|\^/| Maple 2016 (X86 64 LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. #BEGIN OUTFILE1 # before write maple top matter # before write_ats library and user def block #BEGIN ATS LIBRARY BLOCK # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc # End Function number 2 # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc # End Function number 3 # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc # End Function number 4 # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 5 # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 6 # Begin Function number 7 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := sec_temp mod int_trunc(glob_sec_in_minute); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," 0.0 Seconds"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " 0.0 Seconds") end if; fprintf(fd, "\n") end proc # End Function number 7 # Begin Function number 8 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year)); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour)); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod int_trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" 0.0 Seconds\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" 0.0 Seconds\n") end if end proc # End Function number 8 # Begin Function number 9 > zero_ats_ar := proc(arr_a) > global ATS_MAX_TERMS; > local iii; > iii := 1; > while (iii <= ATS_MAX_TERMS) do # do number 1 > arr_a [iii] := glob__0; > iii := iii + 1; > od;# end do number 1 > end; zero_ats_ar := proc(arr_a) local iii; global ATS_MAX_TERMS; iii := 1; while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1 end do end proc # End Function number 9 # Begin Function number 10 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > global ATS_MAX_TERMS; > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := glob__0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 7 > ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]); > fi;# end if 7; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; global ATS_MAX_TERMS; ret_ats := glob__0; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]) end if; iii_ats := iii_ats + 1 end do end if; ret_ats end proc # End Function number 10 # Begin Function number 11 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global ATS_MAX_TERMS; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := glob__0; > if (jjj_att < mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 7 > ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / c(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global ATS_MAX_TERMS; ret_att := glob__0; if jjj_att < mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/c(mmm_att) end if; ret_att end proc # End Function number 11 # Begin Function number 12 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc # End Function number 12 # Begin Function number 13 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc # End Function number 13 # Begin Function number 14 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc # End Function number 14 # Begin Function number 15 > logitem_good_digits := proc(file,rel_error) > global glob_small_float,glob_prec; > local good_digits; > fprintf(file,""); > fprintf(file,"%d",glob_min_good_digits); > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float, glob_prec; fprintf(file, ""); fprintf(file, "%d", glob_min_good_digits); fprintf(file, "") end proc # End Function number 15 # Begin Function number 16 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc # End Function number 16 # Begin Function number 17 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc # End Function number 17 # Begin Function number 18 > logitem_h_reason := proc(file) > global glob_h_reason; > fprintf(file,""); > if (glob_h_reason = 1) then # if number 6 > fprintf(file,"Max H"); > elif > (glob_h_reason = 2) then # if number 7 > fprintf(file,"Display Interval"); > elif > (glob_h_reason = 3) then # if number 8 > fprintf(file,"Optimal"); > elif > (glob_h_reason = 4) then # if number 9 > fprintf(file,"Pole Accuracy"); > elif > (glob_h_reason = 5) then # if number 10 > fprintf(file,"Min H (Pole)"); > elif > (glob_h_reason = 6) then # if number 11 > fprintf(file,"Pole"); > elif > (glob_h_reason = 7) then # if number 12 > fprintf(file,"Opt Iter"); > else > fprintf(file,"Impossible"); > fi;# end if 12 > fprintf(file,""); > end; logitem_h_reason := proc(file) global glob_h_reason; fprintf(file, ""); if glob_h_reason = 1 then fprintf(file, "Max H") elif glob_h_reason = 2 then fprintf(file, "Display Interval") elif glob_h_reason = 3 then fprintf(file, "Optimal") elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy") elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)") elif glob_h_reason = 6 then fprintf(file, "Pole") elif glob_h_reason = 7 then fprintf(file, "Opt Iter") else fprintf(file, "Impossible") end if; fprintf(file, "") end proc # End Function number 18 # Begin Function number 19 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc # End Function number 19 # Begin Function number 20 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc # End Function number 20 # Begin Function number 21 > chk_data := proc() > global glob_max_iter,ALWAYS, ATS_MAX_TERMS; > local errflag; > errflag := false; > if (glob_max_iter < 2) then # if number 12 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 12; > if (errflag) then # if number 12 > quit; > fi;# end if 12 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, ATS_MAX_TERMS; errflag := false; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc # End Function number 21 # Begin Function number 22 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := c(clock_sec2); > sub1 := c(t_end2-t_start2); > sub2 := c(t2-t_start2); > if (sub1 = glob__0) then # if number 12 > sec_left := glob__0; > else > if (sub2 > glob__0) then # if number 13 > rrr := (sub1/sub2); > sec_left := rrr * c(ms2) - c(ms2); > else > sec_left := glob__0; > fi;# end if 13 > fi;# end if 12; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := c(clock_sec2); sub1 := c(t_end2 - t_start2); sub2 := c(t2 - t_start2); if sub1 = glob__0 then sec_left := glob__0 else if glob__0 < sub2 then rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2) else sec_left := glob__0 end if end if; sec_left end proc # End Function number 22 # Begin Function number 23 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 12 > rrr := (glob__100*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 12; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := glob__100*sub2/sub1 else rrr := 0. end if; rrr end proc # End Function number 23 # Begin Function number 24 > comp_rad_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 12 > ret := float_abs(term1 * glob_h / term2); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM TWO TERM RADIUS ANALYSIS > end; comp_rad_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2) else ret := glob_larger_float end if; ret end proc # End Function number 24 # Begin Function number 25 > comp_ord_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM ORDER ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 12 > ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no)); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM TWO TERM ORDER ANALYSIS > end; comp_ord_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)* c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no)) else ret := glob_larger_float end if; ret end proc # End Function number 25 # Begin Function number 26 > c := proc(in_val) > #To Force Conversion when needed > local ret; > ret := evalf(in_val); > ret; > #End Conversion > end; c := proc(in_val) local ret; ret := evalf(in_val); ret end proc # End Function number 26 # Begin Function number 27 > comp_rad_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret,temp; > temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3); > if (float_abs(temp) > glob__0) then # if number 12 > ret := float_abs((term2*glob_h*term1)/(temp)); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM THREE TERM RADIUS ANALYSIS > end; comp_rad_from_three_terms := proc(term1, term2, term3, last_no) local ret, temp; global glob_h, glob_larger_float; temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2 - term1*term3*c(last_no) + term1*term3); if glob__0 < float_abs(temp) then ret := float_abs(term2*glob_h*term1/temp) else ret := glob_larger_float end if; ret end proc # End Function number 27 # Begin Function number 28 > comp_ord_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM ORDER ANALYSIS > local ret; > ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3)); > ret; > #TOP THREE TERM ORDER ANALYSIS > end; comp_ord_from_three_terms := proc(term1, term2, term3, last_no) local ret; ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3 - glob__4*term2*term2*c(last_no) + glob__4*term2*term2 + term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no)) /(term2*term2*c(last_no) - glob__2*term2*term2 - term1*term3*c(last_no) + term1*term3)); ret end proc # End Function number 28 # Begin Function number 29 > comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > #TOP SIX TERM RADIUS ANALYSIS > global glob_h,glob_larger_float,glob_six_term_ord_save; > local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs; > if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 12 > rm0 := term6/term5; > rm1 := term5/term4; > rm2 := term4/term3; > rm3 := term3/term2; > rm4 := term2/term1; > nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2; > nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3; > dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; > dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; > ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; > ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; > if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 13 > rad_c := glob_larger_float; > ord_no := glob_larger_float; > else > if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2; > if (float_abs(rcs) <> glob__0) then # if number 15 > if (rcs > glob__0) then # if number 16 > rad_c := sqrt(rcs) * float_abs(glob_h); > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 16 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 15 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 14 > fi;# end if 13 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 12; > glob_six_term_ord_save := ord_no; > rad_c; > #BOTTOM SIX TERM RADIUS ANALYSIS > end; comp_rad_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no, ds1, rcs; global glob_h, glob_larger_float, glob_six_term_ord_save; if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and term2 <> glob__0 and term1 <> glob__0 then rm0 := term6/term5; rm1 := term5/term4; rm2 := term4/term3; rm3 := term3/term2; rm4 := term2/term1; nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1 + c(last_no - 3)*rm2; nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2 + c(last_no - 4)*rm3; dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; if float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0 then rad_c := glob_larger_float; ord_no := glob_larger_float else if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2; if float_abs(rcs) <> glob__0 then if glob__0 < rcs then rad_c := sqrt(rcs)*float_abs(glob_h) else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if; glob_six_term_ord_save := ord_no; rad_c end proc # End Function number 29 # Begin Function number 30 > comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > global glob_six_term_ord_save; > #TOP SIX TERM ORDER ANALYSIS > #TOP SAVED FROM SIX TERM RADIUS ANALYSIS > glob_six_term_ord_save; > #BOTTOM SIX TERM ORDER ANALYSIS > end; comp_ord_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) global glob_six_term_ord_save; glob_six_term_ord_save end proc # End Function number 30 # Begin Function number 31 > factorial_2 := proc(nnn) > ret := nnn!; > ret;; > end; Warning, `ret` is implicitly declared local to procedure `factorial_2` factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc # End Function number 31 # Begin Function number 32 > factorial_1 := proc(nnn) > global ATS_MAX_TERMS,array_fact_1; > local ret; > if (nnn <= ATS_MAX_TERMS) then # if number 12 > if (array_fact_1[nnn] = 0) then # if number 13 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 13; > else > ret := factorial_2(nnn); > fi;# end if 12; > ret; > end; factorial_1 := proc(nnn) local ret; global ATS_MAX_TERMS, array_fact_1; if nnn <= ATS_MAX_TERMS then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc # End Function number 32 # Begin Function number 33 > factorial_3 := proc(mmm,nnn) > global ATS_MAX_TERMS,array_fact_2; > local ret; > if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 12 > if (array_fact_2[mmm,nnn] = 0) then # if number 13 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 13; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 12; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global ATS_MAX_TERMS, array_fact_2; if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc # End Function number 33 # Begin Function number 34 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc # End Function number 34 # Begin Function number 35 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc # End Function number 35 # Begin Function number 36 > float_abs := proc(x) > abs(x); > end; float_abs := proc(x) abs(x) end proc # End Function number 36 # Begin Function number 37 > expt := proc(x,y) > x^y; > end; expt := proc(x, y) x^y end proc # End Function number 37 # Begin Function number 38 > neg := proc(x) > -x; > end; neg := proc(x) -x end proc # End Function number 38 # Begin Function number 39 > int_trunc := proc(x) > trunc(x); > end; int_trunc := proc(x) trunc(x) end proc # End Function number 39 # Begin Function number 40 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer))); > omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,""); > omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,""); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS))); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(glob__10, c(-glob_desired_digits_correct))* c(float_abs(c(estimated_answer))); omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, ""); omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "") ; omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := c(float_abs(desired_abs_gbl_error)/( sqrt(c(estimated_steps))*c(ATS_MAX_TERMS))); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc # End Function number 40 #END ATS LIBRARY BLOCK #BEGIN USER FUNCTION BLOCK #BEGIN BLOCK 3 #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(c(1.0)/ ( c(x) - c(6.0) ) / ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )) ; > end; exact_soln_y := proc(x) return c(1.0)/((c(x) - c(6.0))*(c(x) - c(6.0))*(c(x) - c(6.0))* (c(x) - c(6.0))*(c(x) - c(6.0))) 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_5D0, > array_const_6D0, #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_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > 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_5D0, array_const_6D0, 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_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, 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_5D0, > array_const_6D0, #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_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > 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_5D0, array_const_6D0, 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_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, 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_5D0, > array_const_6D0, #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_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > 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_5D0, array_const_6D0, 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_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, 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_5D0, > array_const_6D0, #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_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > 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_5D0, array_const_6D0, 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_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, 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_5D0, > array_const_6D0, #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_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > 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)*53*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_5D0, array_const_6D0, 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_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, 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)*53*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_5D0, > array_const_6D0, #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_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > 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_5D0, array_const_6D0, 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_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, 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_5D0, > array_const_6D0, #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_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > 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_5D0, array_const_6D0, 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_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, 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_5D0, > array_const_6D0, #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_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > 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 neg ID_CONST $eq_no = 1 > array_tmp1[1] := neg(array_const_5D0[1]); > #emit pre sub LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_x[1] - array_const_6D0[1]; > #emit pre div CONST - LINEAR $eq_no = 1 i = 1 > array_tmp3[1] := array_tmp1[1] / array_tmp2[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 1 > array_tmp4[1] := array_x[1] - array_const_6D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp5[1] := array_tmp3[1] / array_tmp4[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 1 > array_tmp6[1] := array_x[1] - array_const_6D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp7[1] := array_tmp5[1] / array_tmp6[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 1 > array_tmp8[1] := array_x[1] - array_const_6D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp9[1] := array_tmp7[1] / array_tmp8[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 1 > array_tmp10[1] := array_x[1] - array_const_6D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp11[1] := array_tmp9[1] / array_tmp10[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 1 > array_tmp12[1] := array_x[1] - array_const_6D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp13[1] := array_tmp11[1] / array_tmp12[1]; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp14[1] := array_const_0D0[1] + array_tmp13[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_tmp14[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 sub LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_x[2]; > #emit pre div CONST - LINEAR $eq_no = 1 i = 2 > array_tmp3[2] := neg(array_tmp3[1])* array_tmp2[2] / array_tmp2[1]; > #emit pre div CONST - LINEAR $eq_no = 1 i = 3 > #emit pre div CONST - LINEAR $eq_no = 1 i = 4 > #emit pre div CONST - LINEAR $eq_no = 1 i = 5 > #emit pre sub LINEAR - CONST $eq_no = 1 i = 2 > array_tmp4[2] := array_x[2]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp5[2] := (array_tmp3[2] - array_tmp5[1] * array_tmp4[2]) / array_tmp4[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 2 > array_tmp6[2] := array_x[2]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp7[2] := (array_tmp5[2] - array_tmp7[1] * array_tmp6[2]) / array_tmp6[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 2 > array_tmp8[2] := array_x[2]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp9[2] := (array_tmp7[2] - array_tmp9[1] * array_tmp8[2]) / array_tmp8[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 2 > array_tmp10[2] := array_x[2]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp11[2] := (array_tmp9[2] - array_tmp11[1] * array_tmp10[2]) / array_tmp10[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 2 > array_tmp12[2] := array_x[2]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp13[2] := (array_tmp11[2] - array_tmp13[1] * array_tmp12[2]) / array_tmp12[1]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp14[2] := array_tmp13[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_tmp14[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 > array_tmp3[3] := neg(array_tmp3[2])* array_tmp2[2] / array_tmp2[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp5[3] := (array_tmp3[3] - array_tmp5[2] * array_tmp4[2]) / array_tmp4[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp7[3] := (array_tmp5[3] - array_tmp7[2] * array_tmp6[2]) / array_tmp6[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp9[3] := (array_tmp7[3] - array_tmp9[2] * array_tmp8[2]) / array_tmp8[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp11[3] := (array_tmp9[3] - array_tmp11[2] * array_tmp10[2]) / array_tmp10[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp13[3] := (array_tmp11[3] - array_tmp13[2] * array_tmp12[2]) / array_tmp12[1]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp14[3] := array_tmp13[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_tmp14[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 > array_tmp3[4] := neg(array_tmp3[3])* array_tmp2[2] / array_tmp2[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp5[4] := (array_tmp3[4] - array_tmp5[3] * array_tmp4[2]) / array_tmp4[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp7[4] := (array_tmp5[4] - array_tmp7[3] * array_tmp6[2]) / array_tmp6[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp9[4] := (array_tmp7[4] - array_tmp9[3] * array_tmp8[2]) / array_tmp8[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp11[4] := (array_tmp9[4] - array_tmp11[3] * array_tmp10[2]) / array_tmp10[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp13[4] := (array_tmp11[4] - array_tmp13[3] * array_tmp12[2]) / array_tmp12[1]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp14[4] := array_tmp13[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_tmp14[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 > array_tmp3[5] := neg(array_tmp3[4])* array_tmp2[2] / array_tmp2[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp5[5] := (array_tmp3[5] - array_tmp5[4] * array_tmp4[2]) / array_tmp4[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp7[5] := (array_tmp5[5] - array_tmp7[4] * array_tmp6[2]) / array_tmp6[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp9[5] := (array_tmp7[5] - array_tmp9[4] * array_tmp8[2]) / array_tmp8[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp11[5] := (array_tmp9[5] - array_tmp11[4] * array_tmp10[2]) / array_tmp10[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp13[5] := (array_tmp11[5] - array_tmp13[4] * array_tmp12[2]) / array_tmp12[1]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp14[5] := array_tmp13[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_tmp14[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 div CONST LINEAR (NOP) $eq_no = 1 i = 1 > array_tmp3[kkk] := array_tmp1[1] * array_tmp2[kkk]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp5[kkk] := neg(ats(kkk,array_tmp4,array_tmp5,2)) / array_tmp4[1]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp7[kkk] := neg(ats(kkk,array_tmp6,array_tmp7,2)) / array_tmp6[1]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp9[kkk] := neg(ats(kkk,array_tmp8,array_tmp9,2)) / array_tmp8[1]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp11[kkk] := neg(ats(kkk,array_tmp10,array_tmp11,2)) / array_tmp10[1]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp13[kkk] := neg(ats(kkk,array_tmp12,array_tmp13,2)) / array_tmp12[1]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp14[kkk] := array_tmp13[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_tmp14[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_5D0, array_const_6D0, 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_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, 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] := neg(array_const_5D0[1]); array_tmp2[1] := array_x[1] - array_const_6D0[1]; array_tmp3[1] := array_tmp1[1]/array_tmp2[1]; array_tmp4[1] := array_x[1] - array_const_6D0[1]; array_tmp5[1] := array_tmp3[1]/array_tmp4[1]; array_tmp6[1] := array_x[1] - array_const_6D0[1]; array_tmp7[1] := array_tmp5[1]/array_tmp6[1]; array_tmp8[1] := array_x[1] - array_const_6D0[1]; array_tmp9[1] := array_tmp7[1]/array_tmp8[1]; array_tmp10[1] := array_x[1] - array_const_6D0[1]; array_tmp11[1] := array_tmp9[1]/array_tmp10[1]; array_tmp12[1] := array_x[1] - array_const_6D0[1]; array_tmp13[1] := array_tmp11[1]/array_tmp12[1]; array_tmp14[1] := array_const_0D0[1] + array_tmp13[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp14[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_tmp2[2] := array_x[2]; array_tmp3[2] := neg(array_tmp3[1])*array_tmp2[2]/array_tmp2[1]; array_tmp4[2] := array_x[2]; array_tmp5[2] := (-array_tmp4[2]*array_tmp5[1] + array_tmp3[2])/array_tmp4[1]; array_tmp6[2] := array_x[2]; array_tmp7[2] := (-array_tmp6[2]*array_tmp7[1] + array_tmp5[2])/array_tmp6[1]; array_tmp8[2] := array_x[2]; array_tmp9[2] := (-array_tmp8[2]*array_tmp9[1] + array_tmp7[2])/array_tmp8[1]; array_tmp10[2] := array_x[2]; array_tmp11[2] := (-array_tmp10[2]*array_tmp11[1] + array_tmp9[2])/array_tmp10[1]; array_tmp12[2] := array_x[2]; array_tmp13[2] := (-array_tmp12[2]*array_tmp13[1] + array_tmp11[2])/array_tmp12[1]; array_tmp14[2] := array_tmp13[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp14[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_tmp3[3] := neg(array_tmp3[2])*array_tmp2[2]/array_tmp2[1]; array_tmp5[3] := (-array_tmp4[2]*array_tmp5[2] + array_tmp3[3])/array_tmp4[1]; array_tmp7[3] := (-array_tmp6[2]*array_tmp7[2] + array_tmp5[3])/array_tmp6[1]; array_tmp9[3] := (-array_tmp8[2]*array_tmp9[2] + array_tmp7[3])/array_tmp8[1]; array_tmp11[3] := (-array_tmp10[2]*array_tmp11[2] + array_tmp9[3])/array_tmp10[1]; array_tmp13[3] := (-array_tmp12[2]*array_tmp13[2] + array_tmp11[3])/array_tmp12[1]; array_tmp14[3] := array_tmp13[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp14[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_tmp3[4] := neg(array_tmp3[3])*array_tmp2[2]/array_tmp2[1]; array_tmp5[4] := (-array_tmp4[2]*array_tmp5[3] + array_tmp3[4])/array_tmp4[1]; array_tmp7[4] := (-array_tmp6[2]*array_tmp7[3] + array_tmp5[4])/array_tmp6[1]; array_tmp9[4] := (-array_tmp8[2]*array_tmp9[3] + array_tmp7[4])/array_tmp8[1]; array_tmp11[4] := (-array_tmp10[2]*array_tmp11[3] + array_tmp9[4])/array_tmp10[1]; array_tmp13[4] := (-array_tmp12[2]*array_tmp13[3] + array_tmp11[4])/array_tmp12[1]; array_tmp14[4] := array_tmp13[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp14[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_tmp3[5] := neg(array_tmp3[4])*array_tmp2[2]/array_tmp2[1]; array_tmp5[5] := (-array_tmp4[2]*array_tmp5[4] + array_tmp3[5])/array_tmp4[1]; array_tmp7[5] := (-array_tmp6[2]*array_tmp7[4] + array_tmp5[5])/array_tmp6[1]; array_tmp9[5] := (-array_tmp8[2]*array_tmp9[4] + array_tmp7[5])/array_tmp8[1]; array_tmp11[5] := (-array_tmp10[2]*array_tmp11[4] + array_tmp9[5])/array_tmp10[1]; array_tmp13[5] := (-array_tmp12[2]*array_tmp13[4] + array_tmp11[5])/array_tmp12[1]; array_tmp14[5] := array_tmp13[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp14[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_tmp3[kkk] := array_tmp1[1]*array_tmp2[kkk]; array_tmp5[kkk] := neg(ats(kkk, array_tmp4, array_tmp5, 2))/array_tmp4[1]; array_tmp7[kkk] := neg(ats(kkk, array_tmp6, array_tmp7, 2))/array_tmp6[1]; array_tmp9[kkk] := neg(ats(kkk, array_tmp8, array_tmp9, 2))/array_tmp8[1]; array_tmp11[kkk] := neg(ats(kkk, array_tmp10, array_tmp11, 2))/array_tmp10[1]; array_tmp13[kkk] := neg(ats(kkk, array_tmp12, array_tmp13, 2))/array_tmp12[1]; array_tmp14[kkk] := array_tmp13[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_tmp14[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_5D0, > array_const_6D0, > #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_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 30; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=64; > max_terms:=30; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_y_init:= Array(0..(30),[]); > array_norms:= Array(0..(30),[]); > array_fact_1:= Array(0..(30),[]); > array_1st_rel_error:= Array(0..(2),[]); > array_last_rel_error:= Array(0..(2),[]); > array_est_rel_error:= Array(0..(2),[]); > array_max_est_error:= Array(0..(2),[]); > array_type_pole:= Array(0..(2),[]); > array_type_real_pole:= Array(0..(2),[]); > array_type_complex_pole:= Array(0..(2),[]); > array_est_digits:= Array(0..(2),[]); > array_y:= Array(0..(30),[]); > array_x:= Array(0..(30),[]); > array_tmp0:= Array(0..(30),[]); > array_tmp1:= Array(0..(30),[]); > array_tmp2:= Array(0..(30),[]); > array_tmp3:= Array(0..(30),[]); > array_tmp4:= Array(0..(30),[]); > array_tmp5:= Array(0..(30),[]); > array_tmp6:= Array(0..(30),[]); > array_tmp7:= Array(0..(30),[]); > array_tmp8:= Array(0..(30),[]); > array_tmp9:= Array(0..(30),[]); > array_tmp10:= Array(0..(30),[]); > array_tmp11:= Array(0..(30),[]); > array_tmp12:= Array(0..(30),[]); > array_tmp13:= Array(0..(30),[]); > array_tmp14:= Array(0..(30),[]); > array_m1:= Array(0..(30),[]); > array_y_higher := Array(0..(2) ,(0..30+ 1),[]); > array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]); > array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]); > array_y_set_initial := Array(0..(2) ,(0..30+ 1),[]); > array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]); > array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_fact_2 := Array(0..(30) ,(0..30+ 1),[]); > # before generate constants > # before generate globals definition > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > # before generate const definition > # before arrays initialized > term := 1; > while (term <= 30) do # do number 1 > array_y_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_norms[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_fact_1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_max_est_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_digits[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_y[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_x[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp5[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp6[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp7[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp8[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp9[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp10[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp11[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp12[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp13[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp14[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher_work[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher_work2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_set_initial[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_rad_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_ord_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=30) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_fact_2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > # before symbols initialized > #BEGIN SYMBOLS INITIALIZATED > zero_ats_ar(array_y); > zero_ats_ar(array_x); > zero_ats_ar(array_tmp0); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_tmp3); > zero_ats_ar(array_tmp4); > zero_ats_ar(array_tmp5); > zero_ats_ar(array_tmp6); > zero_ats_ar(array_tmp7); > zero_ats_ar(array_tmp8); > zero_ats_ar(array_tmp9); > zero_ats_ar(array_tmp10); > zero_ats_ar(array_tmp11); > zero_ats_ar(array_tmp12); > zero_ats_ar(array_tmp13); > zero_ats_ar(array_tmp14); > 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_5D0); > array_const_5D0[1] := c(5.0); > zero_ats_ar(array_const_6D0); > array_const_6D0[1] := c(6.0); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_h := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 1000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 30; > glob_iolevel := INFO; > # set default block > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := (0.0); > glob_max_minutes := (15.0); > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/sing7_backpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = neg ( 5.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=64;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := c(3.0);"); > 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 := 1;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(6.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > 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,""); > omniout_str(ALWAYS,"return(c(1.0)/ ( c(x) - c(6.0) ) / ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )) ;"); > 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(3.0); > x_end := c(2.0); > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_type_given_pole := 1; > array_given_rad_poles[1,1] := c(6.0); > #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 ) = neg ( 5.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; "); > 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,"2016-08-26T17:09:04-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sing7_back") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = neg ( 5.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ") > ; > 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,"sing7_back diffeq.mxt") > ; > logitem_str(html_log_file,"sing7_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_5D0, array_const_6D0, 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_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 30; Digits := 64; max_terms := 30; glob_html_log := true; array_y_init := Array(0 .. 30, []); array_norms := Array(0 .. 30, []); array_fact_1 := Array(0 .. 30, []); array_1st_rel_error := Array(0 .. 2, []); array_last_rel_error := Array(0 .. 2, []); array_est_rel_error := Array(0 .. 2, []); array_max_est_error := Array(0 .. 2, []); array_type_pole := Array(0 .. 2, []); array_type_real_pole := Array(0 .. 2, []); array_type_complex_pole := Array(0 .. 2, []); array_est_digits := Array(0 .. 2, []); array_y := Array(0 .. 30, []); array_x := Array(0 .. 30, []); array_tmp0 := Array(0 .. 30, []); array_tmp1 := Array(0 .. 30, []); array_tmp2 := Array(0 .. 30, []); array_tmp3 := Array(0 .. 30, []); array_tmp4 := Array(0 .. 30, []); array_tmp5 := Array(0 .. 30, []); array_tmp6 := Array(0 .. 30, []); array_tmp7 := Array(0 .. 30, []); array_tmp8 := Array(0 .. 30, []); array_tmp9 := Array(0 .. 30, []); array_tmp10 := Array(0 .. 30, []); array_tmp11 := Array(0 .. 30, []); array_tmp12 := Array(0 .. 30, []); array_tmp13 := Array(0 .. 30, []); array_tmp14 := Array(0 .. 30, []); array_m1 := Array(0 .. 30, []); array_y_higher := Array(0 .. 2, 0 .. 31, []); array_y_higher_work := Array(0 .. 2, 0 .. 31, []); array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []); array_y_set_initial := Array(0 .. 2, 0 .. 31, []); array_given_rad_poles := Array(0 .. 2, 0 .. 4, []); array_given_ord_poles := Array(0 .. 2, 0 .. 4, []); array_rad_test_poles := Array(0 .. 2, 0 .. 5, []); array_ord_test_poles := Array(0 .. 2, 0 .. 5, []); array_fact_2 := Array(0 .. 30, 0 .. 