1.6e-30 relative error = 1.4767187105214930561750150058526e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.888 y[1] (closed_form) = -1.0837024288385295996293719960113 y[1] (numeric) = -1.0837024288385295996293719960097 absolute error = 1.6e-30 relative error = 1.4764200553788720330138258247768e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.889 y[1] (closed_form) = -1.0839214181903943716305409903873 y[1] (numeric) = -1.0839214181903943716305409903857 absolute error = 1.6e-30 relative error = 1.4761217678226141699556766707607e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.89 y[1] (closed_form) = -1.084140226512996828104611474551 y[1] (numeric) = -1.0841402265129968281046114745494 absolute error = 1.6e-30 relative error = 1.4758238472030527234986013443016e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.891 y[1] (closed_form) = -1.0843588540097922603561506815363 y[1] (numeric) = -1.0843588540097922603561506815347 absolute error = 1.6e-30 relative error = 1.4755262928720008979406106510715e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.892 y[1] (closed_form) = -1.0845773008839689677886905468049 y[1] (numeric) = -1.0845773008839689677886905468032 absolute error = 1.7e-30 relative error = 1.5674309231941694748211821481295e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.893 y[1] (closed_form) = -1.0847955673384486070711804079716 y[1] (numeric) = -1.08479556733844860707118040797 absolute error = 1.6e-30 relative error = 1.4749322804900540528700571717912e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.894 y[1] (closed_form) = -1.0850136535758865410274958435374 y[1] (numeric) = -1.0850136535758865410274958435357 absolute error = 1.7e-30 relative error = 1.5668005599720325777668003215433e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.895 y[1] (closed_form) = -1.0852315597986721872480926686421 y[1] (numeric) = -1.0852315597986721872480926686405 absolute error = 1.6e-30 relative error = 1.4743397255207225932429890712797e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.896 y[1] (closed_form) = -1.0854492862089293664229029004597 y[1] (numeric) = -1.0854492862089293664229029004581 absolute error = 1.6e-30 relative error = 1.4740439929609285518210633885555e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.897 y[1] (closed_form) = -1.085666833008516650394577260115 y[1] (numeric) = -1.0856668330085166503945772601133 absolute error = 1.7e-30 relative error = 1.5658579117583341846438919983248e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.898 y[1] (closed_form) = -1.0858842003990277099311864921022 y[1] (numeric) = -1.0858842003990277099311864921005 absolute error = 1.7e-30 relative error = 1.5655444653999978793097783526534e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.899 y[1] (closed_form) = -1.0861013885817916622175014562941 y[1] (numeric) = -1.0861013885817916622175014562924 absolute error = 1.7e-30 relative error = 1.5652314027697029519196075337459e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (closed_form) = -1.0863183977578734180639795819257 y[1] (numeric) = -1.086318397757873418063979581924 absolute error = 1.7e-30 relative error = 1.5649187231927083881113939890012e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.901 y[1] (closed_form) = -1.0865352281280740288325928675998 y[1] (numeric) = -1.0865352281280740288325928675982 absolute error = 1.6e-30 relative error = 1.4725707538784024872958324960372e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.902 y[1] (closed_form) = -1.0867518798929310330786401665586 y[1] (numeric) = -1.0867518798929310330786401665569 absolute error = 1.7e-30 relative error = 1.5642945105072994188892231903819e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.903 y[1] (closed_form) = -1.0869683532527188029076940123762 y[1] (numeric) = -1.0869683532527188029076940123746 absolute error = 1.6e-30 relative error = 1.4719839774654432568522325148782e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.904 y[1] (closed_form) = -1.0871846484074488900468397170265 y[1] (numeric) = -1.0871846484074488900468397170249 absolute error = 1.6e-30 relative error = 1.4716911265659824548855360042562e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.905 y[1] (closed_form) = -1.0874007655568703716293719111304 y[1] (numeric) = -1.0874007655568703716293719111288 absolute error = 1.6e-30 relative error = 1.4713986330335363488618336481126e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.906 y[1] (closed_form) = -1.0876167049004701956921210952779 y[1] (numeric) = -1.0876167049004701956921210952762 absolute error = 1.7e-30 relative error = 1.5630506522567342559733994164967e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.907 y[1] (closed_form) = -1.0878324666374735263845901318031 y[1] (numeric) = -1.0878324666374735263845901318014 absolute error = 1.7e-30 relative error = 1.5627406352880391201694830181141e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.908 y[1] (closed_form) = -1.0880480509668440888890879284541 y[1] (numeric) = -1.0880480509668440888890879284524 absolute error = 1.7e-30 relative error = 1.5624309960294242769810222316422e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.909 y[1] (closed_form) = -1.0882634580872845140510548491992 y[1] (numeric) = -1.0882634580872845140510548491975 absolute error = 1.7e-30 relative error = 1.5621217338197631217117929937654e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.91 y[1] (closed_form) = -1.0884786881972366827187816331298 y[1] (numeric) = -1.0884786881972366827187816331282 absolute error = 1.6e-30 relative error = 1.4699415039994550761112291030266e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.911 y[1] (closed_form) = -1.0886937414948820697917308102142 y[1] (numeric) = -1.0886937414948820697917308102126 absolute error = 1.6e-30 relative error = 1.4696511415625893647823642563933e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.912 y[1] (closed_form) = -1.088908618178142087976676772703 y[1] (numeric) = -1.0889086181781420879766767727014 absolute error = 1.6e-30 relative error = 1.4693611321370265249653267381869e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.913 y[1] (closed_form) = -1.089123318444678431250887793451 y[1] (numeric) = -1.0891233184446784312508877934493 absolute error = 1.7e-30 relative error = 1.5608884423002561920359877819782e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.914 y[1] (closed_form) = -1.0893378424918934180315803774641 y[1] (numeric) = -1.0893378424918934180315803774624 absolute error = 1.7e-30 relative error = 1.5605810554705401031218969546954e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.915 y[1] (closed_form) = -1.0895521905169303340508833907792 y[1] (numeric) = -1.0895521905169303340508833907775 absolute error = 1.7e-30 relative error = 1.5602740417542063940829453144530e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.916 y[1] (closed_form) = -1.0897663627166737749355564314937 y[1] (numeric) = -1.089766362716673774935556431492 absolute error = 1.7e-30 relative error = 1.5599674005004866119247211968327e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.917 y[1] (closed_form) = -1.0899803592877499884907138915571 y[1] (numeric) = -1.0899803592877499884907138915555 absolute error = 1.6e-30 relative error = 1.4679163586447772722615038376239e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.918 y[1] (closed_form) = -1.0901941804265272166868131049712 y[1] (numeric) = -1.0901941804265272166868131049696 absolute error = 1.6e-30 relative error = 1.4676284543860035284910147565873e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.919 y[1] (closed_form) = -1.0904078263291160373491718884929 y[1] (numeric) = -1.0904078263291160373491718884913 absolute error = 1.6e-30 relative error = 1.4673408988510639852375433842773e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.92 y[1] (closed_form) = -1.0906212971913697055492876549513 y[1] (numeric) = -1.0906212971913697055492876549497 absolute error = 1.6e-30 relative error = 1.4670536914329579308091205664846e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.921 y[1] (closed_form) = -1.0908345932088844946972371170395 y[1] (numeric) = -1.0908345932088844946972371170379 absolute error = 1.6e-30 relative error = 1.4667668315260470948027719247437e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.922 y[1] (closed_form) = -1.0910477145770000373344424010914 y[1] (numeric) = -1.0910477145770000373344424010898 absolute error = 1.6e-30 relative error = 1.4664803185260519243068072230340e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.923 y[1] (closed_form) = -1.0912606614907996656260961560552 y[1] (numeric) = -1.0912606614907996656260961560535 absolute error = 1.7e-30 relative error = 1.5578312863194258640764422486332e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.924 y[1] (closed_form) = -1.0914734341451107515525449727968 y[1] (numeric) = -1.0914734341451107515525449727952 absolute error = 1.6e-30 relative error = 1.4659083308364616966070695095250e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.925 y[1] (closed_form) = -1.0916860327345050467989371231669 y[1] (numeric) = -1.0916860327345050467989371231653 absolute error = 1.6e-30 relative error = 