31, []); term := 1; while term <= 30 do array_y_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 30 do array_fact_1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_real_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do ; term := 1; while term <= 30 do array_y[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_x[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp5[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp6[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp7[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp8[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp9[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp10[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 30 do array_tmp11[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 30 do array_tmp12[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 30 do array_tmp13[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 30 do array_tmp14[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher_work[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_rad_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_ord_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 30 do term := 1; while term <= 30 do array_fact_2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; zero_ats_ar(array_y); zero_ats_ar(array_x); zero_ats_ar(array_tmp0); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2); zero_ats_ar(array_tmp3); zero_ats_ar(array_tmp4); zero_ats_ar(array_tmp5); zero_ats_ar(array_tmp6); zero_ats_ar(array_tmp7); zero_ats_ar(array_tmp8); zero_ats_ar(array_tmp9); zero_ats_ar(array_tmp10); zero_ats_ar(array_tmp11); zero_ats_ar(array_tmp12); zero_ats_ar(array_tmp13); zero_ats_ar(array_tmp14); 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_5D0); array_const_5D0[1] := c(5.0); zero_ats_ar(array_const_6D0); array_const_6D0[1] := c(6.0); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_h := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 1000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 30; glob_iolevel := INFO; glob_orig_start_sec := elapsed_time_seconds(); glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/sing7_backpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = neg ( 5.0 ) / \ ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) /\ ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=64;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := c(3.0);"); 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 := 1;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(6.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); 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, ""); omniout_str(ALWAYS, "return(c(1.0)/ ( c(x) - c(6.0) ) / ( c(x) - c(6.\ 0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )) ;\ "); 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(3.0); x_end := c(2.0); array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_type_given_pole := 1; array_given_rad_poles[1, 1] := c(6.0); 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 ) = neg ( 5.0 ) \ / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0\ ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6\ .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, "2016-08-26T17:09:04-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sing7_back"); logitem_str(html_log_file, "diff ( y , x , 1 ) = ne\ g ( 5.0 ) / ( x - 6.0 ) / ( x - 6.0 ) \ / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6\ .0 ) / ( x - 6.0 ) ; "); 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, "sing7_back diffeq.mxt"); logitem_str(html_log_file, "sing7_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/sing7_backpostode.ode################# diff ( y , x , 1 ) = neg ( 5.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=64; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := c(3.0); x_end := c(2.0); array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_type_given_pole := 1; array_given_rad_poles[1,1] := c(6.0); #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(c(1.0)/ ( c(x) - c(6.0) ) / ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )/ ( c(x) - c(6.0) )) ; end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop memory used=4.0MB, alloc=40.3MB, time=0.09 x[1] = 2.999 y[1] (closed_form) = -0.0041083744802657093950780428399777 y[1] (numeric) = -0.0041083744802657093944857661080764 absolute error = 5.9227673190131747068171893954906e-22 relative error = 1.4416327789647158292137470656978e-17 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 64 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.998 y[1] (closed_form) = -0.0041015363085463932069181756758744 y[1] (numeric) = -0.0041015363085463932057357894065657 absolute error = 1.1823862693086793667282175364401e-21 relative error = 2.8827887414892189421896662900447e-17 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 64 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.997 y[1] (closed_form) = -0.0040947117904110049780678777201631 y[1] (numeric) = -0.0040947117904110049762975404599509 absolute error = 1.7703372602122282351285122475233e-21 relative error = 4.3234722022634256643534768105309e-17 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 64 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.996 y[1] (closed_form) = -0.0040879008940647811499001256073957 y[1] (numeric) = -0.0040879008940647811475439872921659 absolute error = 2.3561383152297782109631676002449e-21 relative error = 5.7636874676943681814732105802677e-17 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 64 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.995 y[1] (closed_form) = -0.0040811035877975467982956684209535 y[1] (numeric) = -0.0040811035877975467953558704131728 absolute error = 2.9397980077806853263474892971272e-21 relative error = 7.2034388359331232243867457156676e-17 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 64 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.994 y[1] (closed_form) = -0.0040743198399834625427422014083783 y[1] (numeric) = -0.0040743198399834625392208765341194 absolute error = 3.5213248742588514171045382113724e-21 relative error = 8.6427305969016519230562692621790e-17 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 64 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.993 y[1] (closed_form) = -0.0040675496190807722965461955972546 y[1] (numeric) = -0.0040675496190807722924454681830498 absolute error = 4.1007274142048662307742267261038e-21 relative error = 1.0081567032319551154750745127198e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.992 y[1] (closed_form) = -0.0040607928936315518550835510449983 y[1] (numeric) = -0.004060792893631551850405536954521 absolute error = 4.6780140904772923135834240066508e-21 relative error = 1.1519952415730716709862324585498e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.991 y[1] (closed_form) = -0.0040540496322614583190274918609333 y[1] (numeric) = -0.0040540496322614583137742985315102 absolute error = 5.2531933294230972281758663715522e-21 relative error = 1.2957891012529918597573091262068e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (closed_form) = -0.0040473198036794803495043186704984 y[1] (numeric) = -0.0040473198036794803436780451494511 absolute error = 5.8262735210472376282287646172088e-21 relative error = 1.4395387079989288812304553839120e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.989 y[1] (closed_form) = -0.0040406033766776892521397790949967 y[1] (numeric) = -0.0040406033766776892457425160758153 absolute error = 6.3972630191813996905643501162352e-21 relative error = 1.5832444867284721880603862046796e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.988 y[1] (closed_form) = -0.004033900320130990886970909340439 y[1] (numeric) = -0.0040339003201309908800047391987871 absolute error = 6.9661701416519003799982403575067e-21 relative error = 1.7269068615522188506847799037931e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.987 y[1] (closed_form) = -0.0040272106029968784012102403689784 y[1] (numeric) = -0.0040272106029968783936772371985317 absolute error = 7.5330031704467539969514733328694e-21 relative error = 1.8705262557763962634878170401636e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.986 y[1] (closed_form) = -0.0040205341943151857818612506082185 y[1] (numeric) = -0.0040205341943151857737634802563366 absolute error = 8.0977703518819084327884061623927e-21 relative error = 2.0141030919054762241420241351120e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.985 y[1] (closed_form) = -0.0040138710632078422251958839781218 y[1] (numeric) = -0.0040138710632078422165354040813551 absolute error = 8.6604798967666555329274502583130e-21 relative error = 2.1576377916447804175879343667676e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.984 y[1] (closed_form) = -0.0040072211788786273201168374219896 y[1] (numeric) = -0.0040072211788786273108956974414214 absolute error = 9.2211399805682199430048830955042e-21 relative error = 2.3011307759030773359859657560725e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.983 y[1] (closed_form) = -0.0040005845106129270424391563554543 y[1] (numeric) = -0.0040005845106129270326593976118788 absolute error = 9.7797587435755307887528014445483e-21 relative error = 2.4445824647951706658503445604244e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.982 y[1] (closed_form) = -0.0039939610277774905571374597328887 y[1] (numeric) = -0.0039939610277774905468011154418265 absolute error = 1.0336344291062180515779735073227e-20 relative error = 2.5879932776444791734508651348498e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.981 y[1] (closed_form) = -0.0039873506998201878256168490101593 y[1] (numeric) = -0.0039873506998201878147259443167108 absolute error = 1.0890904693448575191115601911392e-20 relative error = 2.7313636329856081194447749222696e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (closed_form) = -0.0039807534962697680150772373911478 y[1] (numeric) = -0.0039807534962697680036337894046845 absolute error = 1.1443447986463280544200640074859e-20 relative error = 2.8746939485669122335781020202090e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.979 y[1] (closed_form) = -0.0039741693867356187070524676166617 y[1] (numeric) = -0.0039741693867356186950584854453581 absolute error = 1.1993982171303568000959789580373e-20 relative error = 3.0179846413530502801733004798283e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.978 y[1] (closed_form) = -0.0039675983409075259022171684208513 y[1] (numeric) = -0.0039675983409075258896746532060561 absolute error = 1.2542515214795164940708813689921e-20 relative error = 3.1612361275275312449981726752154e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.977 y[1] (closed_form) = -0.0039610403285554348185658318734518 y[1] (numeric) = -0.0039610403285554348054767768239006 absolute error = 1.3089055049551213381885349201235e-20 relative error = 3.3044488224952521739896362994447e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.976 y[1] (closed_form) = -0.0039544953195292114800800763763693 y[1] (numeric) = -0.0039544953195292114664464668022389 absolute error = 1.3633609574130441278986165181500e-20 relative error = 3.4476231408850276941850333740173e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.975 y[1] (closed_form) = -0.0039479632837584050930114933194635 y[1] (numeric) = -0.003947963283758405078835306666269 absolute error = 1.4176186653194550589620305038330e-20 relative error = 3.5907594965521112470933276870147e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.974 y[1] (closed_form) = -0.0039414441912520112069188595508464 y[1] (numeric) = -0.0039414441912520111922020654331815 absolute error = 1.4716794117664826247255607696122e-20 relative error = 3.7338583025807080646187029016315e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.973 y[1] (closed_form) = -0.0039349380120982356576098331084949 y[1] (numeric) = -0.003934938012098235642354393343617 absolute error = 1.5255439764877970152042476061769e-20 relative error = 3.8769199712864799175297538116280e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.972 y[1] (closed_form) = -0.0039284447164642592891485363182159 y[1] (numeric) = -0.0039284447164642592733564049594747 absolute error = 1.5792131358741164269042816750446e-20 relative error = 4.0199449142190416663486554863809e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.971 y[1] (closed_form) = -0.0039219642745960034521016686126328 y[1] (numeric) = -0.0039219642745960034357747919827464 absolute error = 1.6326876629886366900272951753327e-20 relative error = 4.1629335421644496444163969801272e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (closed_form) = -0.0039154966568178962752069814904192 y[1] (numeric) = -0.0039154966568178962583472982145953 absolute error = 1.6859683275823846174186143602921e-20 relative error = 4.3058862651476819027723755239041e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.969 y[1] (closed_form) = -0.0039090418335326397076590901368851 y[1] (numeric) = -0.0039090418335326396902685311757901 absolute error = 1.7390558961094954773572329512164e-20 relative error = 4.4488034924351103463693613324290e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.968 y[1] (closed_form) = -0.0039025997752209773292186905875625 y[1] (numeric) = -0.0039025997752209773112991792701383 absolute error = 1.7919511317424149900338881420516e-20 relative error = 4.5916856325369647910280600111873e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.967 y[1] (closed_form) = -0.003896170452441462925362298155847 y[1] (numeric) = -0.0038961704524414629069157502119768 absolute error = 1.8446547943870262453255857932195e-20 relative error = 4.7345330932097889704192167222498e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.966 y[1] (closed_form) = -0.0038897538358302298247006223831775 y[1] (numeric) = -0.0038897538358302298057289459762005 absolute error = 1.8971676406977019372501456365298e-20 relative error = 4.8773462814588885222454214532425e-16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.965 y[1] (closed_form) = -0.0038833498961007609959046462237191 y[1] (numeric) = -0.0038833498961007609764097419827963 absolute error = 1.9494904240922823082727379624023e-20 relative error = 5.0201256035407709826794856362595e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.964 y[1] (closed_form) = -0.0038769586040436599013893827620472 y[1] (numeric) = -0.0038769586040436598813731438143774 absolute error = 2.0016238947669791944378779890617e-20 relative error = 5.1628714649655778180014646974942e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.963 y[1] (closed_form) = -0.0038705799305264221050161416977984 y[1] (numeric) = -0.0038705799305264220844804537006863 absolute error = 2.0535687997112065601148511155643e-20 relative error = 5.3055842704995085222620966104038e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.962 y[1] (closed_form) = -0.0038642138464932076310849503305178 y[1] (numeric) = -0.0038642138464932076100316915032944 absolute error = 2.1053258827223379089719802689021e-20 relative error = 5.4482644241672368096866109129712e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.961 y[1] (closed_form) = -0.0038578603229646140718995400547569 y[1] (numeric) = -0.003857860322964614050330581210553 absolute error = 2.1568958844203909556354348365754e-20 relative error = 5.5909123292543189304195336819017e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (closed_form) = -0.0038515193310374504411980296425951 y[1] (numeric) = -0.0038515193310374504191152342199687 absolute error = 2.2082795422626399403413390268532e-20 relative error = 5.7335283883095941380982693933111e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.959 y[1] (closed_form) = -0.0038451908418845117707531110598515 y[1] (numeric) = -0.0038451908418845117481583351542699 absolute error = 2.2594775905581559667556862431722e-20 relative error = 5.8761130031475773376308782115907e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.958 y[1] (closed_form) = -0.0038388748267543544474561724439467 y[1] (numeric) = -0.0038388748267543544243512648391239 absolute error = 2.3104907604822757410149260435581e-20 relative error = 6.0186665748508439414415848176190e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.957 y[1] (closed_form) = -0.0038325712569710722882103763752763 y[1] (numeric) = -0.0038325712569710722645971785743663 absolute error = 2.3613197800909990879309828469230e-20 relative error = 6.1611895037724069623361502072105e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.956 y[1] (closed_form) = -0.0038262801039340733499682499086228 y[1] (numeric) = -0.0038262801039340733258485961652696 absolute error = 2.4119653743353156182078126278614e-20 relative error = 6.3036821895380863710283087644013e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.955 y[1] (closed_form) = -0.0038200013391178574722598362041077 y[1] (numeric) = -0.0038200013391178574476355535533531 absolute error = 2.4624282650754609184323278047626e-20 relative error = 6.4461450310488707462580171564232e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.954 y[1] (closed_form) = -0.0038137349340717945495679062149797 y[1] (numeric) = -0.0038137349340717945244408145040287 absolute error = 2.5127091710951026335305442761870e-20 relative error = 6.5885784264832712453222770333432e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.953 y[1] (closed_form) = -0.0038074808604199035309171329576557 y[1] (numeric) = -0.0038074808604199035052890448765011 absolute error = 2.5628088081154568093200515063449e-20 relative error = 6.7309827732996679227297779813558e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.952 y[1] (closed_form) = -0.0038012390898606321440544906123635 y[1] (numeric) = -0.0038012390898606321179272117242701 absolute error = 2.6127278888093348607423006128885e-20 relative error = 6.8733584682386484245815585212844e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.951 y[1] (closed_form) = -0.00379500959416663734160845628397 y[1] (numeric) = -0.0037950095941666373149837850558188 absolute error = 2.6624671228151215293226709782224e-20 relative error = 7.0157059073253390861712990202216e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (closed_form) = -0.003788792345184566466624863894591 y[1] (numeric) = -0.0037887923451845664395045917270841 absolute error = 2.7120272167506841913827378932692e-20 relative error = 7.1580254858717284601907390622116e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.949 y[1] (closed_form) = -0.0037825873148348391348874875838706 y[1] (numeric) = -0.0037825873148348391072733988415985 absolute error = 2.7614088742272138765175475458312e-20 relative error = 7.3003175984789833028180509817107e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.948 y[1] (closed_form) = -0.0037763944751114298314416163598805 y[1] (numeric) = -0.0037763944751114298033354884012505 absolute error = 2.8106127958629983538509371682909e-20 relative error = 7.4425826390397570448597987899442e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.947 y[1] (closed_form) = -0.0037702137980816512187490227729405 y[1] (numeric) = -0.0037702137980816511901526259799692 absolute error = 2.8596396792971276415939437301929e-20 relative error = 7.5848210007404907750103655182686e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop memory used=48.3MB, alloc=40.3MB, time=0.74 x[1] = 2.946 y[1] (closed_form) = -0.0037640452558859381539128262748435 y[1] (numeric) = -0.0037640452558859381248279240828121 absolute error = 2.9084902192031322934550510505665e-20 relative error = 7.7270330760637067621864399736140e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.945 y[1] (closed_form) = -0.0037578888207376324124208068745308 y[1] (numeric) = -0.0037578888207376323828491558015052 absolute error = 2.9571651073025548134863599412450e-20 relative error = 7.8692192567902945437883139686600e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.944 y[1] (closed_form) = -0.0037517444649227681158657369048157 y[1] (numeric) = -0.0037517444649227680858090865810312 absolute error = 3.0056650323784545489966567793930e-20 relative error = 8.0113799340017896066343511834188e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.943 y[1] (closed_form) = -0.0037456121607998578611112683689116 y[1] (numeric) = -0.0037456121607998578305713615660232 absolute error = 3.0539906802888464092207310201628e-20 relative error = 8.1535154980826446872100468753619e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.942 y[1] (closed_form) = -0.0037394918807996795483818406349611 y[1] (numeric) = -0.0037394918807996795173604132951604 absolute error = 3.1021427339800737555040803424857e-20 relative error = 8.2956263387224937177686016322145e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.941 y[1] (closed_form) = -0.0037333835974250639057649583852025 y[1] (numeric) = -0.0037333835974250638742637396502013 absolute error = 3.1501218735001158068432725813385e-20 relative error = 8.4377128449184084447158802151982e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (closed_form) = -0.0037272872832506827076240328966126 y[1] (numeric) = -0.0037272872832506826756447451364943 absolute error = 3.1979287760118299027146360093311e-20 relative error = 8.5797754049771477456090162409545e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.939 y[1] (closed_form) = -0.0037212029109228376844297811236562 y[1] (numeric) = -0.0037212029109228376519741399655949 absolute error = 3.2455641158061289632275540189437e-20 relative error = 8.7218144065173996709947529777138e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.938 y[1] (closed_form) = -0.0037151304531592501215279368620387 y[1] (numeric) = -0.0037151304531592500885976512188877 absolute error = 3.2930285643150944847533774097495e-20 relative error = 8.8638302364720162372108778754419e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.937 y[1] (closed_form) = -0.0037090698827488511443707466850426 y[1] (numeric) = -0.0037090698827488511109675187837923 absolute error = 3.3403227901250254073067683406677e-20 relative error = 9.0058232810902409961718116105084e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.936 y[1] (closed_form) = -0.0037030211725515726877494005501637 y[1] (numeric) = -0.0037030211725515726538749259602695 absolute error = 3.3874474589894231880930860533902e-20 relative error = 9.1477939259399294080575494124736e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.935 y[1] (closed_form) = -0.0036969842954981391465741831614289 y[1] (numeric) = -0.0036969842954981391122301508230098 absolute error = 3.4344032338419134137831476437645e-20 relative error = 9.2897425559097620427237212732078e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.934 y[1] (closed_form) = -0.0036909592245898597057587275291672 y[1] (numeric) = -0.0036909592245898596709468197810762 absolute error = 3.4811907748091042822352798306319e-20 relative error = 9.4316695552114506355495363457488e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.933 y[1] (closed_form) = -0.0036849459328984213467743068803722 y[1] (numeric) = -0.0036849459328984213114961994881384 absolute error = 3.5278107392233822825539526643175e-20 relative error = 9.5735753073819370233398034607340e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.932 y[1] (closed_form) = -0.003678944393565682528449615324487 y[1] (numeric) = -0.0036789443935656824927069775081306 absolute error = 3.5742637816356454005543866848977e-20 relative error = 9.7154601952855849857970722701292e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.931 y[1] (closed_form) = -0.0036729545798034675396009616559187 y[1] (numeric) = -0.0036729545798034675033954561176389 absolute error = 3.6205505538279741748932848731630e-20 relative error = 9.8573246011163650179802161291016e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (closed_form) = -0.0036669764648933615210872345593818 y[1] (numeric) = -0.0036669764648933614844205175111194 absolute error = 3.6666717048262409273271939558533e-20 relative error = 9.9991689064000320590664765144953e-16 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 18 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.929 y[1] (closed_form) = -0.0036610100221865061548933914599409 y[1] (numeric) = -0.0036610100221865061177671126508143 absolute error = 3.7126278809126574887718807807460e-20 relative error = 1.0140993491996296202635107629158e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.928 y[1] (closed_form) = -0.0036550552251033960178555775081179 y[1] (numeric) = -0.0036550552251033959802713802517353 absolute error = 3.7584197256382617410584535415231e-20 relative error = 1.0282798738100986413592296941415e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.927 y[1] (closed_form) = -0.0036491120471336755976502958925343 y[1] (numeric) = -0.0036491120471336755596098170941809 absolute error = 3.8040478798353432925147000046379e-20 relative error = 1.0424585024248207276758990853710e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.926 y[1] (closed_form) = -0.0036431804618359369686793260082526 y[1] (numeric) = -0.0036431804618359369301841961919546 absolute error = 3.8495129816298086037431913880171e-20 relative error = 1.0566352729312488802045622588516e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.925 y[1] (closed_form) = -0.003637260442837518125491322157382 y[1] (numeric) = -0.0036372604428375180865431654928471 absolute error = 3.8948156664534858782210473985939e-20 relative error = 1.0708102231510929311040519837071e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.924 y[1] (closed_form) = -0.0036313519638343019713902225978593 y[1] (numeric) = -0.0036313519638343019319906569272956 absolute error = 3.9399565670563700306098118006463e-20 relative error = 1.0849833908405331429741960860333e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.923 y[1] (closed_form) = -0.0036254549985905159598897570639812 y[1] (numeric) = -0.0036254549985905159200403939287931 absolute error = 3.9849363135188080439375858191954e-20 relative error = 1.0991548136904331212067447694218e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.922 y[1] (closed_form) = -0.0036195695209385323866824605347474 y[1] (numeric) = -0.0036195695209385323463849052021112 absolute error = 4.0297555332636250250993461501887e-20 relative error = 1.1133245293265520418677772033923e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.921 y[1] (closed_form) = -0.0036136955047786693298006821990392 y[1] (numeric) = -0.0036136955047786692890565336883573 absolute error = 4.0744148510681912664151732253831e-20 relative error = 1.1274925753097561975557861405468e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (closed_form) = -0.0036078329240789922356561214348795 y[1] (numeric) = -0.0036078329240789921944669725441152 absolute error = 4.1189148890764306192898719411371e-20 relative error = 1.1416589891362298636701208535889e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.919 y[1] (closed_form) = -0.003601981752875116148653427357459 y[1] (numeric) = -0.0036019817528751161070208646893513 absolute error = 4.1632562668107704843311199832395e-20 relative error = 1.1558238082376854875149903575261e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.918 y[1] (closed_form) = -0.0035961419652700085820823652703501 y[1] (numeric) = -0.0035961419652700085400079692585098 absolute error = 4.2074396011840337206067672383591e-20 relative error = 1.1699870699815732026547905181090e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.917 y[1] (closed_form) = -0.0035903135354337930280019823486359 y[1] (numeric) = -0.0035903135354337929854873272835231 absolute error = 4.2514655065112727750551730453173e-20 relative error = 1.1841488116712896709271200634903e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.916 y[1] (closed_form) = -0.0035844964376035531038390962629572 y[1] (numeric) = -0.0035844964376035530608857503177417 absolute error = 4.2953345945215463314054460667956e-20 relative error = 1.1983090705463862545104915316969e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.915 y[1] (closed_form) = -0.0035786906460831373334322843903306 y[1] (numeric) = -0.0035786906460831372900418096466342 absolute error = 4.3390474743696387763170846042744e-20 relative error = 1.2124678837827765204344236221791e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.914 y[1] (closed_form) = -0.0035728961352429645602613679207506 y[1] (numeric) = -0.0035728961352429645164353203942733 absolute error = 4.3826047526477227788107438726529e-20 relative error = 1.2266252884929430799103210966820e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.913 y[1] (closed_form) = -0.0035671128795198299906111647270093 y[1] (numeric) = -0.0035671128795198299463510943930396 absolute error = 4.4260070333969652774336221168826e-20 relative error = 1.2407813217261437648523071150869e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.912 y[1] (closed_form) = -0.0035613408534167118644270274869486 y[1] (numeric) = -0.0035613408534167118197344783057578 absolute error = 4.4692549181190771679842008933000e-20 relative error = 1.2549360204686171439479705186874e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.911 y[1] (closed_form) = -0.0035555800315025787516283893998019 y[1] (numeric) = -0.0035555800315025787065048993419239 absolute error = 4.5123490057878069830117381342816e-20 relative error = 1.2690894216437873806298269104137e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (closed_form) = -0.0035498303884121974716552090878715 y[1] (numeric) = -0.0035498303884121974261023101592678 absolute error = 4.5552898928603788527059379237886e-20 relative error = 1.2832415621124684352891672535213e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.909 y[1] (closed_form) = -0.0035440918988459416340308390871979 y[1] (numeric) = -0.0035440918988459415880500573543091 absolute error = 4.5980781732888750352015507645007e-20 relative error = 1.2973924786730676140648809427363e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.908 y[1] (closed_form) = -0.0035383645375696007977334388709855 y[1] (numeric) = -0.0035383645375696007513262944856698 absolute error = 4.6407144385315633027412354169563e-20 relative error = 1.3115422080617884665307917212048e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.907 y[1] (closed_form) = -0.0035326482794141902471766137814284 y[1] (numeric) = -0.0035326482794141902003446210057867 absolute error = 4.6831992775641694685677814085228e-20 relative error = 1.3256907869528330345960342500559e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.906 y[1] (closed_form) = -0.0035269430992757613826084857325097 y[1] (numeric) = -0.0035269430992757613353531529635987 absolute error = 4.7255332768910953378536936824175e-20 relative error = 1.3398382519586034549240264130244e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.905 y[1] (closed_form) = -0.0035212489721152127227468902508203 y[1] (numeric) = -0.0035212489721152126750697200452545 absolute error = 4.7677170205565823644221215854239e-20 relative error = 1.3539846396299029171666573852936e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.904 y[1] (closed_form) = -0.0035155658729581015174768475051586 y[1] (numeric) = -0.0035155658729581014693793366036004 absolute error = 4.8097510901558212934681178396767e-20 relative error = 1.3681299864561359803014139432451e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.903 y[1] (closed_form) = -0.0035098937768944559684448725995485 y[1] (numeric) = -0.0035098937768944559199285119510885 absolute error = 4.8516360648460080689531840300296e-20 relative error = 1.3822743288655082493503072706874e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.902 y[1] (closed_form) = -0.0035042326590785880553930727284975 y[1] (numeric) = -0.0035042326590785880064593475149241 absolute error = 4.8933725213573462828189425415519e-20 relative error = 1.3964177032252254147506394587658e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.901 y[1] (closed_form) = -0.0034985824947289069660843259771673 y[1] (numeric) = -0.0034985824947289069167347156371274 absolute error = 4.9349610340039964416475162330824e-20 relative error = 1.4105601458416916566388628333092e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (closed_form) = -0.0034929432591277331276781487512501 y[1] (numeric) = -0.0034929432591277330779141270043004 absolute error = 4.9764021746949723248867422155281e-20 relative error = 1.4247016929607074163000360078643e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.899 y[1] (closed_form) = -0.0034873149276211128374251361995574 y[1] (numeric) = -0.0034873149276211127872481710701076 absolute error = 5.0176965129449847072576410499708e-20 relative error = 1.4388423807676665370266679868934e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.898 y[1] (closed_form) = -0.0034816974756186334905561027037067 y[1] (numeric) = -0.0034816974756186334399676565448544 absolute error = 5.0588446158852327164695539697043e-20 relative error = 1.4529822453877527766220655662070e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.897 y[1] (closed_form) = -0.0034760908785932394032502577101362 y[1] (numeric) = -0.0034760908785932393522517872273948 absolute error = 5.0998470482741430958849951856304e-20 relative error = 1.4671213228861356937746595320518e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.896 y[1] (closed_form) = -0.0034704951120810482285749260255497 y[1] (numeric) = -0.0034704951120810481771678823004691 absolute error = 5.1407043725080576403014911217353e-20 relative error = 1.4812596492681659105211815826112e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.895 y[1] (closed_form) = -0.0034649101516811679632974613425867 y[1] (numeric) = -0.003464910151681167911483289856268 absolute error = 5.1814171486318690715514410522309e-20 relative error = 1.4953972604795697530079963229775e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.894 y[1] (closed_form) = -0.0034593359730555145434781073620878 y[1] (numeric) = -0.0034593359730555144912582480185917 absolute error = 5.2219859343496056191632819175316e-20 relative error = 1.5095341924066432727513609547193e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.893 y[1] (closed_form) = -0.0034537725519286300267606325850877 y[1] (numeric) = -0.0034537725519286299741365197347381 absolute error = 5.2624112850349645698779222609775e-20 relative error = 1.5236704808764456505888892325593e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.892 y[1] (closed_form) = -0.0034482198640875013592856028142004 y[1] (numeric) = -0.0034482198640875013062586652767824 absolute error = 5.3026937537417950483734747635728e-20 relative error = 1.5378061616569919855060357327392e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.891 y[1] (closed_form) = -0.0034426778853813797251591597821814 y[1] (numeric) = -0.0034426778853813796717308208700361 absolute error = 5.3428338912145302901187126021956e-20 relative error = 1.5519412704574454705129913105084e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop memory used=94.9MB, alloc=44.3MB, time=1.43 x[1] = 2.89 y[1] (closed_form) = -0.003437146591721600476418145266291 y[1] (numeric) = -0.0034371465917216004225898228073053 absolute error = 5.3828322458985696658513509885440e-20 relative error = 1.5660758429283089577389906587174e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.889 y[1] (closed_form) = -0.0034316259590814036414403477009852 y[1] (numeric) = -0.0034316259590814035872134540614791 absolute error = 5.4226893639506107157611612585978e-20 relative error = 1.5802099146616159149026779573869e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.888 y[1] (closed_form) = -0.0034261159634957550097565528181125 y[1] (numeric) = -0.0034261159634957549551324949256232 absolute error = 5.4624057892489314500500105968416e-20 relative error = 1.5943435211911207753088565677839e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.887 y[1] (closed_form) = -0.0034206165810611677912289513720974 y[1] (numeric) = -0.0034206165810611677362091307380612 absolute error = 5.5019820634036231711411360390746e-20 relative error = 1.6084766979924886835136634171392e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.886 y[1] (closed_form) = -0.0034151277879355248475682956957787 y[1] (numeric) = -0.0034151277879355247921541084381109 absolute error = 5.5414187257667740714182572653004e-20 relative error = 1.6226094804834846387919579856352e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.885 y[1] (closed_form) = -0.0034096495603379014941700028281388 y[1] (numeric) = -0.0034096495603379014383628396937128 absolute error = 5.5807163134426038589914596505096e-20 relative error = 1.6367419040241620385324994903505e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.884 y[1] (closed_form) = -0.0034041818745483888702571754048947 y[1] (numeric) = -0.0034041818745483888140584217919192 absolute error = 5.6198753612975496626110881822178e-20 relative error = 1.6508740039170506236783038069189e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.883 y[1] (closed_form) = -0.0033987247069079178753262525529166 y[1] (numeric) = -0.0033987247069079178187372885332136 absolute error = 5.6588964019703034654831355888353e-20 relative error = 1.6650058154073438283214237249063e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.882 y[1] (closed_form) = -0.0033932780338180836698987118250772 y[1] (numeric) = -0.0033932780338180836129209121662592 absolute error = 5.6977799658818013163797360730051e-20 relative error = 1.6791373736830855355532821442636e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.881 y[1] (closed_form) = -0.003387841831740970738589919898091 y[1] (numeric) = -0.0033878418317409706812246540856394 absolute error = 5.7365265812451645650863414388201e-20 relative error = 1.6932687138753562416636076353152e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (closed_form) = -0.0033824160771989785135138744761813 y[1] (numeric) = -0.0033824160771989784557625067354253 absolute error = 5.7751367740755933678829114782442e-20 relative error = 1.7073998710584586307729752519885e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.879 y[1] (closed_form) = -0.0033770007467746475560501927412978 y[1] (numeric) = -0.0033770007467746474979140820592957 absolute error = 5.8136110682002127074199478820986e-20 relative error = 1.7215308802501025619759424564859e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.878 y[1] (closed_form) = -0.0033715958171104862950072829087187 y[1] (numeric) = -0.00337159581711048623648778305604 absolute error = 5.8519499852678711700213936095505e-20 relative error = 1.7356617764115894710637903331897e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.877 y[1] (closed_form) = -0.0033662012649087983192231851271279 y[1] (numeric) = -0.003366201264908798260321644679539 absolute error = 5.8901540447588927221252608330538e-20 relative error = 1.7497925944479961888879337908284e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.876 y[1] (closed_form) = -0.0033608170669315102226530862459082 y[1] (numeric) = -0.0033608170669315101633708486059604 absolute error = 5.9282237639947817262592938179196e-20 relative error = 1.7639233692083581784171510261013e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.875 y[1] (closed_form) = -0.0033554432 y[1] (numeric) = -0.0033554431999999999403384034185212 absolute error = 5.9661596581478814356429722388595e-20 relative error = 1.7780541354858521925339020010410e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.874 y[1] (closed_form) = -0.0033500796409949259909525600741339 y[1] (numeric) = -0.003350079640994925930912937671624 absolute error = 6.0039622402509862052086696165724e-20 relative error = 1.7921849280179783546071579230940e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.873 y[1] (closed_form) = -0.0033447263668560563711012984427811 y[1] (numeric) = -0.003344726366856056310684978230712 absolute error = 6.0416320212069076555437552053033e-20 relative error = 1.8063157814867416638713485646256e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.872 y[1] (closed_form) = -0.0033393833545820991876121754783259 y[1] (numeric) = -0.003339383354582099126820480380346 absolute error = 6.0791695097979950249718204978560e-20 relative error = 1.8204467305188329276332515714126e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.871 y[1] (closed_form) = -0.0033340505812305329377434917156476 y[1] (numeric) = -0.0033340505812305328765777395886915 absolute error = 6.1165752126956099437149785473601e-20 relative error = 1.8345778096858091223208975424833e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (closed_form) = -0.0033287280239174376882996439937289 y[1] (numeric) = -0.0033287280239174376267611476490333 absolute error = 6.1538496344695558628102808318527e-20 relative error = 1.8487090535042731853808464719083e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.869 y[1] (closed_form) = -0.0033234156598173267341224911006682 y[1] (numeric) = -0.0033234156598173266722125583246936 absolute error = 6.1909932775974623691916779902822e-20 relative error = 1.8628404964360532400225049830238e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.868 y[1] (closed_form) = -0.0033181134661629787937283661634666 y[1] (numeric) = -0.0033181134661629787314482997387254 absolute error = 6.2280066424741246170945733019805e-20 relative error = 1.8769721728883812548004995139756e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.867 y[1] (closed_form) = -0.0033128214202452707402060149834797 y[1] (numeric) = -0.0033128214202452706775571127092717 absolute error = 6.2648902274207981046928374124307e-20 relative error = 1.8911041172140711400184980879650e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.866 y[1] (closed_form) = -0.0033075394994130108654979514570697 y[1] (numeric) = -0.0033075394994130108024815061701252 absolute error = 6.3016445286944490236381259522565e-20 relative error = 1.9052363637116962829302823804173e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.865 y[1] (closed_form) = -0.0033022676810727726761949032727598 y[1] (numeric) = -0.0033022676810727726128122028677902 absolute error = 6.3382700404969604079384250573012e-20 relative error = 1.9193689466257665237063123374004e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.864 y[1] (closed_form) = -0.0032970059426887292189801733744113 y[1] (numeric) = -0.0032970059426887291552325008245683 absolute error = 6.3747672549842943073869003547903e-20 relative error = 1.9335019001469045741264974645999e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.863 y[1] (closed_form) = -0.0032917542617824879338678653573148 y[1] (numeric) = -0.0032917542617824878697564987345587 absolute error = 6.4111366622756102095332999870915e-20 relative error = 1.9476352584120218809523919542831e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.862 y[1] (closed_form) = -0.0032865126159329260333860141526854 y[1] (numeric) = -0.003286512615932925968912226648062 absolute error = 6.4473787504623399329783192258044e-20 relative error = 1.9617690555044939359245649098976e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.861 y[1] (closed_form) = -0.003281280982776026405862727187303 y[1] (numeric) = -0.0032812809827760263410277871311308 absolute error = 6.4834940056172192135664309804072e-20 relative error = 1.9759033254543350343234619258534e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (closed_form) = -0.0032760593400047140409804758097651 y[1] (numeric) = -0.0032760593400047139757856466917323 absolute error = 6.5194829118032762038546810914754e-20 relative error = 1.9900381022383724840246700459019e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.859 y[1] (closed_form) = -0.0032708476653686929757706822831913 y[1] (numeric) = -0.0032708476653686929102172227723635 absolute error = 6.5553459510827771050437980492614e-20 relative error = 2.0041734197804202669721245202698e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.858 y[1] (closed_form) = -0.0032656459366742837592277241858148 y[1] (numeric) = -0.0032656459366742836933168881505535 absolute error = 6.5910836035261291493736322897668e-20 relative error = 2.0183093119514521549854526729097e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.857 y[1] (closed_form) = -0.0032604541317842614337284257646506 y[1] (numeric) = -0.0032604541317842613674614622924432 absolute error = 6.6266963472207411498073793510341e-20 relative error = 2.0324458125697742818103374401261e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.856 y[1] (closed_form) = -0.003255272228617694031450024781679 y[1] (numeric) = -0.0032552722286176939648281781988806 absolute error = 6.6621846582798418326582130423052e-20 relative error = 2.0465829554011971733135006152865e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.855 y[1] (closed_form) = -0.0032501002051497815839864938044474 y[1] (numeric) = -0.0032501002051497815170110036959348 absolute error = 6.6975490108512561676478187675961e-20 relative error = 2.0607207741592072377166533968764e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.854 y[1] (closed_form) = -0.0032449380394116956433699568507794 y[1] (numeric) = -0.003244938039411695576042058079518 absolute error = 6.7327898771261399087288328907153e-20 relative error = 2.0748593025051377177565393549368e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.853 y[1] (closed_form) = -0.0032397857094904193127107759268964 y[1] (numeric) = -0.0032397857094904192450316986534197 absolute error = 6.7679077273476725578523214245154e-20 relative error = 2.0889985740483391066510022707599e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.852 y[1] (closed_form) = -0.0032346431935285877846766874256066 y[1] (numeric) = -0.0032346431935285877166476571274095 absolute error = 6.8029030298197089627171305214427e-20 relative error = 2.1031386223463490297438483340226e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.851 y[1] (closed_form) = -0.0032295104697243293860381457015995 y[1] (numeric) = -0.0032295104697243293176603831924456 absolute error = 6.8377762509153897584001726361874e-20 relative error = 2.1172794809050615936941387683897e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (closed_form) = -0.0032243875163311071265137805390143 y[1] (numeric) = -0.0032243875163311070577885019881572 absolute error = 6.8725278550857108616354364765113e-20 relative error = 2.1314211831788962050684449697016e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.849 y[1] (closed_form) = -0.0032192743116575607501565967964315 y[1] (numeric) = -0.003219274311657560681085013747751 absolute error = 6.9071583048680522253846868566011e-20 relative error = 2.1455637625709658601875235494940e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.848 y[1] (closed_form) = -0.0032141708340673492875282383798077 y[1] (numeric) = -0.0032141708340673492181115577708611 absolute error = 6.9416680608946660602244134678067e-20 relative error = 2.1597072524332449080718231507253e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.847 y[1] (closed_form) = -0.0032090770619789941069153049775527 y[1] (numeric) = -0.0032090770619789940371547291585414 absolute error = 6.9760575819011247279615567796962e-20 relative error = 2.1738516860667362883232184127514e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.846 y[1] (closed_form) = -0.0032039929738657224628483488163023 y[1] (numeric) = -0.003203992973865722392745075568955 absolute error = 7.0103273247347285117848464198165e-20 relative error = 2.1879970967216382457733788799841e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.845 y[1] (closed_form) = -0.0031989185482553115401907901827341 y[1] (numeric) = -0.0031989185482553114697460127391053 absolute error = 7.0444777443628734661591943360371e-20 relative error = 2.2021435175975105237222218450591e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.844 y[1] (closed_form) = -0.0031938537637299329920715747271969 y[1] (numeric) = -0.0031938537637299329212864817883831 absolute error = 7.0785092938813795485774539447615e-20 relative error = 2.2162909818434400375829679651308e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.843 y[1] (closed_form) = -0.0031887985989259979699419527396006 y[1] (numeric) = -0.0031887985989259978988177284943728 absolute error = 7.1124224245227792341969496751447e-20 relative error = 2.2304395225582060307434168621037e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.842 y[1] (closed_form) = -0.0031837530325340026440432907869833 y[1] (numeric) = -0.0031837530325340025725811149303377 absolute error = 7.1462175856645668133074614352987e-20 relative error = 2.2445891727904447144461866877947e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.841 y[1] (closed_form) = -0.0031787170432983742125793294449096 y[1] (numeric) = -0.0031787170432983741407803771965355 absolute error = 7.1798952248374085705027783893265e-20 relative error = 2.2587399655388133934838166774192e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (closed_form) = -0.0031736906100173173978927774602678 y[1] (numeric) = -0.0031736906100173173257582195829347 absolute error = 7.2134557877333140433594791168048e-20 relative error = 2.2728919337521540794978149041839e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.839 y[1] (closed_form) = -0.0031686737115426614279525826694723 y[1] (numeric) = -0.0031686737115426613554835854873346 absolute error = 7.2468997182137685573642140352604e-20 relative error = 2.2870451103296565936639446595647e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.838 y[1] (closed_form) = -0.0031636663267797075014646434813133 y[1] (numeric) = -0.0031636663267797074286623688981351 absolute error = 7.2802274583178272327744244392909e-20 relative error = 2.3011995281210211605392819940190e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.837 y[1] (closed_form) = -0.0031586684346870767349251218349678 y[1] (numeric) = -0.0031586684346870766617907273522661 absolute error = 7.3134394482701706580470944155165e-20 relative error = 2.3153552199266204948398438380075e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.836 y[1] (closed_form) = -0.0031536800142765585899418893776481 y[1] (numeric) = -0.0031536800142765585164765281127569 absolute error = 7.3465361264891224234257612275126e-20 relative error = 2.3295122184976613829108806604342e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.835 y[1] (closed_form) = -0.0031487010446129597791559832891499 y[1] (numeric) = -0.0031487010446129597053608039932036 memory used=141.4MB, alloc=44.3MB, time=2.11 absolute error = 7.3795179295946287072375707534511e-20 relative error = 2.3436705565363457606452496886986e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.834 y[1] (closed_form) = -0.0031437315048139536491012668277221 y[1] (numeric) = -0.0031437315048139535749774139035601 absolute error = 7.4123852924162001064196216512562e-20 relative error = 2.3578302666960312895986341898025e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.833 y[1] (closed_form) = -0.0031387713740499300383467823982469 y[1] (numeric) = -0.0031387713740499299638953959182388 absolute error = 7.4451386480008159017671597957616e-20 relative error = 2.3719913815813914330437510742670e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.832 y[1] (closed_form) = -0.0031338206315438456092725518641623 y[1] (numeric) = -0.0031338206315438455344947675879543 absolute error = 7.4777784276207909473753280764514e-20 relative error = 2.3861539337485750336990930134526e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.831 y[1] (closed_form) = -0.0031288792565710746518358200528139 y[1] (numeric) = -0.0031288792565710745767327694449979 absolute error = 7.5103050607816053727311109809406e-20 relative error = 2.4003179557053653948611822362809e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (closed_form) = -0.0031239472284592603576909530533877 y[1] (numeric) = -0.0031239472284592602822637633010907 absolute error = 7.5427189752296972849028038562531e-20 relative error = 2.4144834799113388666627710739302e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.829 y[1] (closed_form) = -0.0031190245265881665630323930901006 y[1] (numeric) = -0.0031190245265881664872821871204984 absolute error = 7.5750205969602186572707488933505e-20 relative error = 2.4286505387780229391729090319941e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.828 y[1] (closed_form) = -0.0031141111303895299585362365832556 y[1] (numeric) = -0.0031141111303895298824641330810081 absolute error = 7.6072103502247545902451794933349e-20 relative error = 2.4428191646690538440483075705746e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.827 y[1] (closed_form) = -0.0031092070193469127647821415988725 y[1] (numeric) = -0.0031092070193469126883892550234824 absolute error = 7.6392886575390061284247677347855e-20 relative error = 2.4569893899003336664389717461299e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.826 y[1] (closed_form) = -0.0031043121729955558715433853451773 y[1] (numeric) = -0.003104312172995555794830825948273 absolute error = 7.6712559396904368176628423733541e-20 relative error = 2.4711612467401869688446322974487e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.825 y[1] (closed_form) = -0.0030994265709222324393389818119967 y[1] (numeric) = -0.0030994265709222323623078556545378 absolute error = 7.7031126157458831845272035821859e-20 relative error = 2.4853347674095169286121025252827e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.824 y[1] (closed_form) = -0.0030945501927651019616478341772835 y[1] (numeric) = -0.0030945501927651018842992431466922 absolute error = 7.7348591030591293196639721113275e-20 relative error = 2.4995099840819609907573013048818e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.823 y[1] (closed_form) = -0.0030896830182135647861909363333039 y[1] (numeric) = -0.0030896830182135647085259781605194 absolute error = 7.7664958172784457456059415422117e-20 relative error = 2.5136869288840460377893266674459e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.822 y[1] (closed_form) = -0.0030848250270081170936936529226052 y[1] (numeric) = -0.0030848250270081170157134211990643 absolute error = 7.7980231723540927486014198841975e-20 relative error = 2.5278656338953430782076334753686e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.821 y[1] (closed_form) = -0.0030799761989402063325460977294541 y[1] (numeric) = -0.0030799761989402062542516819239962 absolute error = 7.8294415805457883530805181556652e-20 relative error = 2.5420461311486214553370636826910e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (closed_form) = -0.0030751365138520871077855962541089 y[1] (numeric) = -0.0030751365138520870291780817298074 absolute error = 7.8607514524301411164222362696869e-20 relative error = 2.5562284526300025781591984025290e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.819 y[1] (closed_form) = -0.0030703059516366775228311599127426 y[1] (numeric) = -0.0030703059516366774439116279436622 absolute error = 7.8919531969080479207374781655240e-20 relative error = 2.5704126302791131757922473840483e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.818 y[1] (closed_form) = -0.0030654844922374159724058166621798 y[1] (numeric) = -0.0030654844922374158931753444500592 absolute error = 7.9230472212120569374402665568309e-20 relative error = 2.5845986959892380772654634200305e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.817 y[1] (closed_form) = -0.0030606721156481183850885360524965 y[1] (numeric) = -0.0030606721156481183055481967433595 absolute error = 7.9540339309136959394418909718166e-20 relative error = 2.5987866816074725182278665499264e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.816 y[1] (closed_form) = -0.0030558688019128359139433558680881 y[1] (numeric) = -0.0030558688019128358340942185687804 absolute error = 7.9849137299307661348704792063995e-20 relative error = 2.6129766189348739762248855807874e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.815 y[1] (closed_form) = -0.0030510745311257130736791627346611 y[1] (numeric) = -0.0030510745311257129935222925293151 absolute error = 8.0156870205346016952915003642595e-20 relative error = 2.6271685397266135361703723083806e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.814 y[1] (closed_form) = -0.003046289283430846322799400450891 y[1] (numeric) = -0.003046289283430846242335858417318 absolute error = 8.0463542033572951504829559810069e-20 relative error = 2.6413624756921267876353167724294e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.813 y[1] (closed_form) = -0.0030415130390221430892067774538526 y[1] (numeric) = -0.0030415130390221430084376206798637 absolute error = 8.0769156773988888209024631832168e-20 relative error = 2.6555584584952642555684898131133e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.812 y[1] (closed_form) = -0.0030367457781431812377338188509102 y[1] (numeric) = -0.0030367457781431811566601004505649 absolute error = 8.1073718400345324580720494716705e-20 relative error = 2.6697565197544413660581620010400e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.811 y[1] (closed_form) = -0.0030319874810870689780758589512211 y[1] (numeric) = -0.003031987481087068896698628081005 absolute error = 8.1377230870216072622002317904909e-20 relative error = 2.6839566910427879487379955807338e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (closed_form) = -0.0030272381281963052116087973105244 y[1] (numeric) = -0.0030272381281963051299290991854562 absolute error = 8.1679698125068164454598124911755e-20 relative error = 2.6981590038882972774341782896452e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.809 y[1] (closed_form) = -0.0030224976998626403155796450661427 y[1] (numeric) = -0.0030224976998626402335985209758103 absolute error = 8.1981124090332425084437612553154e-20 relative error = 2.7123634897739746506448646826408e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.808 y[1] (closed_form) = -0.0030177661765269373631635688873278 y[1] (numeric) = -0.0030177661765269372808820562118541 absolute error = 8.2281512675473713964305348245727e-20 relative error = 2.7265701801379855134370117982938e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.807 y[1] (closed_form) = -0.0030130435386790337778867973009496 y[1] (numeric) = -0.0030130435386790336953059295268888 absolute error = 8.2580867774060837012041855125643e-20 relative error = 2.7407791063738031223397415409389e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.806 y[1] (closed_form) = -0.0030083297668576034209203885753165 y[1] (numeric) = -0.0030083297668576033380411953114804 absolute error = 8.2879193263836130732935951394931e-20 relative error = 2.7549902998303557548074319147902e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.805 y[1] (closed_form) = -0.0030036248416500191097554708563885 y[1] (numeric) = -0.0030036248416500190265789778496038 absolute error = 8.3176493006784720086191136218257e-20 relative error = 2.7692037918121734648198331273407e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.804 y[1] (closed_form) = -0.0029989287436922155667761539511093 y[1] (numeric) = -0.0029989287436922154833033831019058 absolute error = 8.3472770849203451726637515362347e-20 relative error = 2.7834196135795343861806224731674e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.803 y[1] (closed_form) = -0.0029942414536685527962518781418635 y[1] (numeric) = -0.002994241453668552712483847520094 absolute error = 8.3768030621769504244198443135012e-20 relative error = 2.7976377963486105850699537110397e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.802 y[1] (closed_form) = -0.0029895629523116798882765087935255 y[1] (numeric) = -0.0029895629523116798042142326539169 absolute error = 8.4062276139608677015007432408402e-20 relative error = 2.8118583712916134634007222522664e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.801 y[1] (closed_form) = -0.0029848932204023992481870063791007 y[1] (numeric) = -0.0029848932204023991638314951767374 absolute error = 8.4355511202363359269505662783781e-20 relative error = 2.8260813695369387145224567823807e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (closed_form) = -0.00298023223876953125 y[1] (numeric) = -0.0029802322387695311653522604057398 absolute error = 8.4647739594260180974333311257515e-20 relative error = 2.8403068221693108328109608379251e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.799 y[1] (closed_form) = -0.0029755799882897793124100686105117 y[1] (numeric) = -0.0029755799882897792274711035263343 absolute error = 8.4938965084177347116358654855866e-20 relative error = 2.8545347602299271786760642521014e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.798 y[1] (closed_form) = -0.0029709364498875953958989880705429 y[1] (numeric) = -0.0029709364498875953106697966448313 absolute error = 8.5229191425711656968767167174463e-20 relative error = 2.8687652147166016005141041647241e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.797 y[1] (closed_form) = -0.0029663016045350459195106339432652 y[1] (numeric) = -0.00296630160453504583399221158602 absolute error = 8.5518422357245209910758368909429e-20 relative error = 2.8829982165839076151260383610796e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.796 y[1] (closed_form) = -0.0029616754332516780958516397215057 y[1] (numeric) = -0.0029616754332516780100449781194939 absolute error = 8.5806661602011799364070716379538e-20 relative error = 2.8972337967433211481163999592211e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.795 y[1] (closed_form) = -0.0029570579171043866828832980047398 y[1] (numeric) = -0.0029570579171043865967893851365768 absolute error = 8.6093912868162996401274043535366e-20 relative error = 2.9114719860633628357826318047059e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.794 y[1] (closed_form) = -0.0029524490372072811510755581530497 y[1] (numeric) = -0.0029524490372072810646953783042158 absolute error = 8.6380179848833924572534735588198e-20 relative error = 2.9257128153697398899986912550278e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.793 y[1] (closed_form) = -0.0029478487747215532644993182106839 y[1] (numeric) = -0.0029478487747215531778338519884752 absolute error = 8.6665466222208727489370631446171e-20 relative error = 2.9399563154454875275911912427348e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.792 y[1] (closed_form) = -0.0029432571108553450744385315146825 y[1] (numeric) = -0.0029432571108553449874887558630968 absolute error = 8.6949775651585730695770354606026e-20 relative error = 2.9542025170311099657007414966257e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.791 y[1] (closed_form) = -0.0029386740268636173241089494777961 y[1] (numeric) = -0.0029386740268636172368758376923538 absolute error = 8.7233111785442299348955086703420e-20 relative error = 2.9684514508247209846155744751294e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (closed_form) = -0.0029340995040480182630756016535392 y[1] (numeric) = -0.0029340995040480181755601233960398 absolute error = 8.7515478257499393224009454948783e-20 relative error = 2.9827031474821840595589838261074e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.789 y[1] (closed_form) = -0.002929533523756752869966372448179 y[1] (numeric) = -0.0029295335237567527821694937613931 absolute error = 8.7796878686785820548601936222053e-20 relative error = 2.9969576376172520629065689344398e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.788 y[1] (closed_form) = -0.0029249760673844524820842708328028 y[1] (numeric) = -0.0029249760673844523940069541551006 absolute error = 8.8077316677702192166053720387492e-20 relative error = 3.0112149518017065383037672549018e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.787 y[1] (closed_form) = -0.0029204271163720448305262052209679 y[1] (numeric) = -0.0029204271163720447421694094008833 absolute error = 8.8356795820084577517098058793603e-20 relative error = 3.0254751205654965481486665554878e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.786 y[1] (closed_form) = -0.0029158866522066244794212704059756 y[1] (numeric) = -0.0029158866522066243907859507167077 absolute error = 8.8635319689267863922799487962085e-20 relative error = 3.0397381743968770958996218184456e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.785 y[1] (closed_form) = -0.0029113546564213236679067271883089 y[1] (numeric) = -0.0029113546564213235789938353421601 absolute error = 8.8912891846148820643273701796447e-20 relative error = 3.0540041437425471246617562662289e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.784 y[1] (closed_form) = -0.002906831110595183553465008159529 y[1] (numeric) = -0.0029068311105951834642754923222801 absolute error = 8.9189515837248869179063988531669e-20 relative error = 3.0682730590077870935010027012157e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.783 y[1] (closed_form) = -0.0029023159963530258552502151348642 y[1] (numeric) = -0.0029023159963530257657850199400876 absolute error = 8.9465195194776561274288792989435e-20 relative error = 3.0825449505565961329289399756656e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.782 y[1] (closed_form) = -0.0028978092953653248960376850333076 y[1] (numeric) = -0.0028978092953653248062977515966179 absolute error = 8.9739933436689766072976853989978e-20 relative error = 3.0968198487118287809962998467310e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.781 y[1] (closed_form) = -0.0028933109893480800414352916813302 y[1] (numeric) = -0.0028933109893480799514215576145726 absolute error = 9.0013734066757567872351246083538e-20 relative error = 3.1110977837553313014276616255961e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (closed_form) = -0.0028888210600626885350002211539505 y[1] (numeric) = -0.0028888210600626884447136205793286 absolute error = 9.0286600574621875909211270765617e-20 relative error = 3.1253787859280775852245158055973e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.779 y[1] (closed_form) = -0.0028843394893158187279100079540976 y[1] (numeric) = -0.0028843394893158186373514715182389 memory used=188.2MB, alloc=44.3MB, time=2.79 absolute error = 9.0558536435858747607991243265091e-20 relative error = 3.1396628854303046371585631575607e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.778 y[1] (closed_form) = -0.0028798662589592837018416486567674 y[1] (numeric) = -0.002879866258959283611012103544728 absolute error = 9.0829545112039426711547556638208e-20 relative error = 3.1539501124216476485718225180684e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.777 y[1] (closed_form) = -0.0028754013508899152837176186967938 y[1] (numeric) = -0.0028754013508899151926179886460027 absolute error = 9.1099630050791097708239726610361e-20 relative error = 3.1682404970212746578948485748722e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.776 y[1] (closed_form) = -0.0028709447470494384509826068461201 y[1] (numeric) = -0.0028709447470494383596138121602627 absolute error = 9.1368794685857357961427181267888e-20 relative error = 3.1825340693080208002891102805826e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.775 y[1] (closed_form) = -0.002866496429424346126079750695825 y[1] (numeric) = -0.0028664964294243460344427082586666 absolute error = 9.1637042437158408940101113730675e-20 relative error = 3.1968308593205221478143510088704e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.774 y[1] (closed_form) = -0.0028620563800457743588001052170088 y[1] (numeric) = -0.0028620563800457742668957285061578 absolute error = 9.1904376710850967942009519270739e-20 relative error = 3.2111308970573491415165431149562e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.773 y[1] (closed_form) = -0.0028576245809893778951840053097259 y[1] (numeric) = -0.002857624580989377803013204410338 absolute error = 9.2170800899387901693313348430103e-20 relative error = 3.2254342124771396168268620827813e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.772 y[1] (closed_form) = -0.0028532010143752061316578922468273 y[1] (numeric) = -0.0028532010143752060392215738652497 absolute error = 9.2436318381577583201532283482292e-20 relative error = 3.2397408354987314236569388440384e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.771 y[1] (closed_form) = -0.0028487856623675794530950631657994 y[1] (numeric) = -0.0028487856623675793603941306431564 absolute error = 9.2700932522642973231299747515555e-20 relative error = 3.2540507960012946425705030486803e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (closed_form) = -0.0028443785071749659534936723420131 y[1] (numeric) = -0.0028443785071749658605290256677327 absolute error = 9.2964646674280427765248145414008e-20 relative error = 3.2683641238244633984064049625533e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.769 y[1] (closed_form) = -0.002839979531049858537970162976393 y[1] (numeric) = -0.0028399795310498584447426988016748 absolute error = 9.3227464174718232805186777468502e-20 relative error = 3.2826808487684672727228991757512e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.768 y[1] (closed_form) = -0.0028355887162886524047711387341376 y[1] (numeric) = -0.0028355887162886523112817503853627 absolute error = 9.3489388348774867861616124117608e-20 relative error = 3.2970010005942623164279893359079e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.767 y[1] (closed_form) = -0.0028312060452315229060114953631499 y[1] (numeric) = -0.0028312060452315228122610728552329 absolute error = 9.3750422507916999472543040708988e-20 relative error = 3.3113246090236616639555695851204e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.766 y[1] (closed_form) = -0.0028268315002623037858514244852452 y[1] (numeric) = -0.002826831500262303691840854534928 absolute error = 9.4010569950317206085521591934102e-20 relative error = 3.3256517037394657503420551890894e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.765 y[1] (closed_form) = -0.0028224650638083657948296741735869 y[1] (numeric) = -0.0028224650638083657005598402126755 absolute error = 9.4269833960911435629843565910324e-20 relative error = 3.3399823143855921325531719143757e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.764 y[1] (closed_form) = -0.0028181067183404956790752042893647 y[1] (numeric) = -0.0028181067183404955845469864779085 absolute error = 9.4528217811456197098840908374258e-20 relative error = 3.3543164705672049164055709468021e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.763 y[1] (closed_form) = -0.0028137564463727755431241088322913 y[1] (numeric) = -0.0028137564463727754483383840717058 absolute error = 9.4785724760585487455339180134203e-20 relative error = 3.3686542018508437904229534637741e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.762 y[1] (closed_form) = -0.0028094142304624625850733928454889 y[1] (numeric) = -0.0028094142304624624900310347916215 absolute error = 9.5042358053867455166416439240167e-20 relative error = 3.3829955377645526679614262888637e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.761 y[1] (closed_form) = -0.0028050800532098692028078877878226 y[1] (numeric) = -0.0028050800532098691075097668639618 absolute error = 9.5298120923860801666775458095823e-20 relative error = 3.3973405077980079389338672820128e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (closed_form) = -0.0028007538972582434700412668273836 y[1] (numeric) = -0.0028007538972582433744882502372127 absolute error = 9.5553016590170922043228681175718e-20 relative error = 3.4116891414026463324581561671608e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.759 y[1] (closed_form) = -0.0027964357452936499809167802999351 y[1] (numeric) = -0.0027964357452936498851097320404293 absolute error = 9.5807048259505786226024588719160e-20 relative error = 3.4260414679917923917492232854073e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.758 y[1] (closed_form) = -0.0027921255800448510619179716966192 y[1] (numeric) = -0.0027921255800448509658577525708876 absolute error = 9.6060219125731561966010934716494e-20 relative error = 3.4403975169407855625699852007817e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.757 y[1] (closed_form) = -0.0027878233842831883498442560766431 y[1] (numeric) = -0.0027878233842831882535317237067152 absolute error = 9.6312532369927980869934454011754e-20 relative error = 3.4547573175871068965513720924992e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.756 y[1] (closed_form) = -0.002783529140822464734610845823177 y[1] (numeric) = -0.0027835291408224646380468546627336 absolute error = 9.6563991160443448759517865098796e-20 relative error = 3.4691208992305053706868073578353e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.755 y[1] (closed_form) = -0.0027792428325188266656370932541249 y[1] (numeric) = -0.002779242832518826568822494601175 absolute error = 9.6814598652949901613333115210301e-20 relative error = 3.4834882911331238243016747394211e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.754 y[1] (closed_form) = -0.0027749644422706468205918858431953 y[1] (numeric) = -0.0027749644422706467235275278526979 absolute error = 9.7064357990497408343904606950264e-20 relative error = 3.4978595225196245147935024962162e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.753 y[1] (closed_form) = -0.0027706939530184071352692777798779 y[1] (numeric) = -0.0027706939530184070379560054763094 absolute error = 9.7313272303568521655927396686711e-20 relative error = 3.5122346225773142934338075754109e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.752 y[1] (closed_form) = -0.0027664313477445821933720713782256 y[1] (numeric) = -0.0027664313477445820958107266680932 absolute error = 9.7561344710132378224972851206741e-20 relative error = 3.5266136204562694025177753301811e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.751 y[1] (closed_form) = -0.0027621766094735229749855735120937 y[1] (numeric) = -0.0027621766094735228771769951963951 absolute error = 9.7808578315698549429577779053908e-20 relative error = 3.5409965452694598951432019830836e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (closed_form) = -0.0027579297212713409625282458866717 y[1] (numeric) = -0.0027579297212713408644732696733011 absolute error = 9.8054976213370643863172406133149e-20 relative error = 3.5553834260928736788953976748433e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.749 y[1] (closed_form) = -0.0027536906662457926029704436303868 y[1] (numeric) = -0.0027536906662457925046699021464872 absolute error = 9.8300541483899662845897532488042e-20 relative error = 3.5697742919656401847100374816217e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.748 y[1] (closed_form) = -0.0027494594275461641251168944848172 y[1] (numeric) = -0.0027494594275461640265716172890801 absolute error = 9.8545277195737110149991580820488e-20 