1.4656228549450677741555835530680e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.926 y[1] (closed_form) = -1.0918984574532990223424472870959 y[1] (numeric) = -1.0918984574532990223424472870942 absolute error = 1.7e-30 relative error = 1.5569213312792959489153245056649e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.927 y[1] (closed_form) = -1.0921107084955542077363975595155 y[1] (numeric) = -1.0921107084955542077363975595139 absolute error = 1.6e-30 relative error = 1.4650529360746702366108781816132e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.928 y[1] (closed_form) = -1.0923227860550775300906006172872 y[1] (numeric) = -1.0923227860550775300906006172855 absolute error = 1.7e-30 relative error = 1.5563165226457904631621202478015e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.929 y[1] (closed_form) = -1.0925346903254216527472574797095 y[1] (numeric) = -1.0925346903254216527472574797078 absolute error = 1.7e-30 relative error = 1.5560146648466046749203432462654e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.93 y[1] (closed_form) = -1.0927464214998853136517488147424 y[1] (numeric) = -1.0927464214998853136517488147407 absolute error = 1.7e-30 relative error = 1.5557131705511409163305658866552e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.931 y[1] (closed_form) = -1.0929579797715136634176652269667 y[1] (numeric) = -1.092957979771513663417665226965 absolute error = 1.7e-30 relative error = 1.5554120391301689372329862528745e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.932 y[1] (closed_form) = -1.093169365333098603085428412664 y[1] (numeric) = -1.0931693653330986030854284126624 absolute error = 1.6e-30 relative error = 1.4636341364290477658302625774604e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.933 y[1] (closed_form) = -1.0933805783771791215738614824 y[1] (numeric) = -1.0933805783771791215738614823983 absolute error = 1.7e-30 relative error = 1.5548108624017993163088647059420e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.934 y[1] (closed_form) = -1.0935916190960416328240731322788 y[1] (numeric) = -1.0935916190960416328240731322771 absolute error = 1.7e-30 relative error = 1.5545108158429497282054070453115e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.935 y[1] (closed_form) = -1.0938024876817203126350266917691 y[1] (numeric) = -1.0938024876817203126350266917674 absolute error = 1.7e-30 relative error = 1.5542111296556804252268001434578e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.936 y[1] (closed_form) = -1.0940131843259974351901713888221 y[1] (numeric) = -1.0940131843259974351901713888204 absolute error = 1.7e-30 relative error = 1.5539118032177469057258456188122e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.937 y[1] (closed_form) = -1.0942237092204037092745194520772 y[1] (numeric) = -1.0942237092204037092745194520755 absolute error = 1.7e-30 relative error = 1.5536128359082904574400036646229e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.938 y[1] (closed_form) = -1.0944340625562186141815589154218 y[1] (numeric) = -1.0944340625562186141815589154201 absolute error = 1.7e-30 relative error = 1.5533142271078343988982874655087e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.939 y[1] (closed_form) = -1.0946442445244707353093982021949 y[1] (numeric) = -1.0946442445244707353093982021932 absolute error = 1.7e-30 relative error = 1.5530159761982803328165539205959e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.94 y[1] (closed_form) = -1.094854255315938099445544745049 y[1] (numeric) = -1.0948542553159380994455447450473 absolute error = 1.7e-30 relative error = 1.5527180825629044114372515729076e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.941 y[1] (closed_form) = -1.0950640951211485097397260430628 y[1] (numeric) = -1.0950640951211485097397260430611 absolute error = 1.7e-30 relative error = 1.5524205455863536137698687140217e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.942 y[1] (closed_form) = -1.0952737641303798803641676702742 y[1] (numeric) = -1.0952737641303798803641676702725 absolute error = 1.7e-30 relative error = 1.5521233646546420346885058596089e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.943 y[1] (closed_form) = -1.0954832625336605708607488295345 y[1] (numeric) = -1.0954832625336605708607488295328 absolute error = 1.7e-30 relative error = 1.5518265391551471858431771795986e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.944 y[1] (closed_form) = -1.0956925905207697201744620926103 y[1] (numeric) = -1.0956925905207697201744620926086 absolute error = 1.7e-30 relative error = 