relative error = 3.5841691718901536621812561492227e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.747 y[1] (closed_form) = -0.0027452359883631567107530108600376 y[1] (numeric) = -0.0027452359883631566119638244549497 absolute error = 9.8789186405087857146093820801542e-20 relative error = 3.5985680948321961025776093991210e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.746 y[1] (closed_form) = -0.0027410203319287720184595492853784 y[1] (numeric) = -0.0027410203319287719194272771294156 absolute error = 9.9032272155962764571510621249081e-20 relative error = 3.6129710897210597908238704280928e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.745 y[1] (closed_form) = -0.0027368124415161980589045363971166 y[1] (numeric) = -0.0027368124415161979596299989168855 absolute error = 9.9274537480231062115226940818203e-20 relative error = 3.6273781854496694877019945703618e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.744 y[1] (closed_form) = -0.0027326123004396954204257676409721 y[1] (numeric) = -0.0027326123004396953209097822432996 absolute error = 9.9515985397672487008215214209864e-20 relative error = 3.6417894108747042435199679386903e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.743 y[1] (closed_form) = -0.0027284198920544838437215544039678 y[1] (numeric) = -0.0027284198920544837439649354879387 absolute error = 9.9756618916029182801398123542094e-20 relative error = 3.6562047948167188444926571292578e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.742 y[1] (closed_form) = -0.0027242351997566291444717474023656 y[1] (numeric) = -0.0027242351997566290444753063713082 absolute error = 9.9996441031057359507460263171141e-20 relative error = 3.6706243660602648930741966853594e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.741 y[1] (closed_form) = -0.0027200582069829304827153989148294 y[1] (numeric) = -0.0027200582069829303824799441882507 absolute error = 1.0023545472657871627657621184984e-19 relative error = 3.6850481533540115234768888881549e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (closed_form) = -0.0027158888972108079778157439371467 y[1] (numeric) = -0.0027158888972108078773420809626151 absolute error = 1.0047366297453162777002882083936e-19 relative error = 3.6994761854108657536070465005226e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.739 y[1] (closed_form) = -0.0027117272539581906678474806208848 y[1] (numeric) = -0.0027117272539581905671364118858627 absolute error = 1.0071106873502209538963141383232e-19 relative error = 3.7139084909080924746436832544794e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.738 y[1] (closed_form) = -0.0027075732607834048122456135170432 y[1] (numeric) = -0.0027075732607834047112979385606688 absolute error = 1.0094767495637446451484087888772e-19 relative error = 3.7283450984874340794814490659370e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.737 y[1] (closed_form) = -0.0027034269012850625365593892505383 y[1] (numeric) = -0.0027034269012850624353759046753564 absolute error = 1.0118348457518190889345511980544e-19 relative error = 3.7427860367552297312547171054669e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.736 y[1] (closed_form) = -0.0026992881591019508181591033753063 y[1] (numeric) = -0.0026992881591019507167406028589496 absolute error = 1.0141850051635668332582783145252e-19 relative error = 3.7572313342825342731552578732667e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.735 y[1] (closed_form) = -0.0026951570179129208117477893757277 y[1] (numeric) = -0.0026951570179129207100950636825475 absolute error = 1.0165272569318014577660587864880e-19 relative error = 3.7716810196052367807514812440536e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.734 y[1] (closed_form) = -0.0026910334614367775135340161603682 y[1] (numeric) = -0.0026910334614367774116478531530156 absolute error = 1.0188616300735255004209950065192e-19 relative error = 3.7861351212241787580127909868931e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.733 y[1] (closed_form) = -0.0026869174734321697629262190108198 y[1] (numeric) = -0.0026869174734321696608074036617772 absolute error = 1.0211881534904261009553294354460e-19 relative error = 3.8005936676052719782381774500975e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.732 y[1] (closed_form) = -0.0026828090376974805806131708734697 y[1] (numeric) = -0.0026828090376974804782624852765329 absolute error = 1.0235068559693683722659275257002e-19 relative error = 3.8150566871796159710837728567331e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.731 y[1] (closed_form) = -0.0026787081380707178418993661867664 y[1] (numeric) = -0.0026787081380707177393175895684777 absolute error = 1.0258177661828865108589264848698e-19 relative error = 3.8295242083436151568797099067465e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (closed_form) = -0.0026746147584294052841682381921137 y[1] (numeric) = -0.0026746147584294051813561469231464 absolute error = 1.0281209126896726573920748026910e-19 relative error = 3.8439962594590956294222580523842e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.729 y[1] (closed_form) = -0.0026705288826904738473502629536795 y[1] (numeric) = -0.0026705288826904737443086305601731 absolute error = 1.0304163239350635183059400603430e-19 relative error = 3.8584728688534215884228628299185e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.728 y[1] (closed_form) = -0.0026664504948101533462771191816306 y[1] (numeric) = -0.0026664504948101532430067163564781 absolute error = 1.0327040282515247594781302117070e-19 relative error = 3.8729540648196114227913819185048e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.727 y[1] (closed_form) = -0.0026623795787838644738071724847354 y[1] (numeric) = -0.002662379578783864370308767098822 absolute error = 1.0349840538591331827779544455591e-19 relative error = 3.8874398756164534459264970824570e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.726 y[1] (closed_form) = -0.0026583161186461111336116359417302 y[1] (numeric) = -0.0026583161186461110298859930551245 absolute error = 1.0372564288660566963425420899396e-19 relative error = 3.9019303294686212841819837628111e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.725 y[1] (closed_form) = -0.0026542600984703731015148259458244 y[1] (numeric) = -0.0026542600984703729975627078189212 absolute error = 1.0395211812690320893393400007120e-19 relative error = 3.9164254545667889196732397445936e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.724 y[1] (closed_form) = -0.0026502115023689990142859832124083 y[1] (numeric) = -0.0026502115023689989101081493170243 absolute error = 1.0417783389538406219241186921369e-19 relative error = 3.9309252790677453885842109648852e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop memory used=234.8MB, alloc=44.3MB, time=3.48 x[1] = 2.723 y[1] (closed_form) = -0.0026461703144930996847841637152855 y[1] (numeric) = -0.0026461703144930995803813707457074 absolute error = 1.0440279296957814410481333355974e-19 relative error = 3.9454298310945091361306060710586e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.722 y[1] (closed_form) = -0.0026421365190324417423617232001369 y[1] (numeric) = -0.0026421365190324416377347250841226 absolute error = 1.0462699811601428327129059017648e-19 relative error = 3.9599391387364420293310617163168e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.721 y[1] (closed_form) = -0.0026381101002153415974359218836655 y[1] (numeric) = -0.0026381101002153414925854697933984 absolute error = 1.0485045209026713212162173905987e-19 relative error = 3.9744532300493630287337077190079e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (closed_form) = -0.0026340910423085597291421630509013 y[1] (numeric) = -0.0026340910423085596240690054138975 absolute error = 1.0507315763700386258783225324866e-19 relative error = 3.9889721330556615202413850416445e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.719 y[1] (closed_form) = -0.0026300793296171952949863505790756 y[1] (numeric) = -0.002630079329617195189691233089045 absolute error = 1.0529511749003064856831218130430e-19 relative error = 4.0034958757444103081745899939174e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.718 y[1] (closed_form) = -0.0026260749464845810614178060116112 y[1] (numeric) = -0.0026260749464845809559014716392723 absolute error = 1.0551633437233893622150454446915e-19 relative error = 4.0180244860714782707070550604064e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.717 y[1] (closed_form) = -0.0026220778772921786542481257471176 y[1] (numeric) = -0.0026220778772921785485113147509661 absolute error = 1.0573681099615150312187192617549e-19 relative error = 4.0325579919596426788047302276161e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.716 y[1] (closed_form) = -0.0026180881064594741278452832625216 y[1] (numeric) = -0.0026180881064594740218887331995533 absolute error = 1.0595655006296830730550917444372e-19 relative error = 4.0470964212987011797947985661936e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.715 y[1] (closed_form) = -0.0026141056184438738520361901229917 y[1] (numeric) = -0.0026141056184438737458606358593796 absolute error = 1.0617555426361212722746027832316e-19 relative error = 4.0616398019455834466872460428135e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.714 y[1] (closed_form) = -0.0026101303977406007156548229102164 y[1] (numeric) = -0.0026101303977406006092609966319424 absolute error = 1.0639382627827399364751666917061e-19 relative error = 4.0761881617244624943674080226772e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.713 y[1] (closed_form) = -0.0026061624288825906456769011906556 y[1] (numeric) = -0.0026061624288825905390655324140972 absolute error = 1.0661136877655841445602226853044e-19 relative error = 4.0907415284268656637738336086046e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.712 y[1] (closed_form) = -0.0026022016964403894408859643120828 y[1] (numeric) = -0.0026022016964403893340577798945544 absolute error = 1.0682818441752839344598738999658e-19 relative error = 4.1052999298117852751717437773570e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.711 y[1] (closed_form) = -0.0025982481850220499190195422252661 y[1] (numeric) = -0.0025982481850220498119752663755159 absolute error = 1.0704427584975024403261893703350e-19 relative error = 4.1198633936057889516283101494912e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (closed_form) = -0.0025943018792730293763479477428771 y[1] (numeric) = -0.0025943018792730292690883020315389 absolute error = 1.0725964571133819891620805764852e-19 relative error = 4.1344319475031296137919480973934e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.709 y[1] (closed_form) = -0.0025903627638760873586420347342749 y[1] (numeric) = -0.0025903627638760872511677381042761 absolute error = 1.0747429662999881667917835637923e-19 relative error = 4.1490056191658551470738006891687e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.708 y[1] (closed_form) = -0.0025864308235511837424900687769709 y[1] (numeric) = -0.0025864308235511836348018375538957 absolute error = 1.0768823122307518630298776161836e-19 relative error = 4.1635844362239177423255886160792e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.707 y[1] (closed_form) = -0.0025825060430553771259276438073638 y[1] (numeric) = -0.0025825060430553770180261917097729 absolute error = 1.0790145209759093058549504016106e-19 relative error = 4.1781684262752829111040156908433e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.706 y[1] (closed_form) = -0.0025785884071827235273483503984391 y[1] (numeric) = -0.0025785884071827234192343885481451 absolute error = 1.0811396185029400943434758032511e-19 relative error = 4.1927576168860381766079496662468e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.705 y[1] (closed_form) = -0.0025746779007641753916666585039955 y[1] (numeric) = -0.0025746779007641752833408954362952 absolute error = 1.0832576306770032400692027033379e-19 relative error = 4.2073520355905014413706439414051e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.704 y[1] (closed_form) = -0.0025707745086674809027082199107193 y[1] (numeric) = -0.0025707745086674807941713615845822 absolute error = 1.0853685832613712266233592110538e-19 relative error = 4.2219517098913290327853271301828e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.703 y[1] (closed_form) = -0.0025668782157970836008065232939264 y[1] (numeric) = -0.0025668782157970834920592731021402 absolute error = 1.0874725019178620968612556436335e-19 relative error = 4.2365566672596234275385643965520e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.702 y[1] (closed_form) = -0.0025629890070940223045885477426014 y[1] (numeric) = -0.0025629890070940221956316065218745 absolute error = 1.0895694122072695774314194122574e-19 relative error = 4.2511669351350406560218868491876e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.701 y[1] (closed_form) = -0.0025591068675358313359357589667575 y[1] (numeric) = -0.0025591068675358312267698250077784 absolute error = 1.0916593395897912500942142725717e-19 relative error = 4.2657825409258973877882930667921e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (closed_form) = -0.0025552317821364410471104761871179 y[1] (numeric) = -0.0025552317821364409377362452445724 absolute error = 1.0937423094254547792879836242450e-19 relative error = 4.2804035120092776991163499312394e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.699 y[1] (closed_form) = -0.0025513637359460786490413069953954 y[1] (numeric) = -0.0025513637359460785394594722979412 absolute error = 1.0958183469745422053521111447456e-19 relative error = 4.2950298757311395237407583126538e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.698 y[1] (closed_form) = -0.0025475027140511693397650023244597 y[1] (numeric) = -0.0025475027140511692299762545846585 absolute error = 1.0978874773980123127680104887040e-19 relative error = 4.3096616594064207878044027143246e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.697 y[1] (closed_form) = -0.0025436487015742377320257241425797 y[1] (numeric) = -0.0025436487015742376220307515667876 absolute error = 1.0999497257579210827309375542704e-19 relative error = 4.3242988903191452300830726815019e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.696 y[1] (closed_form) = -0.0025398016836738095790363446455992 y[1] (numeric) = -0.0025398016836738094688358329438152 absolute error = 1.1020051170178402393176623994367e-19 relative error = 4.3389415957225279085302275425462e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.695 y[1] (closed_form) = -0.0025359616455443137974100076259472 y[1] (numeric) = -0.0025359616455443136870046400216199 absolute error = 1.1040536760432738984674417811718e-19 relative error = 4.3535898028390803941853748197997e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.694 y[1] (closed_form) = -0.0025321285724159847862737804081215 y[1] (numeric) = -0.0025321285724159846756642376479142 absolute error = 1.1060954276020733289463959942954e-19 relative error = 4.3682435388607156534858463574053e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.693 y[1] (closed_form) = -0.002528302449554765041579808316784 y[1] (numeric) = -0.002528302449554764930766768680299 absolute error = 1.1081303963648498344183137201834e-19 relative error = 4.3829028309488526200179848008944e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.692 y[1] (closed_form) = -0.0025244832622622080646329531456343 y[1] (numeric) = -0.0025244832622622079536170924550957 absolute error = 1.1101586069053857656980844815464e-19 relative error = 4.3975677062345204567399964657532e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.691 y[1] (closed_form) = -0.0025206709958753815638574525823098 y[1] (numeric) = -0.0025206709958753814526394442122054 absolute error = 1.1121800837010436722173885714139e-19 relative error = 4.4122381918184625097049847867180e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (closed_form) = -0.0025168656357667709488286790759282 y[1] (numeric) = -0.0025168656357667708374091939626108 absolute error = 1.1141948511331736016859575237400e-19 relative error = 4.4269143147712399543089513838595e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.689 y[1] (closed_form) = -0.0025130671673441831155996042685226 y[1] (numeric) = -0.0025130671673441830039793109197708 absolute error = 1.1162029334875185568856528701520e-19 relative error = 4.4415961021333351350848392535203e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.688 y[1] (closed_form) = -0.0025092755760506505223550889082211 y[1] (numeric) = -0.0025092755760506504105346534127592 absolute error = 1.1182043549546181184887956414616e-19 relative error = 4.4562835809152546000599946300554e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.687 y[1] (closed_form) = -0.002505490847364335554430618179037 y[1] (numeric) = -0.002505490847364335442410704216016 absolute error = 1.1201991396302102427466123915235e-19 relative error = 4.4709767780976318306907406065694e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.686 y[1] (closed_form) = -0.0025017129667984351777355886777402 y[1] (numeric) = -0.0025017129667984350655168575261771 absolute error = 1.1221873115156312428483440213398e-19 relative error = 4.4856757206313296683840865881998e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.685 y[1] (closed_form) = -0.0024979419199010858796247259003803 y[1] (numeric) = -0.0024979419199010857672078364485589 absolute error = 1.1241688945182139627064899480573e-19 relative error = 4.5003804354375424386129430189899e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.684 y[1] (closed_form) = -0.0024941776922552688962646701272951 y[1] (numeric) = -0.0024941776922552687836502788821267 absolute error = 1.1261439124516841518788307902706e-19 relative error = 4.5150909494078977736275705123346e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.683 y[1] (closed_form) = -0.0024904202694787157255462140732362 y[1] (numeric) = -0.0024904202694787156127349751695807 absolute error = 1.1281123890365550502932863299024e-19 relative error = 4.5298072894045581347623664649495e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.682 y[1] (closed_form) = -0.0024866696372238139245961076557257 y[1] (numeric) = -0.0024866696372238138115886728656737 absolute error = 1.1300743479005201913973206723573e-19 relative error = 4.5445294822603220353334803851529e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.681 y[1] (closed_form) = -0.002482925781177513190945763786789 y[1] (numeric) = -0.0024829257811775130777427825289046 absolute error = 1.1320298125788444323095018794804e-19 relative error = 4.5592575547787249651191514580996e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (closed_form) = -0.0024791886870612317264176042674054 y[1] (numeric) = -0.00247918868706123161301972361593 absolute error = 1.1339788065147532195069575212556e-19 relative error = 4.5739915337341400174110782438402e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.679 y[1] (closed_form) = -0.0024754583406307628827931767167481 y[1] (numeric) = -0.0024754583406307627692010414107661 absolute error = 1.1359213530598200985388392175499e-19 relative error = 4.5887314458718782196215607993881e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.678 y[1] (closed_form) = -0.0024717347276761820883305520556518 y[1] (numeric) = -0.0024717347276761819745448045082166 absolute error = 1.1378574754743524762125169641763e-19 relative error = 4.6034773179082885684275998742629e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.677 y[1] (closed_form) = -0.0024680178340217540542018774415997 y[1] (numeric) = -0.0024680178340217539402231577488221 absolute error = 1.1397871969277756436560665098645e-19 relative error = 4.6182291765308577704295960914686e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.676 y[1] (closed_form) = -0.0024643076455258402599253117764733 y[1] (numeric) = -0.0024643076455258401457542577265718 absolute error = 1.1417105404990150686176889322779e-19 relative error = 4.6329870483983096892987641339985e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.675 y[1] (closed_form) = -0.0024606041480808067168689100337039 y[1] (numeric) = -0.0024606041480808066025061571160162 absolute error = 1.1436275291768769653200095199096e-19 relative error = 4.6477509601407045003838628524778e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.674 y[1] (closed_form) = -0.0024569073276129320089073487334041 y[1] (numeric) = -0.0024569073276129318943535301473614 absolute error = 1.1455381858604271501447417784503e-19 relative error = 4.6625209383595375537443418344465e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.673 y[1] (closed_form) = -0.0024532171700823156093156979874019 y[1] (numeric) = -0.002453217170082315494571444651465 absolute error = 1.1474425333593681913809705289246e-19 relative error = 4.6772970096278379465735182722937e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.672 y[1] (closed_form) = -0.0024495336614827864729877456954481 y[1] (numeric) = -0.0024495336614827863580536862560066 absolute error = 1.1493405943944148612283043422988e-19 relative error = 4.6920792004902668059719248775037e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.671 y[1] (closed_form) = -0.0024458567878418119030696667535876 y[1] (numeric) = -0.0024458567878418117879464275938209 absolute error = 1.1512323915976678982043706610018e-19 relative error = 4.7068675374632152830275100564226e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (closed_form) = -0.0024421865352204066911031045898858 y[1] (numeric) = -0.0024421865352204065757913098385871 absolute error = 1.1531179475129860880645755992804e-19 relative error = 4.7216620470349022591559255302407e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.669 y[1] (closed_form) = -0.00243852288971304252977499402526 y[1] (numeric) = -0.0024385228897130424142752655656243 absolute error = 1.1549972845963566713007233067150e-19 relative error = 4.7364627556654717656507039925861e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.668 y[1] (closed_form) = -0.0024348658374475576973747034217155 y[1] (numeric) = -0.0024348658374475575816876609000891 absolute error = 1.1568704252162640852439856454087e-19 relative error = 4.7512696897870901173897101955850e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop memory used=281.4MB, alloc=44.3MB, time=4.16 x[1] = 2.667 y[1] (closed_form) = -0.002431215364585067013062310380202 y[1] (numeric) = -0.0024312153645850668971885712147963 absolute error = 1.1587373916540570487568305018743e-19 relative error = 4.7660828758040427616408429832546e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.666 y[1] (closed_form) = -0.0024275714573198720620550489387584 y[1] (numeric) = -0.002427571457319871945995228328327 absolute error = 1.1605982061043139974578550675991e-19 relative error = 4.7809023400928308429065731937065e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.665 y[1] (closed_form) = -0.0024239341018793716898421773514917 y[1] (numeric) = -0.002423934101879371573596888283971 absolute error = 1.1624528906752068773830276233676e-19 relative error = 4.7957281090022674847435229731410e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.664 y[1] (closed_form) = -0.002420303284523972764541714152927 y[1] (numeric) = -0.0024203032845239726481115674140406 absolute error = 1.1643014673888633049466165048616e-19 relative error = 4.8105602088535737894899258295662e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.663 y[1] (closed_form) = -0.0024166789915470012065156763827935 y[1] (numeric) = -0.0024166789915470010899012805646208 absolute error = 1.1661439581817271010250767714986e-19 relative error = 4.8253986659404745568304536473698e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.662 y[1] (closed_form) = -0.0024130612092746132843636276155895 y[1] (numeric) = -0.0024130612092746131675655891250977 absolute error = 1.1679803849049172069473724150024e-19 relative error = 4.8402435065292937221245568303525e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.661 y[1] (closed_form) = -0.0024094499240657071764175048592452 y[1] (numeric) = -0.0024094499240657070594364279267867 absolute error = 1.1698107693245849901356335042616e-19 relative error = 4.8550947568590495154211366858971e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (closed_form) = -0.0024058451223118347968638425096333 y[1] (numeric) = -0.0024058451223118346797003291974063 absolute error = 1.1716351331222699471006822514026e-19 relative error = 4.8699524431415493420790550521300e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.659 y[1] (closed_form) = -0.0024022467904371138856226484240321 y[1] (numeric) = -0.0024022467904371137682772986345067 absolute error = 1.1734534978952538114578083907395e-19 relative error = 4.8848165915614843859096849490147e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.658 y[1] (closed_form) = -0.0023986549148981403611153118582303 y[1] (numeric) = -0.002398654914898140243588723342539 absolute error = 1.1752658851569130745892312846299e-19 relative error = 4.8996872282765239357544176493307e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.657 y[1] (closed_form) = -0.0023950694821839009350570355497792 y[1] (numeric) = -0.0023950694821839008173498039160722 absolute error = 1.1770723163370699265409526127507e-19 relative error = 4.9145643794174094364067659626956e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.656 y[1] (closed_form) = -0.0023914904788156859884123846747894 y[1] (numeric) = -0.0023914904788156858705251033965552 absolute error = 1.1788728127823416247031781755116e-19 relative error = 4.9294480710880482647854406517004e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.655 y[1] (closed_form) = -0.0023879178913470027076556338081958 y[1] (numeric) = -0.002387917891347002589588894232547 absolute error = 1.1806673957564882977851690669497e-19 relative error = 4.9443383293656072322615267005897e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.654 y[1] (closed_form) = -0.0023843517063634884804806694279448 y[1] (numeric) = -0.0023843517063634883622350607838689 absolute error = 1.1824560864407591925572700732666e-19 relative error = 4.9592351803006058140396485807209e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.653 y[1] (closed_form) = -0.002380791910482824550108269972216 y[1] (numeric) = -0.0023807919104828244316843793787923 absolute error = 1.1842389059342373707949554629339e-19 relative error = 4.9741386499170091064897886505030e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.652 y[1] (closed_form) = -0.0023772384903546499273416380354912 y[1] (numeric) = -0.002377238490354649808740050510073 absolute error = 1.1860158752541828638220281927436e-19 relative error = 4.9890487642123205133232103381053e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.651 y[1] (closed_form) = -0.0023736914326604755595241000236963 y[1] (numeric) = -0.0023736914326604754407453984900588 absolute error = 1.1877870153363742920126068079609e-19 relative error = 5.0039655491576741615027377306395e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (closed_form) = -0.0023701507241135987555559175302411 y[1] (numeric) = -0.0023701507241135986366006828266962 absolute error = 1.1895523470354489565742338173838e-19 relative error = 5.0188890306979270477744555816821e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.649 y[1] (closed_form) = -0.0023666163514590178661301718928015 y[1] (numeric) = -0.0023666163514590177469989827802774 absolute error = 1.1913118911252414108973389359766e-19 relative error = 5.0338192347517509167047184980800e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.648 y[1] (closed_form) = -0.0023630883014733472183506888941384 y[1] (numeric) = -0.0023630883014733470990441220642263 absolute error = 1.1930656682991205187193891759927e-19 relative error = 5.0487561872117238711031951253728e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.647 y[1] (closed_form) = -0.0023595665609647323038979644279502 y[1] (numeric) = -0.0023595665609647321844165945109177 absolute error = 1.1948136991703250063153542060182e-19 relative error = 5.0636999139444217157095224674849e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.646 y[1] (closed_form) = -0.0023560511167727652199120342112661 y[1] (numeric) = -0.0023560511167727651002564337840363 absolute error = 1.1965560042722975158896085667798e-19 relative error = 5.0786504407905090350180069994578e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.645 y[1] (closed_form) = -0.0023525419557684003617642013365896 y[1] (numeric) = -0.0023525419557684002419349409306879 absolute error = 1.1982926040590171673080811201241e-19 relative error = 5.0936077935648300061116829109796e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.644 y[1] (closed_form) = -0.0023490390648538703668924946680387 y[1] (numeric) = -0.0023490390648538702468901427775056 absolute error = 1.2000235189053306352733454071997e-19 relative error = 5.1085719980564989473739236026459e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.643 y[1] (closed_form) = -0.002345542430962602308878678844029 y[1] (numeric) = -0.0023455424309626021887038019333009 absolute error = 1.2017487691072817490094213040257e-19 relative error = 5.1235430800289906039427003957878e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.642 y[1] (closed_form) = -0.0023420520410591341409475730023399 y[1] (numeric) = -0.0023420520410591340206007355140959 absolute error = 1.2034683748824396214873273943382e-19 relative error = 5.1385210652202301707694922600887e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.641 y[1] (closed_form) = -0.0023385678821390313880723603391846 y[1] (numeric) = -0.002338567882139031267554124702162 absolute error = 1.2051823563702253151868837443774e-19 relative error = 5.1535059793426830541417721610777e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (closed_form) = -0.0023350899412288040868724842994823 y[1] (numeric) = -0.0023350899412288039661834109362586 absolute error = 1.2068907336322370513549151820960e-19 relative error = 5.1684978480834443725249293321383e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.639 y[1] (closed_form) = -0.0023316182053858239724936296179744 y[1] (numeric) = -0.002331618205385823851634276952717 absolute error = 1.2085935266525739696848446805304e-19 relative error = 5.1834966971043281975764323333377e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.638 y[1] (closed_form) = -0.00232815266169824191166217763702 y[1] (numeric) = -0.0023281526616982417906331021032042 absolute error = 1.2102907553381584453076939545453e-19 relative error = 5.1985025520419565361819951228260e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.637 y[1] (closed_form) = -0.002324693297284905581109405363513 y[1] (numeric) = -0.0023246932972849054599111614116073 absolute error = 1.2119824395190569699497228409638e-19 relative error = 5.2135154385078480543604774866440e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.636 y[1] (closed_form) = -0.0023212400992952773905635666408317 y[1] (numeric) = -0.0023212400992952772691967067459518 absolute error = 1.2136685989487996040773393896356e-19 relative error = 5.2285353820885065438812320006056e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.635 y[1] (closed_form) = -0.0023177930549093526495108516483294 y[1] (numeric) = -0.0023177930549093525279759263178596 absolute error = 1.2153492533046980068154977989436e-19 relative error = 5.2435624083455091324346021847997e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.634 y[1] (closed_form) = -0.0023143521513375779769290677466222 y[1] (numeric) = -0.002314352151337577855226625527806 absolute error = 1.2170244221881620503915703415119e-19 relative error = 5.2585965428155942381932806087137e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.633 y[1] (closed_form) = -0.0023109173758207699532007205076937 y[1] (numeric) = -0.0023109173758207698313313079951922 absolute error = 1.2186941251250150258226312085140e-19 relative error = 5.2736378110107492695992513647606e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.632 y[1] (closed_form) = -0.0023074887156300340134149986502203 y[1] (numeric) = -0.0023074887156300338913791604936395 absolute error = 1.2203583815658074465302237242234e-19 relative error = 5.2886862384182980712080685020463e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.631 y[1] (closed_form) = -0.0023040661580666835812709805879909 y[1] (numeric) = -0.0023040661580666834590692594993779 absolute error = 1.2220172108861294565329966226171e-19 relative error = 5.3037418505009881164192606527271e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (closed_form) = -0.0023006496904621594427971834380461 y[1] (numeric) = -0.0023006496904621593204301201993539 absolute error = 1.2236706323869218498340890173336e-19 relative error = 5.3188046726970774479187021426539e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.629 y[1] (closed_form) = -0.0022972393001779493591053676702548 y[1] (numeric) = -0.0022972393001779492365735011407762 absolute error = 1.2253186652947857075868163235202e-19 relative error = 5.3338747304204213666558523087777e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.628 y[1] (closed_form) = -0.0022938349746055079173992921562834 y[1] (numeric) = -0.0022938349746055077947031592800543 absolute error = 1.2269613287622906595890596994976e-19 relative error = 5.3489520490605588701758375008168e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.627 y[1] (closed_form) = -0.0022904367011661766194618852379436 y[1] (numeric) = -0.0022904367011661764966020210511154 absolute error = 1.2285986418682817766237885680952e-19 relative error = 5.3640366539827988411234342769616e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.626 y[1] (closed_form) = -0.0022870444673111042068470576271441 y[1] (numeric) = -0.0022870444673111040838239952653256 absolute error = 1.2302306236181851001303484582489e-19 relative error = 5.3791285705283059867331075661619e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.625 y[1] (closed_form) = -0.0022836582605211672220051325163652 y[1] (numeric) = -0.002283658260521167098819403221934 absolute error = 1.2318572929443118156585237891884e-19 relative error = 5.3942278240141865301163640162206e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.624 y[1] (closed_form) = -0.0022802780683068908045736072637541 y[1] (numeric) = -0.002280278068306890681225740393138 absolute error = 1.2334786687061610765249363202733e-19 relative error = 5.4093344397335736541547983311612e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.623 y[1] (closed_form) = -0.0022769038782083697220676894644441 y[1] (numeric) = -0.0022769038782083695985582124953719 absolute error = 1.2350947696907214840590638330981e-19 relative error = 5.4244484429557126988043390769839e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.622 y[1] (closed_form) = -0.0022735356777951896342077681731843 y[1] (numeric) = -0.0022735356777951895105372067119072 absolute error = 1.2367056146127712307940592284718e-19 relative error = 5.4395698589260461126133401560272e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.621 y[1] (closed_form) = -0.002270173454666348590123688546278 y[1] (numeric) = -0.0022701734546663484662925663347603 absolute error = 1.2383112221151769129256166446152e-19 relative error = 5.4546987128662981592543148709703e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (closed_form) = -0.0022668171964501787576783952664261 y[1] (numeric) = -0.002266817196450178633687234189507 absolute error = 1.2399116107691910183303674754462e-19 relative error = 5.4698350299745593798662711744954e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.619 y[1] (closed_form) = -0.0022634668908042683841561968454359 y[1] (numeric) = -0.0022634668908042682600055169379611 absolute error = 1.2415067990747480964036943358379e-19 relative error = 5.4849788354253708120017792844472e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.618 y[1] (closed_form) = -0.0022601225254153839875635793097473 y[1] (numeric) = -0.0022601225254153838632538987636714 absolute error = 1.2430968054607596159454241365617e-19 relative error = 5.5001301543698079659700862918342e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.617 y[1] (closed_form) = -0.0022567840879993927777931639050527 y[1] (numeric) = -0.0022567840879993926533249990765119 absolute error = 1.2446816482854075172906015532026e-19 relative error = 5.5152890119355645593647866552771e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.616 y[1] (closed_form) = -0.0022534515663011853069040593514286 y[1] (numeric) = -0.0022534515663011851822779247677849 absolute error = 1.2462613458364364648514503641295e-19 relative error = 5.5304554332270360105617625157837e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.615 y[1] (closed_form) = -0.00225012494809459834777450488168 y[1] (numeric) = -0.0022501249480945982229909132485355 absolute error = 1.2478359163314448062057014616415e-19 relative error = 5.5456294433254026919703235354739e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.614 y[1] (closed_form) = -0.0022468042211823380003853358451307 y[1] (numeric) = -0.0022468042211823378754447980533133 absolute error = 1.2494053779181742438357018821953e-19 relative error = 5.5608110672887129438177024187534e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.613 y[1] (closed_form) = -0.0022434893733959030249954290988273 y[1] (numeric) = -0.0022434893733959028998984542313475 absolute error = 1.2509697486747982255921180361024e-19 relative error = 5.5760003301519658492442993702825e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.612 y[1] (closed_form) = -0.0022401803925955084014729007798024 y[1] (numeric) = -0.0022401803925955082762199961187815 absolute error = 1.2525290466102090599256075296726e-19 relative error = 5.5911972569271937714843164369694e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 memory used=328.0MB, alloc=44.3MB, time=4.84 TOP MAIN SOLVE Loop x[1] = 2.611 y[1] (closed_form) = -0.0022368772666700091140484343972305 y[1] (numeric) = -0.0022368772666700089886401054308001 absolute error = 1.2540832896643037618995566542283e-19 relative error = 5.6064018726035446539036809273602e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (closed_form) = -0.0022335799835368241607597125433998 y[1] (numeric) = -0.0022335799835368240351964629725729 absolute error = 1.2556324957082686359668638628792e-19 relative error = 5.6216142021473640836644258576520e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.609 y[1] (closed_form) = -0.0022302885311418607868585109386017 y[1] (numeric) = -0.0022302885311418606611408426841155 absolute error = 1.2571766825448626014637924688717e-19 relative error = 5.6368342705022771197819745957360e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.608 y[1] (closed_form) = -0.0022270028974594389414545890383376 y[1] (numeric) = -0.0022270028974594388155830022474677 absolute error = 1.2587158679086992667441174854731e-19 relative error = 5.6520621025892698863390665200142e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.607 y[1] (closed_form) = -0.0022237230704922159566730770824867 y[1] (numeric) = -0.0022237230704922158306480701358339 absolute error = 1.2602500694665277578471510987261e-19 relative error = 5.6672977233067709316173605352285e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.606 y[1] (closed_form) = -0.0022204490382711114486046152959313 y[1] (numeric) = -0.00222044903827111132242668481418 absolute error = 1.2617793048175123075637478382434e-19 relative error = 5.6825411575307323539050636504024e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.605 y[1] (closed_form) = -0.0022171807888552324393300469990711 y[1] (numeric) = -0.00221718078885523231299968784972 absolute error = 1.2633035914935106107350632099461e-19 relative error = 5.6977924301147106947362524816054e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.604 y[1] (closed_form) = -0.0022139183103317986993040036949735 y[1] (numeric) = -0.0022139183103317985728217089990384 absolute error = 1.2648229469593509515896675058653e-19 relative error = 5.7130515658899476003148864521952e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.603 y[1] (closed_form) = -0.0022106615908160683093842468077253 y[1] (numeric) = -0.0022106615908160681827505079464145 absolute error = 1.2663373886131081088955988425543e-19 relative error = 5.7283185896654502518738525832259e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.602 y[1] (closed_form) = -0.0022074106184512634417961476938134 y[1] (numeric) = -0.0022074106184512633150114543151756 absolute error = 1.2678469337863780446750753391077e-19 relative error = 5.7435935262280715657167330547966e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.601 y[1] (closed_form) = -0.0022041653814084963593241948748356 y[1] (numeric) = -0.0022041653814084962323890349003805 absolute error = 1.2693515997445513822008748711584e-19 relative error = 5.7588764003425901636873481333775e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (closed_form) = -0.0022009258678866956320249151851208 y[1] (numeric) = -0.0022009258678866955049397748164122 absolute error = 1.2708514036870856789648311764236e-19 relative error = 5.7741672367517901148094985589227e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.599 y[1] (closed_form) = -0.0021976920661125325707580837313333 y[1] (numeric) = -0.0021976920661125324435234474565556 absolute error = 1.2723463627477765002804863933479e-19 relative error = 5.7894660601765404488367130273547e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.598 y[1] (closed_form) = -0.0021944639643403478768355762621021 y[1] (numeric) = -0.0021944639643403477494519268625994 absolute error = 1.2738364939950272991536815450250e-19 relative error = 5.8047728953158744424491979474854e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.597 y[1] (closed_form) = -0.0021912415508520785070896867832073 y[1] (numeric) = -0.0021912415508520783795575053399955 absolute error = 1.2753218144321181080267571987298e-19 relative error = 5.8200877668470686788325881554771e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.596 y[1] (closed_form) = -0.0021880248139571847536651930667894 y[1] (numeric) = -0.0021880248139571846259849589670421 absolute error = 1.2768023409974730479740757048050e-19 relative error = 5.8354106994257218813705086936126e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.595 y[1] (closed_form) = -0.0021848137419925775378419031301363 y[1] (numeric) = -0.0021848137419925774100140940736436 absolute error = 1.2782780905649266608987632199643e-19 relative error = 5.8507417176858335221803790626502e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.594 y[1] (closed_form) = -0.0021816083233225459171968568394091 y[1] (numeric) = -0.0021816083233225457892219488450102 absolute error = 1.2797490799439890702529033267943e-19 relative error = 5.8660808462398822062193224978159e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.593 y[1] (closed_form) = -0.0021784085463386848054177885645823 y[1] (numeric) = -0.0021784085463386846772962559765713 absolute error = 1.2812153258801099757758936556557e-19 relative error = 5.8814281096789038316844837571034e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.592 y[1] (closed_form) = -0.0021752143994598229040818793121052 y[1] (numeric) = -0.0021752143994598227758141948066111 absolute error = 1.2826768450549414877183016844332e-19 relative error = 5.8967835325725695274295096067939e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.591 y[1] (closed_form) = -0.002172025871131950845716240029404 y[1] (numeric) = -0.002172025871131950717302874620744 absolute error = 1.2841336540865998059913250275037e-19 relative error = 5.9121471394692633681164066029086e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (closed_form) = -0.0021688429498281495474589718482034 y[1] (numeric) = -0.0021688429498281494189003948952108 absolute error = 1.2855857695299257496548742245138e-19 relative error = 5.9275189548961598678194608587927e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.589 y[1] (closed_form) = -0.0021656656240485187746420439494868 y[1] (numeric) = -0.0021656656240485186459387231618124 absolute error = 1.2870332078767441421303515033653e-19 relative error = 5.9428990033593012527953842184883e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.588 y[1] (closed_form) = -0.0021624938823201059136196155292708 y[1] (numeric) = -0.0021624938823201057847720169736586 absolute error = 1.2884759855561220574973964262057e-19 relative error = 5.9582873093436745141313405834688e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.587 y[1] (closed_form) = -0.0021593277131968349531678050586421 y[1] (numeric) = -0.0021593277131968348241763931651795 absolute error = 1.2899141189346259332072079428224e-19 relative error = 5.9736838973132882409800050273043e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.586 y[1] (closed_form) = -0.0021561671052594356737842777009013 y[1] (numeric) = -0.0021561671052594355446495152692436 absolute error = 1.2913476243165775545185313879093e-19 relative error = 5.9890887917112492350883167397454e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.585 y[1] (closed_form) = -0.0021530120471153730442183804102509 y[1] (numeric) = -0.00215301204711537291494072861582 absolute error = 1.2927765179443089159360175870444e-19 relative error = 6.0045020169598389073241047295171e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.584 y[1] (closed_form) = -0.0021498625273987768245649039271336 y[1] (numeric) = -0.002149862527398776695144822327292 absolute error = 1.2942008159984159649044187052891e-19 relative error = 6.0199235974605894569022925449829e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.583 y[1] (closed_form) = -0.0021467185347703713752568916418247 y[1] (numeric) = -0.0021467185347703712456948381820235 absolute error = 1.2956205345980112329859810110365e-19 relative error = 6.0353535575943598340099250050970e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.582 y[1] (closed_form) = -0.0021435800579174056712952471567604 y[1] (numeric) = -0.0021435800579174055415916781766628 absolute error = 1.2970356898009753597224275695290e-19 relative error = 6.0507919217214114865268060312004e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.581 y[1] (closed_form) = -0.0021404470855535835210552153757756 y[1] (numeric) = -0.0021404470855535833912105856153549 absolute error = 1.2984462976042075143570932632696e-19 relative error = 6.0662387141814838915360920949216e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (closed_form) = -0.002137319606418993989012126121163 y[1] (numeric) = -0.0021373196064189938590268887267755 absolute error = 1.2998523739438747205670797027252e-19 relative error = 6.0816939592938698723167505105347e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.579 y[1] (closed_form) = -0.0021341976092800420217310946633619 y[1] (numeric) = -0.0021341976092800418916057011937959 absolute error = 1.3012539346956600893297377870661e-19 relative error = 6.0971576813574907015073657636195e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.578 y[1] (closed_form) = -0.0021310810829293792764676701790618 y[1] (numeric) = -0.0021310810829293791462025706115608 absolute error = 1.3026509956750099650223601524000e-19 relative error = 6.1126299046509709911283602439308e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.577 y[1] (closed_form) = -0.0021279700161858351517287110673486 y[1] (numeric) = -0.0021279700161858350213243538036106 absolute error = 1.3040435726373799898286737595959e-19 relative error = 6.1281106534327133701472881013493e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.576 y[1] (closed_form) = -0.0021248643978943480191450452858509 y[1] (numeric) = -0.0021248643978943478886018771580029 absolute error = 1.3054316812784800915005636852616e-19 relative error = 6.1435999519409729502694624321606e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.575 y[1] (closed_form) = -0.0021217642169258966560097444551203 y[1] (numeric) = -0.0021217642169258965253282107316685 absolute error = 1.3068153372345183994984320519644e-19 relative error = 6.1590978243939315806337865913520e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.574 y[1] (closed_form) = -0.0021186694621774318778381024550261 y[1] (numeric) = -0.0021186694621774317470186468467817 absolute error = 1.3081945560824440945087002358734e-19 relative error = 6.1746042949897718920912800779645e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.573 y[1] (closed_form) = -0.0021155801225718083703076626368992 y[1] (numeric) = -0.0021155801225718082393507273028803 absolute error = 1.3095693533401891963121972944296e-19 relative error = 6.1901193879067511317414181177746e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.572 y[1] (closed_form) = -0.0021124961870577167199388826345447 y[1] (numeric) = -0.0021124961870577165888449081878538 absolute error = 1.3109397444669092949525422404392e-19 relative error = 6.2056431273032747883990417338648e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.571 y[1] (closed_form) = -0.0021094176446096156428792621108897 y[1] (numeric) = -0.0021094176446096155116486876245674 absolute error = 1.3123057448632232301291216333442e-19 relative error = 6.2211755373179700096622417142857e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (closed_form) = -0.0021063444842276644111559866596517 y[1] (numeric) = -0.0021063444842276642797892496725065 absolute error = 1.3136673698714517237148862487817e-19 relative error = 6.2367166420697588112492754204924e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.569 y[1] (closed_form) = -0.00210327669493765547576436052754 y[1] (numeric) = -0.0021032766949376553442618970499545 absolute error = 1.3150246347758549702749406134566e-19 relative error = 6.2522664656579310792702397941870e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.568 y[1] (closed_form) = -0.00210021426579094728596151186654 y[1] (numeric) = -0.002100214265790947154323756386253 absolute error = 1.3163775548028691904377762475348e-19 relative error = 6.2678250321622173660968971774094e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.567 y[1] (closed_form) = -0.0020971571858643973041370569020165 y[1] (numeric) = -0.0020971571858643971723644423898823 absolute error = 1.3177261451213421519470028390301e-19 relative error = 6.2833923656428614804917326251484e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.566 y[1] (closed_form) = -0.0020941054442602952156346037448046 y[1] (numeric) = -0.0020941054442602950837275616605279 absolute error = 1.3190704208427676631975605859071e-19 relative error = 6.2989684901406928726550122254896e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.565 y[1] (closed_form) = -0.0020910590301062963329001626180817 y[1] (numeric) = -0.0020910590301062962008591229159298 absolute error = 1.3204103970215190440366508878160e-19 relative error = 6.3145534296771988148463115136603e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.564 y[1] (closed_form) = -0.0020880179325553551933357070464287 y[1] (numeric) = -0.0020880179325553550611610981809205 absolute error = 1.3217460886550815785860007605069e-19 relative error = 6.3301472082545963782346913376775e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.563 y[1] (closed_form) = -0.0020849821407856593502383000987434 y[1] (numeric) = -0.002084982140785659217930549030315 absolute error = 1.3230775106842839548185780960471e-19 relative error = 6.3457498498559042066294154692406e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.562 y[1] (closed_form) = -0.0020819516440005633562073611220682 y[1] (numeric) = -0.0020819516440005632237668933227153 absolute error = 1.3244046779935286955994995189778e-19 relative error = 6.3613613784450140877408298187670e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.561 y[1] (closed_form) = -0.0020789264314285229384048015832942 y[1] (numeric) = -0.002078926431428522805832041042192 absolute error = 1.3257276054110215858776194144441e-19 relative error = 6.3769818179667623226187572729233e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (closed_form) = -0.0020759064923230293650549036833211 y[1] (numeric) = -0.0020759064923230292323502729124211 absolute error = 1.3270463077090001006911570550079e-19 relative error = 6.3926111923470008939135048917051e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.559 y[1] (closed_form) = -0.002072891815962544002572952356646 y[1] (numeric) = -0.0020728918159625438697368723962499 absolute error = 1.3283607996039608386277079581114e-19 relative error = 6.4082495254926684336023314452468e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.558 y[1] (closed_form) = -0.0020698823916504330627137601514601 y[1] (numeric) = -0.0020698823916504329297466505757715 absolute error = 1.3296710957568859653560949996882e-19 relative error = 6.4238968412918609908219830034482e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.557 y[1] (closed_form) = -0.0020668782087149025391333453339184 y[1] (numeric) = -0.0020668782087149024060356242565715 absolute error = 1.3309772107734686718247437287784e-19 relative error = 6.4395531636139026004456724796722e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.556 y[1] (closed_form) = -0.0020638792565089333327591364079596 y[1] (numeric) = -0.0020638792565089331995312204875259 memory used=374.7MB, alloc=44.3MB, time=5.52 absolute error = 1.3322791592043376516986141146001e-19 relative error = 6.4552185163094156530406556388492e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.555 y[1] (closed_form) = -0.002060885524410216565366181121385 y[1] (numeric) = -0.002060885524410216432008485566857 absolute error = 1.3335769555452806025841869565695e-19 relative error = 6.4708929232103910668403410761039e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.554 y[1] (closed_form) = -0.0020578970018210890807589349722074 y[1] (numeric) = -0.0020578970018210889472718735484607 absolute error = 1.3348706142374667555695867482777e-19 relative error = 6.4865764081302582623626650204470e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.553 y[1] (closed_form) = -0.0020549136781684691329602932687728 y[1] (numeric) = -0.002054913678168468999344278302006 absolute error = 1.3361601496676684375846232611919e-19 relative error = 6.5022689948639549403042634852330e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.552 y[1] (closed_form) = -0.0020519355429037922608116119649085 y[1] (numeric) = -0.0020519355429037921270670543480603 absolute error = 1.3374455761684816710633508594074e-19 relative error = 6.5179707071879966633377842392119e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.551 y[1] (closed_form) = -0.0020489625855029473483895358192934 y[1] (numeric) = -0.0020489625855029472145168450174388 absolute error = 1.3387269080185458153696769333841e-19 relative error = 6.5336815688605462424374992754919e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (closed_form) = -0.002045994795466212870647517948184 y[1] (numeric) = -0.0020459947954662127366471020039078 absolute error = 1.3400041594427622544245982122379e-19 relative error = 6.5494016036214829283562048770919e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.549 y[1] (closed_form) = -0.0020430321623181933236919725842069 y[1] (numeric) = -0.0020430321623181931895642381229557 absolute error = 1.3412773446125121349518054484568e-19 relative error = 6.5651308351924714088742309836975e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.548 y[1] (closed_form) = -0.0020400746756077558391050528526769 y[1] (numeric) = -0.0020400746756077557048504050880896 absolute error = 1.3425464776458731597366724372023e-19 relative error = 6.5808692872770306124392243215358e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.547 y[1] (closed_form) = -0.0020371223249079669817280876621957 y[1] (numeric) = -0.0020371223249079668473469304014122 absolute error = 1.3438115726078354402720339095657e-19 relative error = 6.5966169835606023188132206339422e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.546 y[1] (closed_form) = -0.0020341750998160297303217464093766 y[1] (numeric) = -0.0020341750998160295958144820583249 absolute error = 1.3450726435105164131426579038486e-19 relative error = 6.6123739477106195773413803112948e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.545 y[1] (closed_form) = -0.0020312329899532206405210271495378 y[1] (numeric) = -0.0020312329899532205058880567182004 absolute error = 1.3463297043133748244789311532782e-19 relative error = 6.6281402033765749334546287327966e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.544 y[1] (closed_form) = -0.002028295984964827189505183217091 y[1] (numeric) = -0.0020282959849648270547469063247487 absolute error = 1.3475827689234237867890002182700e-19 relative error = 6.6439157741900884640163176664923e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.543 y[1] (closed_form) = -0.0020253640745200853018047150219514 y[1] (numeric) = -0.0020253640745200851669215299024071 absolute error = 1.3488318511954429124574459256991e-19 relative error = 6.6597006837649756221209070954309e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.542 y[1] (closed_form) = -0.0020224372483121170556695579323379 y[1] (numeric) = -0.002022437248312116920661861439119 absolute error = 1.3500769649321895281775135494230e-19 relative error = 6.6754949556973148919505578147253e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.541 y[1] (closed_form) = -0.0020195154960578685694245938103749 y[1] (numeric) = -0.002019515496057868434292781421914 absolute error = 1.3513181238846089745629754718377e-19 relative error = 6.6912986135655152542934240442061e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (closed_form) = -0.0020165988074980480672406029254004 y[1] (numeric) = -0.002016598807498047931985068750196 absolute error = 1.3525553417520439951648662053288e-19 relative error = 6.7071116809303834633253420923952e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.539 y[1] (closed_form) = -0.0020136871723970641237507546611434 y[1] (numeric) = -0.0020136871723970639883718914428991 absolute error = 1.3537886321824432190976010283607e-19 relative error = 6.7229341813351911352545257577141e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.538 y[1] (closed_form) = -0.0020107805805429640869447096871279 y[1] (numeric) = -0.002010780580542963951442908809871 absolute error = 1.3550180087725687414583685103355e-19 relative error = 6.7387661383057416494268016304269e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.537 y[1] (closed_form) = -0.0020078790217473726787743731118419 y[1] (numeric) = -0.0020078790217473725431500246050216 absolute error = 1.3562434850682028057031732723633e-19 relative error = 6.7546075753504368624868477321729e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.536 y[1] (closed_form) = -0.0020049824858454307729072976053048 y[1] (numeric) = -0.0020049824858454306371607901488694 absolute error = 1.3574650745643535921224978712566e-19 relative error = 6.7704585159603436361888369675667e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.535 y[1] (closed_form) = -0.0020020909626957343490656876014519 y[1] (numeric) = -0.0020020909626957342131974085309059 absolute error = 1.3586827907054601165392511182820e-19 relative error = 6.7863189836092601794478326328807e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.534 y[1] (closed_form) = -0.0019992044421802736233909004958984 y[1] (numeric) = -0.0019992044421802734874012358073388 absolute error = 1.3598966468855962433314738727555e-19 relative error = 6.8021890017537822052212366990561e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.533 y[1] (closed_form) = -0.0019963229142043723542752782716812 y[1] (numeric) = -0.0019963229142043722181646126268138 absolute error = 1.3611066564486738168621818070532e-19 relative error = 6.8180685938333689028075527291174e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.532 y[1] (closed_form) = -0.0019934463686966273231050732439007 y[1] (numeric) = -0.0019934463686966271868737899750362 absolute error = 1.3623128326886449153787372509489e-19 relative error = 6.8339577832704087261476940725541e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.531 y[1] (closed_form) = -0.0019905747956088479893601546430853 y[1] (numeric) = -0.001990574795608847853008635758115 absolute error = 1.3635151888497032314242584196257e-19 relative error = 6.8498565934702849987120443705444e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (closed_form) = -0.0019877081849159963195180985857177 y[1] (numeric) = -0.0019877081849159961830467247730693 absolute error = 1.3647137381264845827837935447306e-19 relative error = 6.8657650478214413355544613753610e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.529 y[1] (closed_form) = -0.0019848465266161267892121726377327 y[1] (numeric) = -0.0019848465266161266526213232713061 absolute error = 1.3659084936642665579683090982316e-19 relative error = 6.8816831696954468831124066043523e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.528 y[1] (closed_form) = -0.0019819898107303265580946276918034 y[1] (numeric) = -0.0019819898107303264213846808358866 absolute error = 1.3670994685591673002199648645891e-19 relative error = 6.8976109824470613773303823831183e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.527 y[1] (closed_form) = -0.001979138027302655816858604280672 y[1] (numeric) = -0.0019791380273026556800299366948376 absolute error = 1.3682866758583434340026735211125e-19 relative error = 6.9135485094143000206818643536074e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.526 y[1] (closed_form) = -0.0019762911664000883058738477652853 y[1] (numeric) = -0.0019762911664000881689268349092666 absolute error = 1.3694701285601871379225680757517e-19 relative error = 6.9294957739184981786629315006903e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.525 y[1] (closed_form) = -0.0019734492181124520048933070966002 y[1] (numeric) = -0.0019734492181124518678283231351479 absolute error = 1.3706498396145223680037264356003e-19 relative error = 6.9454527992643758963288171552878e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.524 y[1] (closed_form) = -0.0019706121725523699932895650820348 y[1] (numeric) = -0.0019706121725523698561069828897547 absolute error = 1.3718258219228002352253279908250e-19 relative error = 6.9614196087401022354426332334438e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.523 y[1] (closed_form) = -0.0019677800198552014802819143199354 y[1] (numeric) = -0.001967780019855201342982105486106 absolute error = 1.3729980883382935412073418535104e-19 relative error = 6.9773962256173594328035561390734e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.522 y[1] (closed_form) = -0.0019649527501789830046167522262672 y[1] (numeric) = -0.0019649527501789828672000870596381 absolute error = 1.3741666516662904759128697480649e-19 relative error = 6.9933826731514068803198062638294e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.521 y[1] (closed_form) = -0.0019621303537043698031658208950602 y[1] (numeric) = -0.0019621303537043696656326684286314 absolute error = 1.3753315246642874812163879715150e-19 relative error = 7.0093789745811449273898038311166e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (closed_form) = -0.0019593128206345773479086629358654 y[1] (numeric) = -0.0019593128206345772102593909316473 absolute error = 1.3764927200421812841683517934665e-19 relative error = 7.0253851531291785061529419233389e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.519 y[1] (closed_form) = -0.0019565001411953230507675029453978 y[1] (numeric) = -0.0019565001411953229130024778991518 absolute error = 1.3776502504624601037679416150361e-19 relative error = 7.0414012320018805801694828727425e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.518 y[1] (closed_form) = -0.0019536923056347681357645959243397 y[1] (numeric) = -0.0019536923056347679978841830703003 absolute error = 1.3788041285403940350371426250116e-19 relative error = 7.0574272343894554170871567575777e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.517 y[1] (closed_form) = -0.0019508893042234596779739087715124 y[1] (numeric) = -0.00195088930422345953997847208709 absolute error = 1.3799543668442246141708580542680e-19 relative error = 7.0734631834660016858501204977290e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.516 y[1] (closed_form) = -0.00194809112725427280874081900373 y[1] (numeric) = -0.0019480911272542726706307212141946 absolute error = 1.3811009778953535685193599134640e-19 relative error = 7.0895091023895753790040229585861e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.515 y[1] (closed_form) = -0.0019452977650423530866453260879525 y[1] (numeric) = -0.0019452977650423529484209286710994 absolute error = 1.3822439741685307551410797846516e-19 relative error = 7.1055650143022525606490155199708e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.514 y[1] (closed_form) = -0.0019425092079250590336860752600627 y[1] (numeric) = -0.0019425092079250588953477384508585 absolute error = 1.3833833680920412916455353080358e-19 relative error = 7.1216309423301919405906487197729e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.513 y[1] (closed_form) = -0.0019397254462619048361642914687817 y[1] (numeric) = -0.0019397254462619046977123742639926 absolute error = 1.3845191720478918830280749470537e-19 relative error = 7.1377069095836972752367038110624e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.512 y[1] (closed_form) = -0.0019369464704345032097485121508945 y[1] (numeric) = -0.0019369464704345030711833723136949 absolute error = 1.3856513983719963481801039174777e-19 relative error = 7.1537929391572795957861233484452e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.511 y[1] (closed_form) = -0.0019341722708465084282027919419218 y[1] (numeric) = -0.0019341722708465082895247860064858 absolute error = 1.3867800593543603497405273215899e-19 relative error = 7.1698890541297192642543272160464e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (closed_form) = -0.0019314028379235595152628301814016 y[1] (numeric) = -0.0019314028379235593764723134574751 absolute error = 1.3879051672392653309363120317231e-19 relative error = 7.1859952775641278578773297975947e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.509 y[1] (closed_form) = -0.0019286381621132235991462432106426 y[1] (numeric) = -0.0019286381621132234602435697880974 absolute error = 1.3890267342254516630423262166295e-19 relative error = 7.2021116325080098824352102406102e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.508 y[1] (closed_form) = -0.0019258782338849394291849680097074 y[1] (numeric) = -0.0019258782338849392901704907630773 absolute error = 1.3901447724663010070729641000692e-19 relative error = 7.2182381419933243150336309537675e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.507 y[1] (closed_form) = -0.0019231230437299610540695417058645 y[1] (numeric) = -0.0019231230437299609149436122988627 absolute error = 1.3912592940700178933005030874480e-19 relative error = 7.2343748290365459768802495713233e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.506 y[1] (closed_form) = -0.0019203725821613016611967529340975 y[1] (numeric) = -0.0019203725821613015219597218241164 absolute error = 1.3923703110998105221776702998223e-19 relative error = 7.2505217166387267365910265934007e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.505 y[1] (closed_form) = -0.0019176268397136775766139059676579 y[1] (numeric) = -0.0019176268397136774372661224102509 absolute error = 1.3934778355740707902245153245201e-19 relative error = 7.2666788277855565445595947383577e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.504 y[1] (closed_form) = -0.0019148858069434524250546769891387 y[1] (numeric) = -0.0019148858069434522855964890424834 absolute error = 1.3945818794665535444223951401740e-19 relative error = 7.2828461854474242989210266960107e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.503 y[1] (closed_form) = -0.001912149474428581449563273866091 y[1] (numeric) = -0.0019121494744285813099950283954355 absolute error = 1.3956824547065550686406752161024e-19 relative error = 7.2990238125794785436395154208139e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.502 y[1] (closed_form) = -0.001909417832768555990205336355632 y[1] (numeric) = -0.0019094178327685558505273790377229 absolute error = 1.3967795731790908056046372394459e-19 relative error = 7.3152117321216879992476653250278e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.501 y[1] (closed_form) = -0.0019066908725843481213657328155264 y[1] (numeric) = -0.0019066908725843479815784081430191 absolute error = 1.3978732467250723178960583087559e-19 relative error = 7.3314099669989019267632836963530e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop memory used=421.3MB, alloc=44.3MB, time=6.22 x[1] = 2.5 y[1] (closed_form) = -0.0019039685845183554471351222704825 y[1] (numeric) = -0.0019039685845183553072387735563342 absolute error = 1.3989634871414834914609882730778e-19 relative error = 7.3476185401209103253077593455060e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.499 y[1] (closed_form) = -0.0019012509592343460542888570973922 y[1] (numeric) = -0.0019012509592343459142838264792366 absolute error = 1.4000503061815559850824007169222e-19 relative error = 7.3638374743825039639483198599207e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.498 y[1] (closed_form) = -0.0018985379874174036223635016773537 y[1] (numeric) = -0.0018985379874174034822501301218593 absolute error = 1.4011337155549439292586284225142e-19 relative error = 7.3800667926635342482846698734354e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.497 y[1] (closed_form) = -0.0018958296597738726903379361408452 y[1] (numeric) = -0.0018958296597738725501165634480554 absolute error = 1.4022137269278978779118155127231e-19 relative error = 7.3963065178289729222987304318626e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.496 y[1] (closed_form) = -0.0018931259670313040794277018305271 y[1] (numeric) = -0.0018931259670313039390986666381833 absolute error = 1.4032903519234380163340254250788e-19 relative error = 7.4125566727289716059844238142203e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.495 y[1] (closed_form) = -0.0018904268999384004715029263489359 y[1] (numeric) = -0.0018904268999384003310665661367832 absolute error = 1.4043636021215266287621359259885e-19 relative error = 7.4288172801989211692726790327506e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.494 y[1] (closed_form) = -0.0018877324492649621426418410707327 y[1] (numeric) = -0.0018877324492649620020984921648088 absolute error = 1.4054334890592398289562290839443e-19 relative error = 7.4450883630595109427650706553750e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.493 y[1] (closed_form) = -0.0018850426058018328513335728060659 y[1] (numeric) = -0.001885042605801832710683570382972 absolute error = 1.4065000242309385571398450231338e-19 relative error = 7.4613699441167877657877475457802e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.492 y[1] (closed_form) = -0.0018823573603608458808455539277283 y[1] (numeric) = -0.0018823573603608457400892320188844 absolute error = 1.4075632190884388466442129189365e-19 relative error = 7.4776620461622148722755585728272e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.491 y[1] (closed_form) = -0.001879676703774770235272551744804 y[1] (numeric) = -0.0018796767037747700944102432406859 absolute error = 1.4086230850411813635824006214734e-19 relative error = 7.4939646919727306149945392765055e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (closed_form) = -0.0018770006268972569887859682439247 y[1] (numeric) = -0.0018770006268972568478180048982847 absolute error = 1.4096796334564002228632350523679e-19 relative error = 7.5102779043108070286091868663567e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.489 y[1] (closed_form) = -0.0018743291206027857876037055505471 y[1] (numeric) = -0.001874329120602785646530417984618 absolute error = 1.4107328756592910838388386654573e-19 relative error = 7.5266017059245082320992207444737e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.488 y[1] (closed_form) = -0.0018716621757866115042025306111397 y[1] (numeric) = -0.0018716621757866113630242483178218 absolute error = 1.4117828229331785288637023491813e-19 relative error = 7.5429361195475486710288019632080e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.487 y[1] (closed_form) = -0.0018689997833647110432965046870568 y[1] (numeric) = -0.0018689997833647109020135560350885 absolute error = 1.4128294865196827280273717341232e-19 relative error = 7.5592811678993512001694676221010e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.486 y[1] (closed_form) = -0.001866341934273730299106669306316 y[1] (numeric) = -0.0018663419342737301577193815444275 absolute error = 1.4138728776188853933070615135555e-19 relative error = 7.5756368736851050069763251538939e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.485 y[1] (closed_form) = -0.0018636886194709312634488003644851 y[1] (numeric) = -0.0018636886194709311219574996255356 absolute error = 1.4149130073894950253708306502168e-19 relative error = 7.5920032595958233764153467204863e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.484 y[1] (closed_form) = -0.0018610398299341392841676561243624 y[1] (numeric) = -0.0018610398299341391425726674294612 absolute error = 1.4159498869490114562463497937747e-19 relative error = 7.6083803483084012976379055112179e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.483 y[1] (closed_form) = -0.0018583955566616904734477529599043 y[1] (numeric) = -0.0018583955566616903317494002225153 