1.5515300684766063083416250207191e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.945 y[1] (closed_form) = -1.095901748281237580372609981937 y[1] (numeric) = -1.0959017482812375803726099819352 absolute error = 1.8e-30 relative error = 1.6424830080096487381679404058048e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.946 y[1] (closed_form) = -1.0961107360043458500491770314935 y[1] (numeric) = -1.0961107360043458500491770314918 absolute error = 1.7e-30 relative error = 1.5509381891441120372298201123823e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.947 y[1] (closed_form) = -1.0963195538791280074138219140809 y[1] (numeric) = -1.0963195538791280074138219140791 absolute error = 1.8e-30 relative error = 1.6418570604081869130222797378912e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.948 y[1] (closed_form) = -1.0965282020943696430649401399777 y[1] (numeric) = -1.096528202094369643064940139976 absolute error = 1.7e-30 relative error = 1.5503477217941123586967683838381e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.949 y[1] (closed_form) = -1.0967366808386087924462537176792 y[1] (numeric) = -1.0967366808386087924462537176775 absolute error = 1.7e-30 relative error = 1.5500530160987338473458983194707e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.95 y[1] (closed_form) = -1.0969449903001362679863900213251 y[1] (numeric) = -1.0969449903001362679863900213234 absolute error = 1.7e-30 relative error = 1.5497586615850820550557149541813e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.951 y[1] (closed_form) = -1.0971531306669959909209179316523 y[1] (numeric) = -1.0971531306669959909209179316506 absolute error = 1.7e-30 relative error = 1.5494646576513100639588236706760e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.952 y[1] (closed_form) = -1.0973611021269853227963151079938 y[1] (numeric) = -1.0973611021269853227963151079921 absolute error = 1.7e-30 relative error = 1.5491710036969016057112415162741e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.953 y[1] (closed_form) = -1.0975689048676553966553460081481 y[1] (numeric) = -1.0975689048676553966553460081464 absolute error = 1.7e-30 relative error = 1.5488776991226674781933347114963e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.954 y[1] (closed_form) = -1.0977765390763114479033360009882 y[1] (numeric) = -1.0977765390763114479033360009865 absolute error = 1.7e-30 relative error = 1.5485847433307419735588056060491e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.955 y[1] (closed_form) = -1.0979840049400131448548326136238 y[1] (numeric) = -1.097984004940013144854832613622 absolute error = 1.8e-30 relative error = 1.6393681437083781009781070792184e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.956 y[1] (closed_form) = -1.0981913026455749189601506209025 y[1] (numeric) = -1.0981913026455749189601506209007 absolute error = 1.8e-30 relative error = 1.6390586919271236568109484649050e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.957 y[1] (closed_form) = -1.0983984323795662947113033201895 y[1] (numeric) = -1.0983984323795662947113033201878 absolute error = 1.7e-30 relative error = 1.5477079626899378378815823102339e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.958 y[1] (closed_form) = -1.0986053943283122192268279388266 y[1] (numeric) = -1.0986053943283122192268279388249 absolute error = 1.7e-30 relative error = 1.5474163960749352455269829556577e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.959 y[1] (closed_form) = -1.0988121886778933915150186955938 y[1] (numeric) = -1.098812188677893391515018695592 absolute error = 1.8e-30 relative error = 1.6381325385239727407436411697186e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.96 y[1] (closed_form) = -1.0990188156141465914150865810103 y[1] (numeric) = -1.0990188156141465914150865810085 absolute error = 1.8e-30 relative error = 1.6378245526161766699825207021923e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.961 y[1] (closed_form) = -1.0992252753226650082157704345585 y[1] (numeric) = -1.0992252753226650082157704345567 absolute error = 1.8e-30 relative error = 1.6375169316149781816170392117096e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.962 y[1] (closed_form) = -1.0994315679887985689509293800305 y[1] (numeric) = -1.0994315679887985689509293800288 absolute error = 1.7e-30 relative error = 1.5462535818485068757653268730895e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.963 y[1] (closed_form) = -1.0996376937976542663716521333248 y[1] (numeric) = -1.0996376937976542663716521333231 absolute error = 1.7e-30 relative error = 