absolute error = 1.4169835273738896910547704378431e-19 relative error = 7.6247681624856729129970035827886e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.482 y[1] (closed_form) = -0.0018557557906723792655323048466387 y[1] (numeric) = -0.0018557557906723791237309108766684 absolute error = 1.4180139396997030519937628727962e-19 relative error = 7.6411667247764688098979549775214e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.481 y[1] (closed_form) = -0.0018531205230054061233835588422121 y[1] (numeric) = -0.0018531205230054059814794453500816 absolute error = 1.4190411349213056277384264131947e-19 relative error = 7.6575760578156731559746081796812e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (closed_form) = -0.0018504897447203253938193491502692 y[1] (numeric) = -0.0018504897447203252518128367509698 absolute error = 1.4200651239929940314134902710563e-19 relative error = 7.6739961842242806780805184934165e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.479 y[1] (closed_form) = -0.0018478634468969933106622768419672 y[1] (numeric) = -0.0018478634468969931685536850591003 absolute error = 1.4210859178286684702750163855349e-19 relative error = 7.6904271266094534855828136259563e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.478 y[1] (closed_form) = -0.0018452416206355161454395009454003 y[1] (numeric) = -0.001845241620635516003229148215201 absolute error = 1.4221035273019931302246860852870e-19 relative error = 7.7068689075645777384448346114312e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.477 y[1] (closed_form) = -0.0018426242570561985051726994272611 y[1] (numeric) = -0.0018426242570561983628609031026055 absolute error = 1.4231179632465558782647002337494e-19 relative error = 7.7233215496693201605819791896521e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.476 y[1] (closed_form) = -0.0018400113472994917767993256063188 y[1] (numeric) = -0.0018400113472994916343864019607161 absolute error = 1.4241292364560272859863470739496e-19 relative error = 7.7397850754896843989735258360473e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.475 y[1] (closed_form) = -0.0018374028825259427177678467777648 y[1] (numeric) = -0.0018374028825259425752541110093329 absolute error = 1.4251373576843189771703929348990e-19 relative error = 7.7562595075780672290115737994978e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.474 y[1] (closed_form) = -0.0018347988539161421923512073140745 y[1] (numeric) = -0.0018347988539161420497369735495003 absolute error = 1.4261423376457413025626278749976e-19 relative error = 7.7727448684733146065665977198905e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.473 y[1] (closed_form) = -0.0018321992526706740532243082646004 y[1] (numeric) = -0.0018321992526706739105098895630844 absolute error = 1.4271441870151603448731508104529e-19 relative error = 7.7892411807007775672474846428190e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.472 y[1] (closed_form) = -0.0018296040700100641678528395253554 y[1] (numeric) = -0.0018296040700100640250385478825399 absolute error = 1.4281429164281542570333063020513e-19 relative error = 7.8057484667723679733322965010669e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.471 y[1] (closed_form) = -0.0018270132971747295892423390149999 y[1] (numeric) = -0.001827013297174729446328485366883 absolute error = 1.4291385364811689367295875475772e-19 relative error = 7.8222667491866141088443823674964e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (closed_form) = -0.0018244269254249278705978859954526 y[1] (numeric) = -0.0018244269254249277275847802222853 absolute error = 1.4301310577316730402192968479039e-19 relative error = 7.8387960504287161232468519780217e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.469 y[1] (closed_form) = -0.0018218449460407065234463627382253 y[1] (numeric) = -0.0018218449460407063803343136683941 absolute error = 1.4311204906983123384183054827058e-19 relative error = 7.8553363929706013242268151528424e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.468 y[1] (closed_form) = -0.0018192673503218526187747401828916 y[1] (numeric) = -0.0018192673503218524755640555967853 absolute error = 1.4321068458610634182368791495448e-19 relative error = 7.8718877992709793200391907855436e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.467 y[1] (closed_form) = -0.0018166941295878425307393590842785 y[1] (numeric) = -0.0018166941295878423874303457181398 absolute error = 1.4330901336613867321252324926942e-19 relative error = 7.8884502917753970118782939996067e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.466 y[1] (closed_form) = -0.0018141252751777918225026884221702 y[1] (numeric) = -0.0018141252751777916790956519719323 absolute error = 1.4340703645023789987762463826471e-19 relative error = 7.9050238929162934367438208670116e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.465 y[1] (closed_form) = -0.0018115607784504052737555475736003 y[1] (numeric) = -0.0018115607784504051302507926987078 absolute error = 1.4350475487489249579186241131941e-19 relative error = 7.9216086251130544612662667207159e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.464 y[1] (closed_form) = -0.0018090006307839270494842779451382 y[1] (numeric) = -0.0018090006307839269058821082723534 absolute error = 1.4360216967278484821196771718322e-19 relative error = 7.9382045107720673269552365487617e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.463 y[1] (closed_form) = -0.0018064448235760910095438434528283 y[1] (numeric) = -0.001806444823576090865844561580022 absolute error = 1.4369928187280630485029173248755e-19 relative error = 7.9548115722867750473325342095493e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.462 y[1] (closed_form) = -0.0018038933482440711585993274423883 y[1] (numeric) = -0.0018038933482440710148032349423161 absolute error = 1.4379609250007215732716890569347e-19 relative error = 7.9714298320377306574103512325208e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.461 y[1] (closed_form) = -0.0018013461962244322359997763836137 y[1] (numeric) = -0.0018013461962244320921071738076771 absolute error = 1.4389260257593656119162045335495e-19 relative error = 7.9880593123926513159733157432663e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (closed_form) = -0.0017988033589730804451498179722466 y[1] (numeric) = -0.0017988033589730803011610048542392 absolute error = 1.4398881311800739279675418359870e-19 relative error = 8.0047000357064722611216075541960e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.459 y[1] (closed_form) = -0.0017962648279652143219459531513755 y[1] (numeric) = -0.0017962648279652141778612280112145 absolute error = 1.4408472514016104331484358709809e-19 relative error = 8.0213520243214006195307966687474e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.458 y[1] (closed_form) = -0.0017937305946952757418458880441292 y[1] (numeric) = -0.001793730594695275597665548391572 absolute error = 1.4418033965255715017570297100443e-19 relative error = 8.0380153005669690698825193361114e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.457 y[1] (closed_form) = -0.0017912006506769010651407328913508 y[1] (numeric) = -0.0017912006506769009208650752296975 absolute error = 1.4427565766165326621061617896196e-19 relative error = 8.0546898867600893609185683421889e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.456 y[1] (closed_form) = -0.0017886749874428724200013508333118 y[1] (numeric) = -0.0017886749874428722756306706630923 absolute error = 1.4437068017021946678272410335007e-19 relative error = 8.0713758052051056845694424086090e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.455 y[1] (closed_form) = -0.001786153596545069122871589784492 y[1] (numeric) = -0.0017861535965450689784061816071391 absolute error = 1.4446540817735289518343071735623e-19 relative error = 8.0880730781938479046068733728762e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.454 y[1] (closed_form) = -0.0017836364695544192357825757460675 y[1] (numeric) = -0.0017836364695544190912227330675753 absolute error = 1.4455984267849224657304869767967e-19 relative error = 8.1047817280056846412683292169193e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.453 y[1] (closed_form) = -0.0017811235980608512601636857029778 y[1] (numeric) = -0.0017811235980608511155097010375457 absolute error = 1.4465398466543219074257383710082e-19 relative error = 8.1215017769075762122999759764164e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.452 y[1] (closed_form) = -0.001778614973673245966727252782153 y[1] (numeric) = -0.0017786149736732458219794176558153 absolute error = 1.4474783512633773397215232353344e-19 relative error = 8.1382332471541274308630720772990e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.451 y[1] (closed_form) = -0.0017761105880193883610054856264729 y[1] (numeric) = -0.0017761105880193882161640905807143 absolute error = 1.4484139504575852026048655241484e-19 relative error = 8.1549761609876402607472646869082e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (closed_form) = -0.0017736104327459197841195079859889 y[1] (numeric) = -0.0017736104327459196391848425813458 absolute error = 1.4493466540464307219811340650079e-19 relative error = 8.1717305406381663293327592136039e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.449 y[1] (closed_form) = -0.0017711144995182901483618433644869 y[1] (numeric) = -0.0017711144995182900033341961841339 absolute error = 1.4502764718035297175618384563155e-19 relative error = 8.1884964083235592987418401185181e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.448 y[1] (closed_form) = -0.0017686227800207103071750832061238 y[1] (numeric) = -0.0017686227800207101620547418594468 absolute error = 1.4512034134667698126107416334078e-19 relative error = 8.2052737862495270956187336949840e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.447 y[1] (closed_form) = -0.0017661352659561045591108855840778 y[1] (numeric) = -0.0017661352659561044138981367102327 absolute error = 1.4521274887384510482386735200725e-19 relative error = 8.2220626966096839999753214034605e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.446 y[1] (closed_form) = -0.0017636519490460632853548546812552 y[1] (numeric) = -0.0017636519490460631400499839527126 absolute error = 1.4530487072854259049245763851474e-19 relative error = 8.2388631615856025935387357010777e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.445 y[1] (closed_form) = -0.0017611728210307957204042495523727 y[1] (numeric) = -0.0017611728210307955750075416784488 absolute error = 1.4539670787392387339275237320054e-19 relative error = 8.2556752033468655680353990539214e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop memory used=468.0MB, alloc=44.3MB, time=6.91 x[1] = 2.444 y[1] (closed_form) = -0.0017586978736690828554868637473516 y[1] (numeric) = -0.0017586978736690827099986024777251 absolute error = 1.4548826126962646012417304154573e-19 relative error = 8.2724988440511173938446009456128e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.443 y[1] (closed_form) = -0.0017562270987382304743108053780273 y[1] (numeric) = -0.0017562270987382303287312735062425 absolute error = 1.4557953187178475467339118609429e-19 relative error = 8.2893341058441158494532471764737e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.442 y[1] (closed_form) = -0.0017537604880340223207362901436958 y[1] (numeric) = -0.0017537604880340221750657695106519 absolute error = 1.4567052063304382610897544117835e-19 relative error = 8.3061810108597834121419605625235e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.441 y[1] (closed_form) = -0.0017512980333706733979619377159208 y[1] (numeric) = -0.0017512980333706732522007092133477 absolute error = 1.4576122850257311831837266106481e-19 relative error = 8.3230395812202585103312622717716e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (closed_form) = -0.0017488397265807833988194347391519 y[1] (numeric) = -0.0017488397265807832529677783130718 absolute error = 1.4585165642608010204739922920262e-19 relative error = 8.3399098390359466380151184558509e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.439 y[1] (closed_form) = -0.0017463855595152902667717955508132 y[1] (numeric) = -0.0017463855595152901208299902049893 absolute error = 1.4594180534582386950117803861272e-19 relative error = 8.3567918064055713317076975271860e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.438 y[1] (closed_form) = -0.0017439355240434238872118145822954 y[1] (numeric) = -0.0017439355240434237411801383816667 absolute error = 1.4603167620062867176422229758281e-19 relative error = 8.3736855054162250103277493749038e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.437 y[1] (closed_form) = -0.0017414896120526599086586622903066 y[1] (numeric) = -0.0017414896120526597625373923644092 absolute error = 1.4612126992589739929613920735587e-19 relative error = 8.3905909581434196784435889859319e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.436 y[1] (closed_form) = -0.0017390478154486736934519294058302 y[1] (numeric) = -0.0017390478154486735472413419522052 absolute error = 1.4621058745362500575820464626867e-19 relative error = 8.4075081866511374933002433206765e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.435 y[1] (closed_form) = -0.0017366101261552943975437722949197 y[1] (numeric) = -0.0017366101261552942512441425825078 absolute error = 1.4629962971241187542484424482637e-19 relative error = 8.4244372129918811960489018648538e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.434 y[1] (closed_form) = -0.0017341765361144591789911553210874 y[1] (numeric) = -0.0017341765361144590326027576936103 absolute error = 1.4638839762747713443284661569603e-19 relative error = 8.4413780592067244075973980201196e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.433 y[1] (closed_form) = -0.0017317470372861675347515243023774 y[1] (numeric) = -0.0017317470372861673882746321817055 absolute error = 1.4647689212067190611993097895597e-19 relative error = 8.4583307473253617894990403858144e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.432 y[1] (closed_form) = -0.0017293216216484357653865784865367 y[1] (numeric) = -0.0017293216216484356188214643760442 absolute error = 1.4656511411049251070309396372022e-19 relative error = 8.4752952993661590702957100022186e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.431 y[1] (closed_form) = -0.0017269002811972515672801369441231 y[1] (numeric) = -0.0017269002811972514206270724320295 absolute error = 1.4665306451209360954596894022206e-19 relative error = 8.4922717373362029377297417520941e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (closed_form) = -0.0017244830079465287519774189209293 y[1] (numeric) = -0.001724483007946528605236674683628 absolute error = 1.4674074423730129426324580952052e-19 relative error = 8.5092600832313507972377153319437e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.429 y[1] (closed_form) = -0.0017220697939280620922543765167155 y[1] (numeric) = -0.0017220697939280619454262223220893 absolute error = 1.4682815419462612090901971930323e-19 relative error = 8.5262603590362803971378934874076e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.428 y[1] (closed_form) = -0.0017196606311914822945270320857769 y[1] (numeric) = -0.0017196606311914821476117367965008 absolute error = 1.4691529528927608949476365208848e-19 relative error = 8.5432725867245393209216625386841e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.427 y[1] (closed_form) = -0.0017172555118042110972120820051352 y[1] (numeric) = -0.0017172555118042109502099135819656 absolute error = 1.4700216842316956908145221494809e-19 relative error = 8.5602967882585943470579525820355e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.426 y[1] (closed_form) = -0.0017148544278514164946513329468138 y[1] (numeric) = -0.0017148544278514163475625584518657 absolute error = 1.4708877449494816868920221632591e-19 relative error = 8.5773329855898806767182421226203e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.425 y[1] (closed_form) = -0.0017124573714359680862138365403951 y[1] (numeric) = -0.0017124573714359679390387221404055 absolute error = 1.4717511439998955426663971443416e-19 relative error = 8.5943812006588510298283842524899e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.424 y[1] (closed_form) = -0.0017100643346783925501908833393826 y[1] (numeric) = -0.0017100643346783924029296943089624 absolute error = 1.4726118903042021196105313206602e-19 relative error = 8.6114414553950246098521288160545e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.423 y[1] (closed_form) = -0.0017076753097168292421003073283039 y[1] (numeric) = -0.0017076753097168290947533080531758 absolute error = 1.4734699927512815792924772363588e-19 relative error = 8.6285137717170359377098572842327e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.422 y[1] (closed_form) = -0.0017052902887069859170178378453628 y[1] (numeric) = -0.0017052902887069857695852918255873 absolute error = 1.4743254601977559492787812118711e-19 relative error = 8.6455981715326835552346942684805e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.421 y[1] (closed_form) = -0.0017029092638220945755545167661148 y[1] (numeric) = -0.0017029092638220944280366866193033 absolute error = 1.4751783014681151592090284650330e-19 relative error = 8.6626946767389785985668117276678e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.42 y[1] (closed_form) = -0.0017005322272528674331004751153346 y[1] (numeric) = -0.0017005322272528672854976225798503 absolute error = 1.4760285253548425494067752600234e-19 relative error = 8.6798033092221932418853989351377e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.419 y[1] (closed_form) = -0.0016981591712074530119566349651324 y[1] (numeric) = -0.0016981591712074528642690209032784 absolute error = 1.4768761406185398543808205363423e-19 relative error = 8.6969240908579090118764331611218e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.418 y[1] (closed_form) = -0.0016957900879113923559771695555473 y[1] (numeric) = -0.0016957900879113922082050539567421 absolute error = 1.4777211559880516635596108456167e-19 relative error = 8.7140570435110649733330527679526e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.417 y[1] (closed_form) = -0.0016934249696075753673468170573151 y[1] (numeric) = -0.0016934249696075752194904590412562 absolute error = 1.4785635801605893615904697916167e-19 relative error = 8.7312021890360057862840059932565e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.416 y[1] (closed_form) = -0.0016910638085561972651184013032144 y[1] (numeric) = -0.001691063808556197117178059123029 absolute error = 1.4794034218018545505242962319897e-19 relative error = 8.7483595492765296350443250906420e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.415 y[1] (closed_form) = -0.0016887065970347151651371661621926 y[1] (numeric) = -0.0016887065970347150171130972075764 absolute error = 1.4802406895461619561953839640518e-19 relative error = 8.7655291460659360295810566895170e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.414 y[1] (closed_form) = -0.0016863533273378047809797790371663 y[1] (numeric) = -0.0016863533273378046328722398375101 absolute error = 1.4810753919965618210950791883059e-19 relative error = 8.7827110012270734795855652068526e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.413 y[1] (closed_form) = -0.0016840039917773172455371032506782 y[1] (numeric) = -0.001684003991777317097346349478182 absolute error = 1.4819075377249617860271104306511e-19 relative error = 8.7999051365723870416426168753154e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.412 y[1] (closed_form) = -0.0016816585826822360528710788601198 y[1] (numeric) = -0.001681658582682235904597365332895 absolute error = 1.4827371352722482628215985175539e-19 relative error = 8.8171115739039657398851474256452e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.411 y[1] (closed_form) = -0.0016793170923986341199772867335698 y[1] (numeric) = -0.0016793170923986339716208674187291 absolute error = 1.4835641931484073003739813494632e-19 relative error = 8.8343303350135898605223166579744e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (closed_form) = -0.0016769795132896309680860015359303 y[1] (numeric) = -0.0016769795132896308196471295526658 absolute error = 1.4843887198326449462643693197435e-19 relative error = 8.8515614416827781206271580385506e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.409 y[1] (closed_form) = -0.0016746458377353500231357656403996 y[1] (numeric) = -0.0016746458377353498746146932630489 absolute error = 1.4852107237735071062021819942603e-19 relative error = 8.8688049156828347115688410467106e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.408 y[1] (closed_form) = -0.0016723160581328760350547379097437 y[1] (numeric) = -0.0016723160581328758864517165708438 absolute error = 1.4860302133889989035303048169341e-19 relative error = 8.8860607787748962174732782536856e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.407 y[1] (closed_form) = -0.0016699901668962126154862888025911 y[1] (numeric) = -0.0016699901668962124668015690959208 absolute error = 1.4868471970667035410124458571430e-19 relative error = 8.9033290527099784090945280217323e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.406 y[1] (closed_form) = -0.0016676681564562398935965263692842 y[1] (numeric) = -0.0016676681564562397448303580528941 absolute error = 1.4876616831639006671168666853841e-19 relative error = 8.9206097592290229134781672510552e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.405 y[1] (closed_form) = -0.0016653500192606722896026464268054 y[1] (numeric) = -0.0016653500192606721407552784260369 absolute error = 1.4884736800076842489992080752922e-19 relative error = 8.9379029200629437597965367549967e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.404 y[1] (closed_form) = -0.001663035747774016405662204560014 y[1] (numeric) = -0.001663035747774016256733884970506 absolute error = 1.4892831958950799543767301056561e-19 relative error = 8.9552085569326738017344945930545e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.403 y[1] (closed_form) = -0.0016607253344775290337646076038731 y[1] (numeric) = -0.0016607253344775288847555836945569 absolute error = 1.4900902390931620444759370997386e-19 relative error = 8.9725266915492110168030500185684e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.402 y[1] (closed_form) = -0.001658418771869175280267317935429 y[1] (numeric) = -0.001658418771869175131177836151512 absolute error = 1.4908948178391697802252604167717e-19 relative error = 8.9898573456136646829569925855903e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.401 y[1] (closed_form) = -0.001656116052463586806720455261879 y[1] (numeric) = -0.0016561160524635866575507612278166 absolute error = 1.4916969403406233438542261292839e-19 relative error = 9.0072005408173014328913773897740e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (closed_form) = -0.0016538171687920201866246676489018 y[1] (numeric) = -0.0016538171687920200373750061713578 absolute error = 1.4924966147754392780503398087299e-19 relative error = 9.0245562988415911863904783734471e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.399 y[1] (closed_form) = -0.0016515221134023153777683263082347 y[1] (numeric) = -0.0016515221134023152284389413790302 absolute error = 1.4932938492920454448147767310751e-19 relative error = 9.0419246413582529611015770877619e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.398 y[1] (closed_form) = -0.0016492308788588543097912771719058 y[1] (numeric) = -0.0016492308788588541603824119709562 absolute error = 1.4940886520094955061478725353494e-19 relative error = 9.0593055900293005621047142574574e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.397 y[1] (closed_form) = -0.0016469434577425195866235565391276 y[1] (numeric) = -0.0016469434577425194371354534373693 absolute error = 1.4948810310175829286853664550414e-19 relative error = 9.0766991665070881506482959188556e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.396 y[1] (closed_form) = -0.0016446598426506533034486481071431 y[1] (numeric) = -0.0016446598426506531538815486694477 absolute error = 1.4956709943769545143963564293405e-19 relative error = 9.0941053924343556924192147819100e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.395 y[1] (closed_form) = -0.0016423800261970159778420245056994 y[1] (numeric) = -0.001642380026197015828196169493777 absolute error = 1.4964585501192234594439824249070e-19 relative error = 9.1115242894442742857149207851037e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.394 y[1] (closed_form) = -0.0016401040010117455947368780626903 y[1] (numeric) = -0.0016401040010117454450125074379821 absolute error = 1.4972437062470819432999608967766e-19 relative error = 9.1289558791604913698836525505642e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.393 y[1] (closed_form) = -0.0016378317597413167648701029521375 y[1] (numeric) = -0.0016378317597413166150674558786961 absolute error = 1.4980264707344132501942492283627e-19 relative error = 9.1464001831971758143978235887465e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.392 y[1] (closed_form) = -0.0016355632950484999963627441313009 y[1] (numeric) = -0.0016355632950484998464820589786605 absolute error = 1.4988068515264034249713239559061e-19 relative error = 9.1638572231590628889243436303724e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.391 y[1] (closed_form) = -0.0016332985996123210790902775774885 y[1] (numeric) = -0.0016332985996123209291317919235232 absolute error = 1.4995848565396524654148103442090e-19 relative error = 9.1813270206414991147544463609823e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (closed_form) = -0.0016310376661280205814992313031562 y[1] (numeric) = -0.0016310376661280204314631819369277 absolute error = 1.5003604936622850530925031815395e-19 relative error = 9.1988095972304869979543900835290e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.389 y[1] (closed_form) = -0.001628780487307013459527797476183 y[1] (numeric) = -0.0016287804873070133094144204007769 absolute error = 1.5011337707540608247641692471052e-19 relative error = 9.2163049745027296445971974200391e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop memory used=514.7MB, alloc=44.3MB, time=7.61 x[1] = 2.388 y[1] (closed_form) = -0.0016265270558768487772892227167319 y[1] (numeric) = -0.0016265270558768486270987531520835 absolute error = 1.5019046956464841863849205207865e-19 relative error = 9.2338131740256752584344040677031e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.387 y[1] (closed_form) = -0.0016242773645811695391778962987541 y[1] (numeric) = -0.0016242773645811693889105686844627 absolute error = 1.5026732761429136717273935995880e-19 relative error = 9.2513342173575615213655948310924e-15 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.386 y[1] (closed_form) = -0.0016220314061796726330591845687937 y[1] (numeric) = -0.0016220314061796724827152325669266 absolute error = 1.5034395200186708476364647076258e-19 relative error = 9.2688681260474598570623176438865e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.385 y[1] (closed_form) = -0.0016197891734480688842051844230599 y[1] (numeric) = -0.0016197891734480687337848409209451 absolute error = 1.5042034350211487679207708869091e-19 relative error = 9.2864149216353195781017830539338e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.384 y[1] (closed_form) = -0.0016175506591780432196396891714518 y[1] (numeric) = -0.0016175506591780430691431862844598 absolute error = 1.5049650288699199778758961865604e-19 relative error = 9.3039746256520119169645776581455e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.383 y[1] (closed_form) = -0.0016153158561772149425567765799775 y[1] (numeric) = -0.0016153158561772147919843456542931 absolute error = 1.5057243092568440714247166816983e-19 relative error = 9.3215472596193739412494452221851e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.382 y[1] (closed_form) = -0.0016130847572690981164785413363723 y[1] (numeric) = -0.0016130847572690979658304129517548 absolute error = 1.5064812838461748028510797045778e-19 relative error = 9.3391328450502523534570186877723e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.381 y[1] (closed_form) = -0.0016108573552930620588186026431858 y[1] (numeric) = -0.0016108573552930619080950066157191 absolute error = 1.5072359602746667550937205157043e-19 relative error = 9.3567314034485471756932199413659e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (closed_form) = -0.0016086336431042919435191221236229 y[1] (numeric) = -0.0016086336431042917927202875084547 absolute error = 1.5079883461516815665580935388134e-19 relative error = 9.3743429563092553196418820757665e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.379 y[1] (closed_form) = -0.0016064136135737495124301677433502 y[1] (numeric) = -0.0016064136135737493615563228374209 absolute error = 1.5087384490592937183946149894807e-19 relative error = 9.3919675251185140421549909046101e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.378 y[1] (closed_form) = -0.0016041972595881338951013560216391 y[1] (numeric) = -0.0016041972595881337441527283663995 absolute error = 1.5094862765523958841826790026742e-19 relative error = 9.4096051313536442868077886726951e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.377 y[1] (closed_form) = -0.0016019845740498425366567974428435 y[1] (numeric) = -0.0016019845740498423856336138269631 absolute error = 1.5102318361588038439507199710710e-19 relative error = 9.4272557964831939117648332265439e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.376 y[1] (closed_form) = -0.0015997755498769322334254586995032 y[1] (numeric) = -0.0015997755498769320823279451615671 absolute error = 1.5109751353793609644535495060635e-19 relative error = 9.4449195419669808043019603535723e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.375 y[1] (closed_form) = -0.0015975701800030802760001402164257 y[1] (numeric) = -0.0015975701800030801248285220476215 absolute error = 1.5117161816880422476191969909787e-19 relative error = 9.4625963892561358823279555488027e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.374 y[1] (closed_form) = -0.0015953684573775456993993483360042 y[1] (numeric) = -0.0015953684573775455481538500827984 absolute error = 1.5124549825320579490685278763653e-19 relative error = 9.4802863597931459832486041093717e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.373 y[1] (closed_form) = -0.001593170374965130640007418603764 y[1] (numeric) = -0.0015931703749651304886882640705684 absolute error = 1.5131915453319567686020034367751e-19 relative error = 9.4979894750118966405146551733500e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.372 y[1] (closed_form) = -0.001590975925746141798969319794631 y[1] (numeric) = -0.0015909759257461416475767320464582 absolute error = 1.5139258774817286145390794350827e-19 relative error = 9.5157057563377147481941060949088e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.371 y[1] (closed_form) = -0.0015887851027163520117176376795532 y[1] (numeric) = -0.0015887851027163518602518390446625 absolute error = 1.5146579863489069437869187931251e-19 relative error = 9.5334352251874111139080883669720e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (closed_form) = -0.001586597898886961923310303063699 y[1] (numeric) = -0.0015865978988869617717715151362319 absolute error = 1.5153878792746706795063147166562e-19 relative error = 9.5511779029693229004685151495949e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.369 y[1] (closed_form) = -0.0015844143072845617692586903462403 y[1] (numeric) = -0.0015844143072845616176471339888457 absolute error = 1.5161155635739457082339855399104e-19 relative error = 9.5689338110833559565545333218903e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.368 y[1] (closed_form) = -0.0015822343209510932615267707724068 y[1] (numeric) = -0.0015822343209510931098426661188562 absolute error = 1.5168410465355059583117106133271e-19 relative error = 9.5867029709210270367637098319167e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.367 y[1] (closed_form) = -0.001580057932943811579383058685689 y[1] (numeric) = -0.0015800579329438114276266251434816 absolute error = 1.5175643354220740614641276313161e-19 relative error = 9.6044854038655059113727729571566e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.366 y[1] (closed_form) = -0.001577885136335247464788139456343 y[1] (numeric) = -0.0015778851363352473129595957093008 absolute error = 1.5182854374704215993584056607155e-19 relative error = 9.6222811312916573661416238927065e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.365 y[1] (closed_form) = -0.001575715924213169422001614376219 y[1] (numeric) = -0.0015757159242131692701011783870721 absolute error = 1.5190043598914689369704445613898e-19 relative error = 9.6400901745660830924932328398176e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.364 y[1] (closed_form) = -0.0015735502896805460210933406838426 y[1] (numeric) = -0.0015735502896805458691212296968041 absolute error = 1.5197211098703846445737302660658e-19 relative error = 9.6579125550471634684009364587404e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.363 y[1] (closed_form) = -0.0015713882258555083050448840320121 y[1] (numeric) = -0.0015713882258555081530013145753437 absolute error = 1.5204356945666845101584962860560e-19 relative error = 9.6757482940850992303135601618146e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.362 y[1] (closed_form) = -0.0015692297258713123001281361472714 y[1] (numeric) = -0.0015692297258713121480133240358384 absolute error = 1.5211481211143301440804046132135e-19 relative error = 9.6935974130219530364476992403077e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.361 y[1] (closed_form) = -0.0015670747828763016292490821707338 y[1] (numeric) = -0.0015670747828763014770632425085511 absolute error = 1.5218583966218271777295636777811e-19 relative error = 9.7114599331916909217754072266353e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (closed_form) = -0.001564923390033870227945730227095 y[1] (numeric) = -0.0015649233900338700756890774098627 absolute error = 1.5225665281723230580023469793841e-19 relative error = 9.7293358759202236450344581773270e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.359 y[1] (closed_form) = -0.0015627755405224251627302401574211 y[1] (numeric) = -0.0015627755405224250104029878750506 absolute error = 1.5232725228237044393501632181392e-19 relative error = 9.7472252625254479280872717065390e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.358 y[1] (closed_form) = -0.0015606312275353495514663090855353 y[1] (numeric) = -0.0015606312275353493990686703246658 absolute error = 1.5239763876086941751710569997418e-19 relative error = 9.7651281143172875879535155902317e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.357 y[1] (closed_form) = -0.0015584904442809655854738885815853 y[1] (numeric) = -0.0015584904442809654330060756280905 absolute error = 1.5246781295349479103017882586751e-19 relative error = 9.7830444525977345618403305825353e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.356 y[1] (closed_form) = -0.0015563531839824976530543216536329 y[1] (numeric) = -0.0015563531839824975005165460951179 absolute error = 1.5253777555851502763598482247424e-19 relative error = 9.8009742986608898254930557236305e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.355 y[1] (closed_form) = -0.0015542194398780355641299976527919 y[1] (numeric) = -0.0015542194398780354115224703810808 absolute error = 1.5260752727171106916767198385182e-19 relative error = 9.8189176737930042051882698579960e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.354 y[1] (closed_form) = -0.001552089205220497875693629433407 y[1] (numeric) = -0.0015520892052204977230165606470211 absolute error = 1.5267706878638587675555807907602e-19 relative error = 9.8368745992725190836899063085503e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.353 y[1] (closed_form) = -0.0015499624732775953177632597808333 y[1] (numeric) = -0.0015499624732775951650168589874594 absolute error = 1.5274640079337393225785776101812e-19 relative error = 9.8548450963701070004881426514936e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.352 y[1] (closed_form) = -0.0015478392373317943195401032192785 y[1] (numeric) = -0.0015478392373317941667245792382278 absolute error = 1.5281552398105070066807692452669e-19 relative error = 9.8728291863487121466397162940726e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.351 y[1] (closed_form) = -0.00154571949068028063546732485462 y[1] (numeric) = -0.001545719490680280482582885819278 absolute error = 1.5288443903534205366998481721928e-19 relative error = 9.8908268904635907545272690586315e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (closed_form) = -0.0015436032266349230708888499057254 y[1] (numeric) = -0.0015436032266349229179357032659917 absolute error = 1.5295314663973365451027960066124e-19 relative error = 9.9088382299623513828542802068186e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.349 y[1] (closed_form) = -0.0015414904385222373070082860461843 y[1] (numeric) = -0.001541490438522237153986638570904 absolute error = 1.5302164747528030435827186975822e-19 relative error = 9.9268632260849950971911072834042e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.348 y[1] (closed_form) = -0.0015393811196833498248490256300212 y[1] (numeric) = -0.0015393811196833496717590834094059 absolute error = 1.5308994222061525032112334336751e-19 relative error = 9.9449019000639555463866178055829e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.347 y[1] (closed_form) = -0.0015372752634739619279175763233681 y[1] (numeric) = -0.0015372752634739617747595447714086 absolute error = 1.5315803155195945528239451920490e-19 relative error = 9.9629542731241389351588621567176e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.346 y[1] (closed_form) = -0.0015351728632643138632731466226642 y[1] (numeric) = -0.0015351728632643137100472304795333 absolute error = 1.5322591614313082973087552096397e-19 relative error = 9.9810203664829638931772090490988e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.345 y[1] (closed_form) = -0.0015330739124391490407074872220527 y[1] (numeric) = -0.0015330739124391488874138905564993 absolute error = 1.5329359666555342574589863515704e-19 relative error = 9.9991002013504012409473395843989e-15 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 17 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.344 y[1] (closed_form) = -0.001530978404397678349739960211595 y[1] (numeric) = -0.0015309784043976781963788864233284 absolute error = 1.5336107378826659330455911962612e-19 relative error = 1.0017193798929013652809474249070e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.343 y[1] (closed_form) = -0.001528886332553544574133775656945 y[1] (numeric) = -0.0015288863325535444207054274790109 absolute error = 1.5342834817793409907550274516043e-19 relative error = 1.0035301180413995217359189121040e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.342 y[1] (closed_form) = -0.0015267976903347869036402992434387 y[1] (numeric) = -0.0015267976903347867501448787445855 absolute error = 1.5349542049885320786317418650560e-19 relative error = 1.0053422366993210895599163119798e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.341 y[1] (closed_form) = -0.0015247124711838055426792953762835 y[1] (numeric) = -0.0015247124711838053891170039633197 absolute error = 1.5356229141296372686565978967650e-19 relative error = 1.0071557379847235877129187290518e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (closed_form) = -0.0015226306685573264156639274267743 y[1] (numeric) = -0.0015226306685573262620349658469173 absolute error = 1.5362896157985701290850138941592e-19 relative error = 1.0089706240149394834680759860427e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.339 y[1] (closed_form) = -0.0015205522759263659686802907152544 y[1] (numeric) = -0.0015205522759263658149848590584695 absolute error = 1.5369543165678494281610471450732e-19 relative error = 1.0107868969065801077301587128531e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.338 y[1] (closed_form) = -0.0015184772867761960672322043378541 y[1] (numeric) = -0.0015184772867761959134705020391853 absolute error = 1.5376170229866884708161648018711e-19 relative error = 1.0126045587755395602494310134343e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.337 y[1] (closed_form) = -0.0015164056946063089897629350888139 y[1] (numeric) = -0.0015164056946063088359351609307055 absolute error = 1.5382777415810840699539850695458e-19 relative error = 1.0144236117369986047612780483816e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.336 y[1] (closed_form) = -0.0015143374929303825166664705163057 y[1] (numeric) = -0.0015143374929303823627728226309152 absolute error = 1.5389364788539051539148510459081e-19 relative error = 1.0162440579054285540818215677766e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.335 y[1] (closed_form) = -0.0015122726752762451145018985899217 y[1] (numeric) = -0.0015122726752762449605425744614236 absolute error = 1.5395932412849810117067150022226e-19 relative error = 1.0180658993945951451896574776122e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.334 y[1] (closed_form) = -0.0015102112351858412151253885651889 y[1] (numeric) = -0.00151021123518584106110058503207 absolute error = 1.5402480353311891775814625095563e-19 relative error = 1.0198891383175624043237509226933e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop memory used=561.2MB, alloc=44.3MB, time=8.30 x[1] = 2.333 y[1] (closed_form) = -0.0015081531662151965894552014172917 y[1] (numeric) = -0.0015081531662151964353651146746374 absolute error = 1.5409008674265429565284934622153e-19 relative error = 1.0217137767866965021274261178851e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.332 y[1] (closed_form) = -0.0015060984619343838155860886953255 y[1] (numeric) = -0.0015060984619343836614309142970976 absolute error = 1.5415517439822785922501005385745e-19 relative error = 1.0235398169136695988682902566393e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.331 y[1] (closed_form) = -0.0015040471159274878409703658324611 y[1] (numeric) = -0.0015040471159274876867502986937669 absolute error = 1.5422006713869420791759447859198e-19 relative error = 1.0253672608094636797638332695472e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (closed_form) = -0.0015019991217925716383838698489519 y[1] (numeric) = -0.0015019991217925714840991042483043 absolute error = 1.5428476560064756200667226352654e-19 relative error = 1.0271961105843743804423479949154e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.329 y[1] (closed_form) = -0.0014999544731416419553959320164584 y[1] (numeric) = -0.001499954473141641801046661598028 absolute error = 1.5434927041843037307499485610610e-19 relative error = 1.0290263683480148025687184567283e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.328 y[1] (closed_form) = -0.0014979131636006151570634134261721 y[1] (numeric) = -0.0014979131636006150026498312020302 absolute error = 1.5441358222414189935236426169028e-19 relative error = 1.0308580362093193196645274215313e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.327 y[1] (closed_form) = -0.0014958751868092831615697655320922 y[1] (numeric) = -0.0014958751868092830070920638844454 absolute error = 1.5447770164764674607566120203905e-19 relative error = 1.0326911162765473731518382234384e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.326 y[1] (closed_form) = -0.0014938405364212794685309886369121 y[1] (numeric) = -0.0014938405364212793139893593203287 absolute error = 1.5454162931658337102069506477325e-19 relative error = 1.0345256106572872586499100043378e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.325 y[1] (closed_form) = -0.0014918092061040452796912689636089 y[1] (numeric) = -0.0014918092061040451250859031072364 absolute error = 1.5460536585637255535733495521504e-19 relative error = 1.0363615214584599025540100131384e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.324 y[1] (closed_form) = -0.0014897811895387957117319794232607 y[1] (numeric) = -0.0014897811895387955570630675330349 absolute error = 1.5466891189022583997868152611315e-19 relative error = 1.0381988507863226289253914422836e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.323 y[1] (closed_form) = -0.0014877564804204861009186304610533 y[1] (numeric) = -0.0014877564804204859461863624218994 absolute error = 1.5473226803915392745434304586202e-19 relative error = 1.0400376007464729167214104504696e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.322 y[1] (closed_form) = -0.0014857350724577783993112554500341 y[1] (numeric) = -0.0014857350724577782445158205280591 absolute error = 1.5479543492197504975718635428212e-19 relative error = 1.0418777734438521473946615262646e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.321 y[1] (closed_form) = -0.0014837169593730076622646100180387 y[1] (numeric) = -0.0014837169593730075074061968627154 absolute error = 1.5485841315532330191224392928339e-19 relative error = 1.0437193709827493428899161868564e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (closed_form) = -0.0014817021349021486269454564494155 y[1] (numeric) = -0.0014817021349021484720242530957585 absolute error = 1.5492120335365694171577223032434e-19 relative error = 1.0455623954668048940675561781906e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.319 y[1] (closed_form) = -0.0014796905927947823815950929117118 y[1] (numeric) = -0.0014796905927947822266112867824451 absolute error = 1.5498380612926665567177377813969e-19 relative error = 1.0474068489990142795820988460403e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.318 y[1] (closed_form) = -0.0014776823268140631252661727303316 y[1] (numeric) = -0.0014776823268140629702199506380478 absolute error = 1.5504622209228379129261605746716e-19 relative error = 1.0492527336817317752443191808010e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.317 y[1] (closed_form) = -0.0014756773307366850177637412832299 y[1] (numeric) = -0.0014756773307366848626552894325414 absolute error = 1.5510845185068855590970427328075e-19 relative error = 1.0511000516166741538953802007902e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.316 y[1] (closed_form) = -0.0014736755983528491195212973248544 y[1] (numeric) = -0.0014736755983528489643508013145363 absolute error = 1.5517049601031818213949223424916e-19 relative error = 1.0529488049049243758212908282925e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.315 y[1] (closed_form) = -0.0014716771234662304211435616855786 y[1] (numeric) = -0.0014716771234662302659112065107035 absolute error = 1.5523235517487506014944616278990e-19 relative error = 1.0547989956469352697359182282870e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.314 y[1] (closed_form) = -0.0014696818998939449623485093415759 y[1] (numeric) = -0.0014696818998939448070544793956411 absolute error = 1.5529402994593483686791002228319e-19 relative error = 1.0566506259425332043606897204855e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.313 y[1] (closed_form) = -0.0014676899214665170400420908221742 y[1] (numeric) = -0.0014676899214665168846865698992197 absolute error = 1.5535552092295448228115799193476e-19 relative error = 1.0585036978909217506290278397666e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.312 y[1] (closed_form) = -0.0014657011820278465052599358288746 y[1] (numeric) = -0.0014657011820278463498431071255943 absolute error = 1.5541682870328032296025999171604e-19 relative error = 1.0603582135906853345434709070767e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.311 y[1] (closed_form) = -0.0014637156754351761487111957940556 y[1] (numeric) = -0.0014637156754351759932332419118996 absolute error = 1.5547795388215604295972964713640e-19 relative error = 1.0622141751397928807133405811697e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (closed_form) = -0.0014617333955590591746605429194726 y[1] (numeric) = -0.0014617333955590590191216458667419 absolute error = 1.5553889705273065222927076977761e-19 relative error = 1.0640715846356014466007272899470e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.309 y[1] (closed_form) = -0.0014597543362833267628852010165539 y[1] (numeric) = -0.0014597543362833266072855422104875 absolute error = 1.5559965880606642267928829809815e-19 relative error = 1.0659304441748598475024741874276e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.308 y[1] (closed_form) = -0.0014577784915050557184447382336585 y[1] (numeric) = -0.0014577784915050555627844985025117 absolute error = 1.5566023973114679204018267763476e-19 relative error = 1.0677907558537122722957503473157e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.307 y[1] (closed_form) = -0.0014558058551345362090022035113395 y[1] (numeric) = -0.0014558058551345360532815630964552 absolute error = 1.5572064041488423565480284412180e-19 relative error = 1.0696525217677018899747142855375e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.306 y[1] (closed_form) = -0.0014538364210952395894360373666464 y[1] (numeric) = -0.0014538364210952394336551759245183 absolute error = 1.5578086144212810634279229103143e-19 relative error = 1.0715157440117744470056796007876e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.305 y[1] (closed_form) = -0.0014518701833237863134830333829356 y[1] (numeric) = -0.0014518701833237861576421299872631 absolute error = 1.5584090339567244247492513851610e-19 relative error = 1.0733804246802818555281055328681e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.304 y[1] (closed_form) = -0.0014499071357699139321534695838475 y[1] (numeric) = -0.0014499071357699137762527027275838 absolute error = 1.5590076685626374439489465770066e-19 relative error = 1.0752465658669857724286465622303e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.303 y[1] (closed_form) = -0.0014479472723964451786603687103015 y[1] (numeric) = -0.0014479472723964450226999163076928 absolute error = 1.5596045240260871932538532680337e-19 relative error = 1.0771141696650611693154068094507e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.302 y[1] (closed_form) = -0.0014459905871792561396056833087613 y[1] (numeric) = -0.0014459905871792559835857226973793 absolute error = 1.5601996061138199489463118782783e-19 relative error = 1.0789832381670998934194569392212e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.301 y[1] (closed_form) = -0.001444037074107244512167035488803 y[1] (numeric) = -0.0014440370741072443560877434315692 absolute error = 1.5607929205723380141903801881213e-19 relative error = 1.0808537734651142194505835286170e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (closed_form) = -0.0014420867271822979470294722292816 y[1] (numeric) = -0.001442086727182297790891024916484 absolute error = 1.5613844731279762307682462118123e-19 relative error = 1.0827257776505403924341534227733e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.299 y[1] (closed_form) = -0.0014401395404192624768075252162216 y[1] (numeric) = -0.0014401395404192623206100982675237 absolute error = 1.5619742694869781810701932904533e-19 relative error = 1.0845992528142421615558884714694e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.298 y[1] (closed_form) = -0.0014381955078459110297036893929762 y[1] (numeric) = -0.001438195507845910873447457859419 absolute error = 1.5625623153355720816753166182295e-19 relative error = 1.0864742010465143050412592163452e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.297 y[1] (closed_form) = -0.0014362546235029120281502567051883 y[1] (numeric) = -0.0014362546235029118718353950711836 absolute error = 1.5631486163400463698540584793096e-19 relative error = 1.0883506244370861460961195793820e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.296 y[1] (closed_form) = -0.0014343168814437980721822609405825 y[1] (numeric) = -0.0014343168814437979158089431259 absolute error = 1.5637331781468249843175273014566e-19 relative error = 1.0902285250751250599351183877396e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.295 y[1] (closed_form) = -0.0014323822757349347072901061075249 y[1] (numeric) = -0.0014323822757349345508585054692706 absolute error = 1.5643160063825423415324930735147e-19 relative error = 1.0921079050492399719243376568904e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.294 y[1] (closed_form) = -0.0014304508004554892765012644774342 y[1] (numeric) = -0.0014304508004554891200115538120224 absolute error = 1.5648971066541180089149085759336e-19 relative error = 1.0939887664474848468645219420913e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.293 y[1] (closed_form) = -0.0014285224496973998564412412453484 y[1] (numeric) = -0.0014285224496973996998935927904653 absolute error = 1.5654764845488310762087920855240e-19 relative error = 1.0958711113573621694411777564576e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.292 y[1] (closed_form) = -0.0014265972175653442771248107509772 y[1] (numeric) = -0.0014265972175653441205193961875378 absolute error = 1.5660541456343942263513225876919e-19 relative error = 1.0977549418658264158677370411009e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.291 y[1] (closed_form) = -0.0014246750981767092252293343601478 y[1] (numeric) = -0.001424675098176709068566324814245 absolute error = 1.5666300954590275071190429122668e-19 relative error = 1.0996402600592875167478939578522e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (closed_form) = -0.0014227560856615594306027724443357 y[1] (numeric) = -0.0014227560856615592738823384891825 absolute error = 1.5672043395515318048441394543200e-19 relative error = 1.1015270680236143111831398568781e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.289 y[1] (closed_form) = -0.0014208401741626069357598024246049 y[1] (numeric) = -0.0014208401741626067789821140824687 absolute error = 1.5677768834213620214838691014482e-19 relative error = 1.1034153678441379921514371488999e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.288 y[1] (closed_form) = -0.00141892735783518044812025157635 y[1] (numeric) = -0.00141892735783518029128547832048 absolute error = 1.5683477325586999563203345170770e-19 relative error = 1.1053051616056555431828889836232e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.287 y[1] (closed_form) = -0.0014170176308471947747448472332839 y[1] (numeric) = -0.0014170176308471946178531579898312 absolute error = 1.5689168924345268935619678793849e-19 relative error = 1.1071964513924331663581781012708e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.286 y[1] (closed_form) = -0.0014151109873791203393240781936488 y[1] (numeric) = -0.0014151109873791201823756413435793 absolute error = 1.5694843685006958971122704022322e-19 relative error = 1.1090892392882097016554649816832e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.285 y[1] (closed_form) = -0.0014132074216239527811767495291126 y[1] (numeric) = -0.0014132074216239526241717329101122 absolute error = 1.5700501661900038137655703235461e-19 relative error = 1.1109835273762000376713524641993e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.284 y[1] (closed_form) = -0.0014113069277871826360155986376595 y[1] (numeric) = -0.0014113069277871824789541695460332 absolute error = 1.5706142909162629860838053942809e-19 relative error = 1.1128793177390985137414413503648e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.283 y[1] (closed_form) = -0.0014094095000867650982381232763806 y[1] (numeric) = -0.0014094095000867649411204484689433 absolute error = 1.5711767480743726762026070944391e-19 relative error = 1.1147766124590823134859191293433e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.282 y[1] (closed_form) = -0.0014075151327530898645015524687373 y[1] (numeric) = -0.0014075151327530897073277981646983 absolute error = 1.5717375430403902018092626995630e-19 relative error = 1.1166754136178148498055418816397e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.281 y[1] (closed_form) = -0.0014056238200289510583416686139181 y[1] (numeric) = -0.0014056238200289509011120004967579 absolute error = 1.5722966811716017855294577802177e-19 relative error = 1.1185757232964491413532876192943e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (closed_form) = -0.0014037355561695172355959638435772 y[1] (numeric) = -0.0014037355561695170783105470629179 absolute error = 1.5728541678065931189540555976635e-19 relative error = 1.1204775435756311805068778090087e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.279 y[1] (closed_form) = -0.0014018503354423014703923856837489 y[1] (numeric) = -0.0014018503354423013130513848572169 absolute error = 1.5734100082653196425315510213057e-19 relative error = 1.1223808765355032928672825976209e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.278 y[1] (closed_form) = -0.001399968152127131521465696397242 y[1] (numeric) = -0.0013999681521271313640692756123244 absolute error = 1.5739642078491765425462448984923e-19 relative error = 1.1242857242557074883082443159150e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop memory used=607.8MB, alloc=44.3MB, time=8.98 x[1] = 2.277 y[1] (closed_form) = -0.0013980890005161200785642370144647 y[1] (numeric) = -0.0013980890005161199211125598303579 absolute error = 1.5745167718410684663966201164577e-19 relative error = 1.1261920888153888036017731758389e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.276 y[1] (closed_form) = -0.0013962128749136350887106510184959 y[1] (numeric) = -0.001396212874913634931203880467948 absolute error = 1.5750677055054789573828627720411e-19 relative error = 1.1280999722931986366444886967670e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.275 y[1] (closed_form) = -0.0013943397696362701620808839433593 y[1] (numeric) = -0.0013943397696362700045191825345053 absolute error = 1.5756170140885396102069607703826e-19 relative error = 1.1300093767672980723096002974193e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.274 y[1] (closed_form) = -0.0013924696790128150572665337828683 y[1] (numeric) = -0.0013924696790128148996500635010584 absolute error = 1.5761647028180989483833276729466e-19 relative error = 1.1319203043153611999492406703809e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.273 y[1] (closed_form) = -0.0013906025973842262456863831010701 y[1] (numeric) = -0.001390602597384226088015305410691 absolute error = 1.5767107769037910247524415725382e-19 relative error = 1.1338327570145784225717860148085e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.272 y[1] (closed_form) = -0.0013887385191035975549136970941451 y[1] (numeric) = -0.0013887385191035973971881729404347 absolute error = 1.5772552415371037462845570537630e-19 relative error = 1.1357467369416597577187179388194e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.271 y[1] (closed_form) = -0.0013868774385361308906866225875032 y[1] (numeric) = -0.0013868774385361307329068123983585 absolute error = 1.5777981018914469243551427676597e-19 relative error = 1.1376622461728381300655028551916e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (closed_form) = -0.0013850193500591070373697710706107 y[1] (numeric) = -0.0013850193500591068795358347583887 absolute error = 1.5783393631222200516683176757627e-19 relative error = 1.1395792867838726557708859813222e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.269 y[1] (closed_form) = -0.0013831642480618565366358143855807 y[1] (numeric) = -0.0013831642480618563787479113488927 absolute error = 1.5788790303668798069992054690774e-19 relative error = 1.1414978608500519185989186158712e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.268 y[1] (closed_form) = -0.0013813121269457306441366646035442 y[1] (numeric) = -0.0013813121269457304861949537290434 absolute error = 1.5794171087450072889207989095480e-19 relative error = 1.1434179704461972378379591991218e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.267 y[1] (closed_form) = -0.0013794629811240723639345499550081 y[1] (numeric) = -0.0013794629811240722059391896191706 absolute error = 1.5799536033583749796756237444424e-19 relative error = 1.1453396176466659280408107707952e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.266 y[1] (closed_form) = -0.0013776168050221875604640364364963 y[1] (numeric) = -0.0013776168050221874024151845073949 absolute error = 1.5804885192910134403472152772401e-19 relative error = 1.1472628045253545506100798168548e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.265 y[1] (closed_form) = -0.0013757735930773161477967799054063 y[1] (numeric) = -0.0013757735930773159896945937444786 absolute error = 1.5810218616092777384811695123660e-19 relative error = 1.1491875331557021572527641446929e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.264 y[1] (closed_form) = -0.0013739333397386033559815261078181 y[1] (numeric) = -0.0013739333397386031978261625716267 absolute error = 1.5815536353619136093003048964307e-19 relative error = 1.1511138056106935253280003430137e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.263 y[1] (closed_form) = -0.0013720960394670710742326061695208 y[1] (numeric) = -0.0013720960394670709160242216115085 absolute error = 1.5820838455801233516532699271711e-19 relative error = 1.1530416239628623851118245676932e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.262 y[1] (closed_form) = -0.0013702616867355892707409026283351 y[1] (numeric) = -0.001370261686735589112479652900572 absolute error = 1.5826124972776314598307561653803e-19 relative error = 1.1549709902842946390027238469098e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.261 y[1] (closed_form) = -0.0013684302760288474888819861053758 y[1] (numeric) = -0.0013684302760288473305680265603008 absolute error = 1.5831395954507499923783253377924e-19 relative error = 1.1569019066466315726916788168999e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (closed_form) = -0.001366601801843326419596845213703 y[1] (numeric) = -0.0013666018018433262612303307058586 absolute error = 1.5836651450784436790297331338547e-19 relative error = 1.1588343751210730583203227828020e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.259 y[1] (closed_form) = -0.001364776258687269549721352294253 y[1] (numeric) = -0.0013647762586872693913024371820136 absolute error = 1.5841891511223947668795308509494e-19 relative error = 1.1607683977783807496507662462229e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.258 y[1] (closed_form) = -0.0013629536410806548860413250604209 y[1] (numeric) = -0.0013629536410806547275701632077141 absolute error = 1.5847116185270676069086491059699e-19 relative error = 1.1627039766888812692705605513997e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.257 y[1] (closed_form) = -0.0013611339435551667548507592335142 y[1] (numeric) = -0.0013611339435551665963275040115369 absolute error = 1.5852325522197729819716152819265e-19 relative error = 1.1646411139224693878561990741613e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.256 y[1] (closed_form) = -0.0013593171606541676767915197708419 y[1] (numeric) = -0.0013593171606541675182163240597687 absolute error = 1.5857519571107321773490280928326e-19 relative error = 1.1665798115486111955184794113296e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.255 y[1] (closed_form) = -0.0013575032869326703167534883356888 y[1] (numeric) = -0.0013575032869326701581265045263747 absolute error = 1.5862698380931407949639085055440e-19 relative error = 1.1685200716363472652529753217692e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.254 y[1] (closed_form) = -0.0013556923169573095086148722431132 y[1] (numeric) = -0.00135569231695730934993625223879 absolute error = 1.5867862000432323123555661311745e-19 relative error = 1.1704618962542958085187927230285e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.253 y[1] (closed_form) = -0.0013538842453063143546030852465718 y[1] (numeric) = -0.0013538842453063141958729804645377 absolute error = 1.5873010478203413874996639695544e-19 relative error = 1.1724052874706558229687098584333e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.252 y[1] (closed_form) = -0.0013520790665694803990573132169903 y[1] (numeric) = -0.0013520790665694802402758745902936 absolute error = 1.5878143862669669105582319369084e-19 relative error = 1.1743502473532102323537278176508e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.251 y[1] (closed_form) = -0.0013502767753481418763745780171861 y[1] (numeric) = -0.0013502767753481417175419559963026 absolute error = 1.5883262202088348036384708091588e-19 relative error = 1.1762967779693290186249839181596e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (closed_form) = -0.0013484773662551440329218106995885 y[1] (numeric) = -0.0013484773662551438740381552540924 absolute error = 1.5888365544549605696343029512816e-19 relative error = 1.1782448813859723462559070347944e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.249 y[1] (closed_form) = -0.0013466808339148155226971405630536 y[1] (numeric) = -0.0013466808339148153637626011832824 absolute error = 1.5893453937977115912197643578771e-19 relative error = 1.1801945596696936788074207986280e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.248 y[1] (closed_form) = -0.0013448871729629408765242996042421 y[1] (numeric) = -0.0013448871729629407175390253029552 absolute error = 1.5898527430128691810584939831152e-19 relative error = 1.1821458148866428877589276739536e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.247 y[1] (closed_form) = -0.0013430963780467330445647324995023 y[1] (numeric) = -0.0013430963780467328855288718135332 absolute error = 1.5903586068596903842887609716567e-19 relative error = 1.1840986491025693536277342621019e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.246 y[1] (closed_form) = -0.0013413084438248060119326904634156 y[1] (numeric) = -0.0013413084438248058528463914553187 absolute error = 1.5908629900809695343386780988499e-19 relative error = 1.1860530643828250593995057723207e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.245 y[1] (closed_form) = -0.0013395233649671474871992731590314 y[1] (numeric) = -0.0013395233649671473280626834187215 absolute error = 1.5913658974030995631214803718876e-19 relative error = 1.1880090627923676762922654420240e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.244 y[1] (closed_form) = -0.0013377411361550916635720662912041 y[1] (numeric) = -0.0013377411361550915043853329375908 absolute error = 1.5918673335361330666560012177298e-19 relative error = 1.1899666463957636418763827804545e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.243 y[1] (closed_form) = -0.0013359617520812920525377036071951 y[1] (numeric) = -0.0013359617520812918933009732898108 absolute error = 1.5923673031738431271527548731337e-19 relative error = 1.1919258172571912305729228502612e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.242 y[1] (closed_form) = -0.001334185207449694389755360766608 y[1] (numeric) = -0.0013341852074496942304687796672296 absolute error = 1.5928658109937838926013323823537e-19 relative error = 1.1938865774404436165526573897478e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.241 y[1] (closed_form) = -0.0013324114969755096129898649345525 y[1] (numeric) = -0.0013324114969755094536535787688174 absolute error = 1.5933628616573509148901398848795e-19 relative error = 1.1958489290089319290579674136808e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (closed_form) = -0.0013306406153851869118737780064251 y[1] (numeric) = -0.0013306406153851867524879320254409 absolute error = 1.5938584598098412474848515254690e-19 relative error = 1.1978128740256883001697960116311e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.239 y[1] (closed_form) = -0.0013288725574163868492884830985238 y[1] (numeric) = -0.0013288725574163866898532220904724 absolute error = 1.5943526100805133036873152287994e-19 relative error = 1.1997784145533689050417393889505e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.238 y[1] (closed_form) = -0.0013271073178179545541549733445697 y[1] (numeric) = -0.0013271073178179543946704416363051 absolute error = 1.5948453170826464764920376390118e-19 relative error = 1.2017455526542569946232937657420e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.237 y[1] (closed_form) = -0.0013253448913498929854257091326939 y[1] (numeric) = -0.0013253448913498928258920505913338 absolute error = 1.5953365854136005210527846185538e-19 relative error = 1.2037142903902659208942055626599e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.236 y[1] (closed_form) = -0.0013235852727833362670695747091687 y[1] (numeric) = -0.0013235852727833361074869327436812 absolute error = 1.5958264196548747007672657199251e-19 relative error = 1.2056846298229421546318023581708e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.235 y[1] (closed_form) = -0.001321828456900523093842627572675 y[1] (numeric) = -0.0013218284569005229342111451354584 absolute error = 1.5963148243721666979833248776753e-19 relative error = 1.2076565730134682957331123991182e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.234 y[1] (closed_form) = -0.0013200744384947702076379942947182 y[1] (numeric) = -0.0013200744384947700479578138831751 absolute error = 1.5968018041154312903255351063672e-19 relative error = 1.2096301220226660761135109841638e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.233 y[1] (closed_form) = -0.0013183232123704459442089243364361 y[1] (numeric) = -0.0013183232123704457844801879945422 absolute error = 1.5972873634189387936365921238382e-19 relative error = 1.2116052789109993552035628170351e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.232 y[1] (closed_form) = -0.0013165747733429438500596690979316 y[1] (numeric) = -0.0013165747733429436902825184177982 absolute error = 1.5977715068013332725234204392065e-19 relative error = 1.2135820457385771080656604425987e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.231 y[1] (closed_form) = -0.0013148291162386563692995068418337 y[1] (numeric) = -0.0013148291162386562094740829652646 absolute error = 1.5982542387656905194934454434769e-19 relative error = 1.2155604245651564061519901327224e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (closed_form) = -0.0013130862358949486002558852864376 y[1] (numeric) = -0.00131308623589494844038232890648 absolute error = 1.5987355637995758036620463096830e-19 relative error = 1.2175404174501453907252880797950e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.229 y[1] (closed_form) = -0.0013113461271601321216433025738476 y[1] (numeric) = -0.0013113461271601319617217539363374 absolute error = 1.5992154863751013900077869422030e-19 relative error = 1.2195220264526062389637814827657e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.228 y[1] (closed_form) = -0.0013096087848934388880851939933724 y[1] (numeric) = -0.001309608784893438728115792898474 absolute error = 1.5996940109489838301476257047293e-19 relative error = 1.2215052536312581227716410727717e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.227 y[1] (closed_form) = -0.0013078742039649951947867362882886 y[1] (numeric) = -0.0013078742039649950347696220920285 absolute error = 1.6001711419626010255999290974260e-19 relative error = 1.2234901010444801603162038219656e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.226 y[1] (closed_form) = -0.0013061423792557957111571236032534 y[1] (numeric) = -0.0013061423792557955510924352190484 absolute error = 1.6006468838420490644987598407215e-19 relative error = 1.2254765707503143603131570091662e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.225 y[1] (closed_form) = -0.0013044133056576775831805091483313 y[1] (numeric) = -0.0013044133056576774230683850485114 absolute error = 1.6011212409981988327185758511476e-19 relative error = 1.2274646648064685590808074785735e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.224 y[1] (closed_form) = -0.0013026869780732946043354444720028 y[1] (numeric) = -0.0013026869780732944441760226893275 absolute error = 1.6015942178267524003641632594068e-19 relative error = 1.2294543852703193503844928221493e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.223 y[1] (closed_form) = -0.0013009633914160914548632838577879 y[1] (numeric) = -0.001300963391416091294656701986958 absolute error = 1.6020658187082991845763338187311e-19 relative error = 1.2314457341989150080921243415034e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.222 y[1] (closed_form) = -0.0012992425406102780091866547953935 y[1] (numeric) = -0.0012992425406102778489330499945563 absolute error = 1.6025360480083718895996446794286e-19 relative error = 1.2334387136489784016617850003987e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop memory used=654.5MB, alloc=44.3MB, time=9.66 x[1] = 2.221 y[1] (closed_form) = -0.0012975244205908037112797267356481 y[1] (numeric) = -0.0012975244205908035509792357278979 absolute error = 1.6030049100775022250541464607178e-19 relative error = 1.2354333256769099044822391634329e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (closed_form) = -0.0012958090263033320177926394270087 y[1] (numeric) = -0.0012958090263033318574453985018811 absolute error = 1.6034724092512764033489337314337e-19 relative error = 1.2374295723387902950871447292285e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.219 y[1] (closed_form) = -0.0012940963527042149087330790581218 y[1] (numeric) = -0.0012940963527042147483392240730828 absolute error = 1.6039385498503904171710603154634e-19 relative error = 1.2394274556903836512636923067195e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.218 