1.5459637384100250448593660060889e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.964 y[1] (closed_form) = -1.0998436529340964865944241202885 y[1] (numeric) = -1.0998436529340964865944241202868 absolute error = 1.7e-30 relative error = 1.5456742378472091458754063735286e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.965 y[1] (closed_form) = -1.1000494455827473364248987357562 y[1] (numeric) = -1.1000494455827473364248987357546 absolute error = 1.6e-30 relative error = 1.4544800748955476364714973258129e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.966 y[1] (closed_form) = -1.1002550719279869703568244389027 y[1] (numeric) = -1.1002550719279869703568244389011 absolute error = 1.6e-30 relative error = 1.4542082475441857737127976034182e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.967 y[1] (closed_form) = -1.1004605321539539172456847145512 y[1] (numeric) = -1.1004605321539539172456847145496 absolute error = 1.6e-30 relative error = 1.4539367412553063222955460445327e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.968 y[1] (closed_form) = -1.1006658264445454066566132352894 y[1] (numeric) = -1.1006658264445454066566132352878 absolute error = 1.6e-30 relative error = 1.4536655554833040255534953279491e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.969 y[1] (closed_form) = -1.1008709549834176948861518352737 y[1] (numeric) = -1.1008709549834176948861518352721 absolute error = 1.6e-30 relative error = 1.4533946896837700965552160900951e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.97 y[1] (closed_form) = -1.1010759179539863906574241535935 y[1] (numeric) = -1.1010759179539863906574241535919 absolute error = 1.6e-30 relative error = 1.4531241433134890219774038156853e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.971 y[1] (closed_form) = -1.1012807155394267804883030231387 y[1] (numeric) = -1.101280715539426780488303023137 absolute error = 1.7e-30 relative error = 1.5436572855698375870204442162385e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.972 y[1] (closed_form) = -1.1014853479226741537321548702117 y[1] (numeric) = -1.10148534792267415373215487021 absolute error = 1.7e-30 relative error = 1.5433705071121313095916722481597e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.973 y[1] (closed_form) = -1.1016898152864241272907495507763 y[1] (numeric) = -1.1016898152864241272907495507745 absolute error = 1.8e-30 relative error = 1.6338537172843200650866429043227e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.974 y[1] (closed_form) = -1.1018941178131329699989291813655 y[1] (numeric) = -1.1018941178131329699989291813637 absolute error = 1.8e-30 relative error = 1.6335507839649406163319308268784e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.975 y[1] (closed_form) = -1.1020982556850179266806346264257 y[1] (numeric) = -1.102098255685017926680634626424 absolute error = 1.7e-30 relative error = 1.5425121954696784217118346492177e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.976 y[1] (closed_form) = -1.1023022290840575418758933793661 y[1] (numeric) = -1.1023022290840575418758933793643 absolute error = 1.8e-30 relative error = 1.6329459856900448800841416619073e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 memory used=134.5MB, alloc=44.3MB, time=1.76 TOP MAIN SOLVE Loop x[1] = -1.977 y[1] (closed_form) = -1.1025060381919919832383776219549 y[1] (numeric) = -1.1025060381919919832383776219531 absolute error = 1.8e-30 relative error = 1.6326441195295707011529698953312e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.978 y[1] (closed_form) = -1.1027096831903233646031462660842 y[1] (numeric) = -1.1027096831903233646031462660824 absolute error = 1.8e-30 relative error = 1.6323426078859661765408372132468e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.979 y[1] (closed_form) = -1.1029131642603160687241897734317 y[1] (numeric) = -1.1029131642603160687241897734299 absolute error = 1.8e-30 relative error = 1.6320414501600357956190046734474e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.98 y[1] (closed_form) = -1.103116481582997069681401512326 y[1] (numeric) = -1.1031164815829970696814015123242 absolute error = 1.8e-30 relative error = 1.6317406457538911387594830314367e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.981 y[1] (closed_form) = -1.1033196353391562549566043472836 y[1] (numeric) = -1.1033196353391562549566043472818 absolute error = 1.8e-30 relative error = 1.6314401940709474037351122517970e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.982 y[1] (closed_form) = -1.1035226257093467471782660653698 y[1] (numeric) = -1.1035226257093467471782660653681 absolute error = 1.7e-30 relative error = 1.5405212003761466128109721092467e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.983 y[1] (closed_form) = -1.1037254528738852255345421248616 y[1] (numeric) = -1.1037254528738852255345421248599 absolute error = 1.7e-30 relative error = 1.5402381050228863221097298812694e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.984 y[1] (closed_form) = -1.103928117012852246854289065787 y[1] (numeric) = -1.1039281170128522468542890657853 absolute error = 1.7e-30 relative error = 1.5399553411141244750190744063260e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.985 y[1] (closed_form) = -1.1041306183060925663556967489111 y[1] (numeric) = -1.1041306183060925663556967489094 absolute error = 1.7e-30 relative error = 1.5396729080913120445809351572324e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.986 y[1] (closed_form) = -1.1043329569332154580621923897538 y[1] (numeric) = -1.1043329569332154580621923897521 absolute error = 1.7e-30 relative error = 1.5393908053971149480072241083821e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.987 y[1] (closed_form) = -1.1045351330735950348852741273846 y[1] (numeric) = -1.1045351330735950348852741273829 absolute error = 1.7e-30 relative error = 1.5391090324754108270295569044125e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.988 y[1] (closed_form) = -1.1047371469063705683739366141761 y[1] (numeric) = -1.1047371469063705683739366141744 absolute error = 1.7e-30 relative error = 1.5388275887712858382838113187863e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.989 y[1] (closed_form) = -1.1049389986104468081303558325205 y[1] (numeric) = -1.1049389986104468081303558325188 absolute error = 1.7e-30 relative error = 1.5385464737310314536935888763793e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.99 y[1] (closed_form) = -1.1051406883644943008915050378617 y[1] (numeric) = -1.10514068836449430089150503786 absolute error = 1.7e-30 relative error = 1.5382656868021412708167909474695e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.991 y[1] (closed_form) = -1.1053422163469497092763783943778 y[1] (numeric) = -1.1053422163469497092763783943761 absolute error = 1.7e-30 relative error = 1.5379852274333078331196653966005e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.992 y[1] (closed_form) = -1.1055435827360161301985035103973 y[1] (numeric) = -1.1055435827360161301985035103956 absolute error = 1.7e-30 relative error = 1.5377050950744194601428239919183e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.993 y[1] (closed_form) = -1.105744787709663412943428695263 y[1] (numeric) = -1.1057447877096634129434286952613 absolute error = 1.7e-30 relative error = 1.5374252891765570875238742520274e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.994 y[1] (closed_form) = -1.1059458314456284769108753479934 y[1] (numeric) = -1.1059458314456284769108753479917 absolute error = 1.7e-30 relative error = 1.5371458091919911168414522314267e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.995 y[1] (closed_form) = -1.1061467141214156290212504508558 y[1] (numeric) = -1.1061467141214156290212504508541 absolute error = 1.7e-30 relative error = 1.5368666545741782752455849253989e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.996 y[1] (closed_form) = -1.1063474359142968807862186779712 y[1] (numeric) = -1.1063474359142968807862186779695 absolute error = 1.7e-30 relative error = 1.5365878247777584848394525140598e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.997 y[1] (closed_form) = -1.1065479970013122650430381404474 y[1] (numeric) = -1.1065479970013122650430381404458 absolute error = 1.6e-30 relative error = 1.4459381828315781099084814741756e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.998 y[1] (closed_form) = -1.1067483975592701523523682753958 y[1] (numeric) = -1.1067483975592701523523682753941 absolute error = 1.7e-30 relative error = 1.5360311374735550050470805908754e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 TOP MAIN SOLVE Loop x[1] = -1.999 y[1] (closed_form) = -1.106948637764747567059262846648 y[1] (numeric) = -1.1069486377647475670592628466464 absolute error = 1.6e-30 relative error = 1.4454148507114720893116507826461e-28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = -0.001 Finished! diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; Iterations = 500 Total Elapsed Time = 1 Seconds Elapsed Time(since restart) = 1 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Expected Total Time = 1 Seconds Time to Timeout = 2 Minutes 58 Seconds Percent Done = 0 % > quit memory used=141.0MB, alloc=44.3MB, time=1.84