y[1] (closed_form) = -0.0012923863947604674655086152038045 y[1] (numeric) = -0.001292386394760467305068281585734 absolute error = 1.6044033361807050979791901648194e-19 relative error = 1.2414269777871402370763303500198e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.217 y[1] (closed_form) = -0.0012906791474497425161340341988443 y[1] (numeric) = -0.0012906791474497423556473569455143 absolute error = 1.6048667725333009564271827926560e-19 relative error = 1.2434281406841993828261696600580e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.216 y[1] (closed_form) = -0.0012889746057603053474085250531329 y[1] (numeric) = -0.0012889746057603051868756387346796 absolute error = 1.6053288631845328056386603303402e-19 relative error = 1.2454309464363923579665953788298e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.215 y[1] (closed_form) = -0.001287272764691008483868192380753 y[1] (numeric) = -0.0012872727646910083232892311411446 absolute error = 1.6057896123960841682494710675225e-19 relative error = 1.2474353970982452369955495439209e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.214 y[1] (closed_form) = -0.0012855736192512665333199870526034 y[1] (numeric) = -0.0012855736192512663726950846111012 absolute error = 1.6062490244150214681308517531309e-19 relative error = 1.2494414947239817583448824360632e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.213 y[1] (closed_form) = -0.0012838771644610310987637594048127 y[1] (numeric) = -0.0012838771644610309380930490574279 absolute error = 1.6067071034738480077019978800002e-19 relative error = 1.2514492413675261762871063400756e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.212 y[1] (closed_form) = -0.0012821833953507657565097518513687 y[1] (numeric) = -0.0012821833953507655957933664723129 absolute error = 1.6071638537905577317366775486070e-19 relative error = 1.2534586390825061058798209487942e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.211 y[1] (closed_form) = -0.00128049230696142110029945766686 y[1] (numeric) = -0.0012804923069614209395375297099912 absolute error = 1.6076192795686887785644702088008e-19 relative error = 1.2554696899222553609680154696848e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (closed_form) = -0.0012788038943444098512383805317325 y[1] (numeric) = -0.0012788038943444096904310420319948 absolute error = 1.6080733849973768195631765156999e-19 relative error = 1.2574823959398167852643885439493e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.209 y[1] (closed_form) = -0.0012771181525615820333498351757245 y[1] (numeric) = -0.0012771181525615818724972177505837 absolute error = 1.6085261742514081878349296107716e-19 relative error = 1.2594967591879450765277633572683e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.208 y[1] (closed_form) = -0.0012754350766852002145595331228571 y[1] (numeric) = -0.0012754350766852000536617679737298 absolute error = 1.6089776514912727969545412557456e-19 relative error = 1.2615127817191096038596118090547e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.207 y[1] (closed_form) = -0.0012737546617979148129212991411569 y[1] (numeric) = -0.0012737546617979146519785170548352 absolute error = 1.6094278208632168506746383101553e-19 relative error = 1.2635304655854972181386383124279e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.206 y[1] (closed_form) = -0.001272076902992739467894863539831 y[1] (numeric) = -0.0012720769029927393069071948899014 absolute error = 1.6098766864992953444681859581666e-19 relative error = 1.2655498128390150556133107192466e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.205 y[1] (closed_form) = -0.0012704017953730264764872729434676 y[1] (numeric) = -0.0012704017953730263154548476917252 absolute error = 1.6103242525174243597850537626794e-19 relative error = 1.2675708255312933346721630026617e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.204 y[1] (closed_form) = -0.0012687293340524422940700576145894 y[1] (numeric) = -0.0012687293340524421329930053124461 absolute error = 1.6107705230214331518953589606751e-19 relative error = 1.2695935057136881458116316829793e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.203 y[1] (closed_form) = -0.0012670595141549430996848868000589 y[1] (numeric) = -0.0012670595141549429385633365899473 absolute error = 1.6112155021011160321884183201563e-19 relative error = 1.2716178554372842348211255503513e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.202 y[1] (closed_form) = -0.0012653923308147504256510349509508 y[1] (numeric) = -0.0012653923308147502644851155677224 absolute error = 1.6116591938322840457922552629800e-19 relative error = 1.2736438767528977792049660191639e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.201 y[1] (closed_form) = -0.0012637277791763268512885710170206 y[1] (numeric) = -0.001263727779176326690078410789339 absolute error = 1.6121016022768164453747427271114e-19 relative error = 1.2756715717110791578607734431713e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (closed_form) = -0.0012620658543943517605717703532856 y[1] (numeric) = -0.0012620658543943515993174972050144 absolute error = 1.6125427314827119619836143045032e-19 relative error = 1.2777009423621157140338129266451e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.199 y[1] (closed_form) = -0.0012604065516336971635278341048846 y[1] (numeric) = -0.0012604065516336970022295755564706 absolute error = 1.6129825854841398737787464555879e-19 relative error = 1.2797319907560345115667515843029e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.198 y[1] (closed_form) = -0.0012587498660694035811965842647117 y[1] (numeric) = -0.0012587498660694034198544674345626 absolute error = 1.6134211683014908735063029773952e-19 relative error = 1.2817647189426050844642178307552e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.197 y[1] (closed_form) = -0.0012570957928866559939673839336629 y[1] (numeric) = -0.0012570957928866558325815355395201 absolute error = 1.6138584839414277355605392991974e-19 relative error = 1.2837991289713421797914921179009e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.196 y[1] (closed_form) = -0.0012554443272807598531101116630448 y[1] (numeric) = -0.0012554443272807596916806580233512 absolute error = 1.6142945363969357834752885074184e-19 relative error = 1.2858352228915084939265975853354e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.195 y[1] (closed_form) = -0.0012537954644571171553175961300575 y[1] (numeric) = -0.0012537954644571169938446631653202 absolute error = 1.6147293296473731586833931708936e-19 relative error = 1.2878730027521174021849983436383e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.194 y[1] (closed_form) = -0.0012521491996312025800774927975612 y[1] (numeric) = -0.0012521491996312024185612060317091 absolute error = 1.6151628676585208913786069594578e-19 relative error = 1.2899124706019356818360525726238e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.193 y[1] (closed_form) = -0.001250505528028539689692157645813 y[1] (numeric) = -0.0012505055280285395281326422075497 absolute error = 1.6155951543826327743107676347743e-19 relative error = 1.2919536284894862285303072854928e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.192 y[1] (closed_form) = -0.0012488644448846771917656445437247 y[1] (numeric) = -0.0012488644448846770301630251678762 absolute error = 1.6160261937584850403413381542533e-19 relative error = 1.2939964784630507661566614845712e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.191 y[1] (closed_form) = -0.0012472259454451652639775223576457 y[1] (numeric) = -0.0012472259454451651023319233865031 absolute error = 1.6164559897114258445827252792793e-19 relative error = 1.2960410225706725501483645141914e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (closed_form) = -0.0012455900249655319409637754838593 y[1] (numeric) = -0.0012455900249655317792753208685168 absolute error = 1.6168845461534245519411151306439e-19 relative error = 1.2980872628601590642567567005249e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.189 y[1] (closed_form) = -0.0012439566787112595631256171440473 y[1] (numeric) = -0.0012439566787112594013944304457352 absolute error = 1.6173118669831208308789125004160e-19 relative error = 1.3001352013790847108115998560455e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.188 y[1] (closed_form) = -0.0012423259019577612871876085080092 y[1] (numeric) = -0.0012423259019577611254138128994219 absolute error = 1.6177379560858735542092353242591e-19 relative error = 1.3021848401747934944867859170576e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.187 y[1] (closed_form) = -0.0012406976899903576583270385120112 y[1] (numeric) = -0.0012406976899903574965107567786302 absolute error = 1.6181628173338095077312974556833e-19 relative error = 1.3042361812944016995901528756086e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.186 y[1] (closed_form) = -0.0012390720381042532436970791313232 y[1] (numeric) = -0.001239072038104253081838433672736 absolute error = 1.6185864545858719075119116785815e-19 relative error = 1.3062892267848005608960782613802e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.185 y[1] (closed_form) = -0.0012374489416045133271667888488056 y[1] (numeric) = -0.0012374489416045131652659016800188 absolute error = 1.6190088716878687266147606617916e-19 relative error = 1.3083439786926589280394617240844e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.184 y[1] (closed_form) = -0.0012358283958060406651015931448161 y[1] (numeric) = -0.001235828395806040503158585897564 absolute error = 1.6194300724725208320755162149446e-19 relative error = 1.3104004390644259234896497617364e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.183 y[1] (closed_form) = -0.0012342103960335523030084250241959 y[1] (numeric) = -0.0012342103960335521410234189482449 absolute error = 1.6198500607595099329173366645099e-19 relative error = 1.3124586099463335941227973342042e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.182 y[1] (closed_form) = -0.0012325949376215564528702609005917 y[1] (numeric) = -0.0012325949376215562908433768650391 absolute error = 1.6202688403555263399977383492247e-19 relative error = 1.3145184933843995564111029939224e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.181 y[1] (closed_form) = -0.0012309820159143294309953375837906 y[1] (numeric) = -0.0012309820159143292689266960783589 absolute error = 1.6206864150543165384743200518813e-19 relative error = 1.3165800914244296352472962558640e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (closed_form) = -0.00122937162626589265620688466897 y[1] (numeric) = -0.001229371626265892494096605805297 absolute error = 1.6211027886367305736733185570925e-19 relative error = 1.3186434061120204964226982160798e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.179 y[1] (closed_form) = -0.0012277637640399897081997533146541 y[1] (numeric) = -0.0012277637640399895460479568275771 absolute error = 1.6215179648707692511414893699288e-19 relative error = 1.3207084394925622727771189116055e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.178 y[1] (closed_form) = -0.0012261584246100634458908672255422 y[1] (numeric) = -0.0012261584246100632836976724743791 absolute error = 1.6219319475116311516583388664235e-19 relative error = 1.3227751936112411840387975935926e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.177 y[1] (closed_form) = -0.0012245556033592331855909646340497 y[1] (numeric) = -0.0012245556033592330233564906038738 absolute error = 1.6223447403017594619822826925047e-19 relative error = 1.3248436705130421503725349594186e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.176 y[1] (closed_form) = -0.0012229552956802719388256412071371 y[1] (numeric) = -0.0012229552956802717765500065100482 absolute error = 1.6227563469708886221008700019827e-19 relative error = 1.3269138722427513996541094575680e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.175 y[1] (closed_form) = -0.001221357496975583709634243099562 y[1] (numeric) = -0.0012213574969755835473175659759529 absolute error = 1.6231667712360907897517940462828e-19 relative error = 1.3289858008449590684890130405286e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.174 y[1] (closed_form) = -0.0012197622026571808511756968377864 y[1] (numeric) = -0.0012197622026571806888180951576042 absolute error = 1.6235760168018221229780066185600e-19 relative error = 1.3310594583640617969934851951208e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.173 y[1] (closed_form) = -0.0012181694081466614814708983571043 y[1] (numeric) = -0.0012181694081466613190724896211074 absolute error = 1.6239840873599688814768668329730e-19 relative error = 1.3331348468442653173557677258591e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.172 y[1] (closed_form) = -0.0012165791088751869581118173347979 y[1] (numeric) = -0.0012165791088751867956727186758086 absolute error = 1.6243909865898933474998836069758e-19 relative error = 1.3352119683295870361954466044331e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.171 y[1] (closed_form) = -0.0012149913002834594117680049709222 y[1] (numeric) = -0.0012149913002834592492883331550742 absolute error = 1.6247967181584795670562559316311e-19 relative error = 1.3372908248638586107386912264966e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (closed_form) = -0.0012134059778216993383217235722777 y[1] (numeric) = -0.0012134059778216991758015950002598 absolute error = 1.6252012857201789121700754837364e-19 relative error = 1.3393714184907285188271456349642e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.169 y[1] (closed_form) = -0.0012118231369496232494634447008577 y[1] (numeric) = -0.0012118231369496230869029754091521 absolute error = 1.6256046929170554649377322759312e-19 relative error = 1.3414537512536646227781706762430e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.168 y[1] (closed_form) = -0.001210242773136421381579989262102 y[1] (numeric) = -0.0012102427731364212189792949242189 absolute error = 1.6260069433788312241287557792977e-19 relative error = 1.3435378251959567271140806515909e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.167 y[1] (closed_form) = -0.0012086648818607354627681077372105 y[1] (numeric) = -0.0012086648818607353001273036649174 absolute error = 1.6264080407229311350700312100631e-19 relative error = 1.3456236423607191301779628093839e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.166 y[1] (closed_form) = -0.0012070894586106365378068218140707 y[1] (numeric) = -0.001207089458610636375126022958618 absolute error = 1.6268079885545279435500533710221e-19 relative error = 1.3477112047908931696536129948332e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop memory used=701.2MB, alloc=44.3MB, time=10.33 x[1] = 2.165 y[1] (closed_form) = -0.0012055164988836028509223699495279 y[1] (numeric) = -0.0012055164988836026882016909028692 absolute error = 1.6272067904665868744766185028161e-19 relative error = 1.3498005145292497620070659309100e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.164 y[1] (closed_form) = -0.001203945998186497786180118908238 y[1] (numeric) = -0.001203945998186497623419673904247 absolute error = 1.6276044500399101360181079542013e-19 relative error = 1.3518915736183919358671439472533e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.163 y[1] (closed_form) = -0.0012023779520355478653383210766318 y[1] (numeric) = -0.0012023779520355477025382239923136 absolute error = 1.6280009708431812499552860482848e-19 relative error = 1.3539843841007573593623935019601e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.162 y[1] (closed_form) = -0.0012008123559563208029991133509957 y[1] (numeric) = -0.0012008123559563206401594777076948 absolute error = 1.6283963564330092089673182281724e-19 relative error = 1.3560789480186208614317245537205e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.161 y[1] (closed_form) = -0.0011992492054837036188926676527321 y[1] (numeric) = -0.0011992492054837034560136066173349 absolute error = 1.6287906103539724615725143357173e-19 relative error = 1.3581752674140969471260137380940e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (closed_form) = -0.0011976884961618808071309156378601 y[1] (numeric) = -0.0011976884961618806442125420239938 absolute error = 1.6291837361386627254411156366207e-19 relative error = 1.3602733443291423069178783811430e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.159 y[1] (closed_form) = -0.0011961302235443125622677809480984 y[1] (numeric) = -0.0011961302235443123993102072173255 absolute error = 1.6295757373077286297942728799619e-19 relative error = 1.3623731808055583200367746454997e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.158 y[1] (closed_form) = -0.00119457438319371306200336140375 y[1] (numeric) = -0.001194574383193712899006699666758 absolute error = 1.6299666173699191876002061966370e-19 relative error = 1.3644747788849935518465195475568e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.157 y[1] (closed_form) = -0.0011930209706820288063700108703672 y[1] (numeric) = -0.0011930209706820286433343728881545 absolute error = 1.6303563798221270982753959258688e-19 relative error = 1.3665781406089462452822832091956e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.156 y[1] (closed_form) = -0.0011914699815904170132387761480921 y[1] (numeric) = -0.0011914699815904168501642733331489 absolute error = 1.6307450281494318815955264389971e-19 relative error = 1.3686832680187668063640445126284e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.155 y[1] (closed_form) = -0.0011899214115092240699851481408665 y[1] (numeric) = -0.0011899214115092239068718915583523 absolute error = 1.6311325658251428435177926326334e-19 relative error = 1.3707901631556602838034503118815e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.154 y[1] (closed_form) = -0.0011883752560379640411535887686229 y[1] (numeric) = -0.0011883752560379638780016891375387 absolute error = 1.6315189963108418746130809168072e-19 relative error = 1.3728988280606888427209655185283e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.153 y[1] (closed_form) = -0.0011868315107852972319607955952724 y[1] (numeric) = -0.0011868315107852970687703632896298 absolute error = 1.6319043230564260818034531561490e-19 relative error = 1.3750092647747742324901487218434e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.152 y[1] (closed_form) = -0.0011852901713690088074781649649905 y[1] (numeric) = -0.0011852901713690086442493100149754 absolute error = 1.6322885495001502540972930620487e-19 relative error = 1.3771214753387002487258355239434e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.151 y[1] (closed_form) = -0.0011837512334159874673344115750883 y[1] (numeric) = -0.0011837512334159873040672436682214 absolute error = 1.6326716790686691630114199100380e-19 relative error = 1.3792354617931151894329594680562e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (closed_form) = -0.0011822146925622041757797978717813 y[1] (numeric) = -0.0011822146925622040124744263540734 absolute error = 1.6330537151770796983664340987143e-19 relative error = 1.3813512261785343053326883121826e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.149 y[1] (closed_form) = -0.0011806805444526909469539204415161 y[1] (numeric) = -0.0011806805444526907836104543186198 absolute error = 1.6334346612289628401385329040293e-19 relative error = 1.3834687705353422443825014504289e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.148 y[1] (closed_form) = -0.0011791487847415196851994926912693 y[1] (numeric) = -0.0011791487847415195218180406296268 absolute error = 1.6338145206164254670480227457777e-19 relative error = 1.3855880969037954905067825095689e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.147 y[1] (closed_form) = -0.0011776194090917810802650535724309 y[1] (numeric) = -0.0011776194090917809168457239004167 absolute error = 1.6341932967201420025617563020526e-19 relative error = 1.3877092073240247965544495482933e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.146 y[1] (closed_form) = -0.001176092413175563557240020910559 y[1] (numeric) = -0.0011760924131755633937829216196194 absolute error = 1.6345709929093958989837388130663e-19 relative error = 1.3898321038360376115000938604973e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.145 y[1] (closed_form) = -0.0011745677926739322810659950634458 y[1] (numeric) = -0.0011745677926739321175712338092337 absolute error = 1.6349476125421209603051778392123e-19 relative error = 1.3919567884797205019050471312016e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.144 y[1] (closed_form) = -0.0011730455432769082154687041485416 y[1] (numeric) = -0.0011730455432769080519363882520473 absolute error = 1.6353231589649425044822945110552e-19 relative error = 1.3940832632948415676547456136828e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.143 y[1] (closed_form) = -0.001171525660683447236155465963798 y[1] (numeric) = -0.0011715256606834470725857024124762 absolute error = 1.6356976355132183658072718629386e-19 relative error = 1.3962115303210528519887090884631e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.142 y[1] (closed_form) = -0.0011700081406014192981235239793551 y[1] (numeric) = -0.0011700081406014191345164194282471 absolute error = 1.6360710455110797380347871092943e-19 relative error = 1.3983415915978927458394016283685e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.141 y[1] (closed_form) = -0.0011684929787475876569250954071059 y[1] (numeric) = -0.0011684929787475874932807561799588 absolute error = 1.6364433922714718589236596360792e-19 relative error = 1.4004734491647883864961906282729e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (closed_form) = -0.0011669801708475881437354483669233 y[1] (numeric) = -0.0011669801708475879800539804573039 absolute error = 1.6368146790961945368502449719603e-19 relative error = 1.4026071050610580506105701627954e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.139 y[1] (closed_form) = -0.0011654697126359084940708025680838 y[1] (numeric) = -0.0011654697126359083303523116404896 absolute error = 1.6371849092759425201473170081665e-19 relative error = 1.4047425613259135415587645094814e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.138 y[1] (closed_form) = -0.0011639615998558677300033237180177 y[1] (numeric) = -0.0011639615998558675662479151089831 absolute error = 1.6375540860903457098193061859202e-19 relative error = 1.4068798199984625711777776182717e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.137 y[1] (closed_form) = -0.001162455828259595595720956063765 y[1] (numeric) = -0.0011624558282595954319287347829641 absolute error = 1.6379222128080092162819002000024e-19 relative error = 1.4090188831177111358909044197243e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.136 y[1] (closed_form) = -0.0011609523936080120462803100702283 y[1] (numeric) = -0.001160952393608011882451380801573 absolute error = 1.6382892926865532607711659105579e-19 relative error = 1.4111597527225658872386701439006e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.135 y[1] (closed_form) = -0.0011594512916708067894012932492445 y[1] (numeric) = -0.0011594512916708066255357603519792 absolute error = 1.6386553289726529220645165473508e-19 relative error = 1.4133024308518364968311142684447e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.134 y[1] (closed_form) = -0.0011579525182264188801526415804182 y[1] (numeric) = -0.0011579525182264187162506090902105 absolute error = 1.6390203249020777291530268662784e-19 relative error = 1.4154469195442380157372863275767e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.133 y[1] (closed_form) = -0.0011564560690620163683779768142744 y[1] (numeric) = -0.0011564560690620162044395484443013 absolute error = 1.6393842836997311005017906123518e-19 relative error = 1.4175932208383932283277715928746e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.132 y[1] (closed_form) = -0.0011549619399734759987124812263255 y[1] (numeric) = -0.0011549619399734758347377603683566 absolute error = 1.6397472085796896305322193921708e-19 relative error = 1.4197413367728350005860155812433e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.131 y[1] (closed_form) = -0.0011534701267653629630407461027783 y[1] (numeric) = -0.001153470126765362799029835828254 absolute error = 1.6401091027452422239573997981346e-19 relative error = 1.4218912693860086229041674547566e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (closed_form) = -0.0011519806252509107052468133904904 y[1] (numeric) = -0.0011519806252509105411998164515975 absolute error = 1.6404699693889290785988562925164e-19 relative error = 1.4240430207162741473791136505244e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.129 y[1] (closed_form) = -0.0011504934312520007781078915410795 y[1] (numeric) = -0.0011504934312520006140249103718214 absolute error = 1.6408298116925805173103108887214e-19 relative error = 1.4261965928019087196243245157750e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.128 y[1] (closed_form) = -0.0011490085405991427521836866273846 y[1] (numeric) = -0.001149008540599142588064823344649 absolute error = 1.6411886328273556696312869964856e-19 relative error = 1.4283519876811089051130883233724e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.127 y[1] (closed_form) = -0.0011475259491314541765537483153991 y[1] (numeric) = -0.001147525949131454012399104720021 absolute error = 1.6415464359537810037906738647345e-19 relative error = 1.4305092073919930100686588054159e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.126 y[1] (closed_form) = -0.0011460456526966405912556872418959 y[1] (numeric) = -0.001146045652696640427065364819717 absolute error = 1.6419032242217887096776497978989e-19 relative error = 1.4326682539726033969167942668065e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.125 y[1] (closed_form) = -0.0011445676471509755912775757828096 y[1] (numeric) = -0.0011445676471509754270516757057341 absolute error = 1.6422590007707549333946566766001e-19 relative error = 1.4348291294609087943161184261335e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.124 y[1] (closed_form) = -0.0011430919283592809419582981055544 y[1] (numeric) = -0.0011430919283592807776969212326006 absolute error = 1.6426137687295378640044252200126e-19 relative error = 1.4369918358948066017816853773429e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.123 y[1] (closed_form) = -0.0011416184921949067456500677853553 y[1] (numeric) = -0.0011416184921949065813533146637038 absolute error = 1.6429675312165156730803698234322e-19 relative error = 1.4391563753121251889170834718300e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.122 y[1] (closed_form) = -0.0011401473345397116594977821368392 y[1] (numeric) = -0.0011401473345397114951657530028768 absolute error = 1.6433202913396243076670036295101e-19 relative error = 1.4413227497506261892703654862595e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.121 y[1] (closed_form) = -0.001138678451284043164190331773038 y[1] (numeric) = -0.0011386784512840429998231265533985 absolute error = 1.6436720521963951372543686844380e-19 relative error = 1.4434909612480067888290451659973e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (closed_form) = -0.0011372118383267178835394317600521 y[1] (numeric) = -0.0011372118383267177191371500726529 absolute error = 1.6440228168739924553678325305850e-19 relative error = 1.4456610118419020091693531169513e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.119 y[1] (closed_form) = -0.0011357474915750019547419870923237 y[1] (numeric) = -0.0011357474915750017903047282473986 absolute error = 1.6443725884492508363719713345186e-19 relative error = 1.4478329035698869852748980593047e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.118 y[1] (closed_form) = -0.0011342854069445914491824500761907 y[1] (numeric) = -0.0011342854069445912847103130773195 absolute error = 1.6447213699887123480846405840940e-19 relative error = 1.4500066384694792380398326545098e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.117 y[1] (closed_form) = -0.0011328255803595928436320705835124 y[1] (numeric) = -0.0011328255803595926791251541286461 absolute error = 1.6450691645486636207947274508182e-19 relative error = 1.4521822185781409414715764714252e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.116 y[1] (closed_form) = -0.0011313680077525035417023820280351 y[1] (numeric) = -0.0011313680077525033771607845105178 absolute error = 1.6454159751751727732744840447065e-19 relative error = 1.4543596459332811846081021680660e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.115 y[1] (closed_form) = -0.0011299126850641924454107063301572 y[1] (numeric) = -0.0011299126850641922808345258397446 absolute error = 1.6457618049041261963747579294075e-19 relative error = 1.4565389225722582281647446315283e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.114 y[1] (closed_form) = -0.0011284596082438805767159000761616 y[1] (numeric) = -0.001128459608243880412105234400035 absolute error = 1.6461066567612651947888653568071e-19 relative error = 1.4587200505323817559254466396866e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.113 y[1] (closed_form) = -0.0011270087732491217488830015511236 y[1] (numeric) = -0.0011270087732491215842379481749013 absolute error = 1.6464505337622224875682936642953e-19 relative error = 1.4609030318509151208933085836886e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.112 y[1] (closed_form) = -0.0011255601760457832875358743358505 y[1] (numeric) = -0.0011255601760457831228565304445947 absolute error = 1.6467934389125585679708720963205e-19 relative error = 1.4630878685650775862152639195324e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.111 y[1] (closed_form) = -0.0011241138126080268012573777126239 y[1] (numeric) = -0.0011241138126080266365438401918441 absolute error = 1.6471353752077979232195149070261e-19 relative error = 1.4652745627120465608956562995464e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (closed_form) = -0.0011226696789182890015970272274391 y[1] (numeric) = -0.0011226696789182888368493926640926 memory used=747.8MB, alloc=44.3MB, time=11.00 absolute error = 1.6474763456334651147471169151883e-19 relative error = 1.4674631163289598303134487698613e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.109 y[1] (closed_form) = -0.001121227770967262572346540413091 y[1] (numeric) = -0.0011212277709672624075649050965789 absolute error = 1.6478163531651207195006696592023e-19 relative error = 1.4696535314529177815577500074030e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.108 y[1] (closed_form) = -0.0011197880847538770879440928930303 y[1] (numeric) = -0.0011197880847538769231285528161906 absolute error = 1.6481554007683971328751658816144e-19 relative error = 1.4718458101209856235962973090158e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.107 y[1] (closed_form) = -0.0011183506162852799808685388656082 y[1] (numeric) = -0.0011183506162852798160191897257047 absolute error = 1.6484934913990342338453712031007e-19 relative error = 1.4740399543701956022914909354806e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.106 y[1] (closed_form) = -0.0011169153615768175578852773172763 y[1] (numeric) = -0.0011169153615768173930022145169848 absolute error = 1.6488306280029149128610644685504e-19 relative error = 1.4762359662375492102785294539008e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.105 y[1] (closed_form) = -0.0011154823166520160650058712366759 y[1] (numeric) = -0.0011154823166520159000891898850658 absolute error = 1.6491668135161004630688823070366e-19 relative error = 1.4784338477600193917201509126333e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.104 y[1] (closed_form) = -0.001114051477542562801023951604437 y[1] (numeric) = -0.0011140514775425626360737465179504 absolute error = 1.6495020508648658354214488872236e-19 relative error = 1.4806336009745527419524400231112e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.103 y[1] (closed_form) = -0.0011126228402882872794903610210271 y[1] (numeric) = -0.0011126228402882871145067267244536 absolute error = 1.6498363429657347582320286147481e-19 relative error = 1.4828352279180717020361170120005e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.102 y[1] (closed_form) = -0.0011111964009371424389909135122146 y[1] (numeric) = -0.0011111964009371422739739442396631 absolute error = 1.6501696927255147217305075531828e-19 relative error = 1.4850387306274767482276794446234e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.101 y[1] (closed_form) = -0.0011097721555451859015905673237103 y[1] (numeric) = -0.0011097721555451857365403570195771 absolute error = 1.6505021030413318281740886004692e-19 relative error = 1.4872441111396485763847241059223e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (closed_form) = -0.0011083501001765612793082263883551 y[1] (numeric) = -0.0011083501001765611142248687082885 absolute error = 1.6508335768006655080636758636347e-19 relative error = 1.4894513714914502813197319579207e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.099 y[1] (closed_form) = -0.0011069302309034795284868036258679 y[1] (numeric) = -0.0011069302309034793633703919377296 absolute error = 1.6511641168813831030145251918662e-19 relative error = 1.4916605137197295311165552721083e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.098 y[1] (closed_form) = -0.001105512543806200351923595321646 y[1] (numeric) = -0.0011055125438062001867742227064686 absolute error = 1.6514937261517743158273503975916e-19 relative error = 1.4938715398613207364238022609275e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.097 y[1] (closed_form) = -0.0011040970349730136486264305324102 y[1] (numeric) = -0.0011040970349730134834441897853517 absolute error = 1.6518224074705855283036982633697e-19 relative error = 1.4960844519530472147392709040394e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.096 y[1] (closed_form) = -0.0011026837005002210110614727875774 y[1] (numeric) = -0.001102683700500220845846456418872 absolute error = 1.6521501636870539873470399456374e-19 relative error = 1.4982992520317233496995401817683e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.095 y[1] (closed_form) = -0.0011012725364921172697589633010592 y[1] (numeric) = -0.001101272536492117104511263536965 absolute error = 1.6524769976409418598886717915207e-19 relative error = 1.5005159421341567453887835895582e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.094 y[1] (closed_form) = -0.0010998635390609720851436054836663 y[1] (numeric) = -0.0010998635390609719198633142674093 absolute error = 1.6528029121625701571751748290471e-19 relative error = 1.5027345242971503756808266128909e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.093 y[1] (closed_form) = -0.0010984567043270115864566997563392 y[1] (numeric) = -0.0010984567043270114211439087490539 absolute error = 1.6531279100728525289518492215615e-19 relative error = 1.5049550005575047286284267914070e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.092 y[1] (closed_form) = -0.001097052028418400057637545513929 y[1] (numeric) = -0.0010970520284183998922923460955961 absolute error = 1.6534519941833289280742177415470e-19 relative error = 1.5071773729520199459137120934165e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.091 y[1] (closed_form) = -0.0010956495074712216700320335830761 y[1] (numeric) = -0.0010956495074712215046545168534562 absolute error = 1.6537751672961991460773807652796e-19 relative error = 1.5094016435174979573736705570767e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (closed_form) = -0.0010942491376294622617967576607378 y[1] (numeric) = -0.0010942491376294620963870144403022 absolute error = 1.6540974322043562202307043659466e-19 relative error = 1.5116278142907446106145415317381e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.089 y[1] (closed_form) = -0.0010928509150449911638673770169288 y[1] (numeric) = -0.0010928509150449909984254978477868 absolute error = 1.6544187916914197126030327374458e-19 relative error = 1.5138558873085717957289163718120e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.088 y[1] (closed_form) = -0.0010914548358775430723603652010781 y[1] (numeric) = -0.0010914548358775429068864403479012 absolute error = 1.6547392485317688616613363627349e-19 relative error = 1.5160858646077995651293140954752e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.087 y[1] (closed_form) = -0.0010900608962946999672776806108648 y[1] (numeric) = -0.0010900608962946998017718000618073 absolute error = 1.6550588054905756069234379982621e-19 relative error = 1.5183177482252582485119553211136e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.086 y[1] (closed_form) = -0.0010886690924718730773842945702504 y[1] (numeric) = -0.0010886690924718729118465480378667 absolute error = 1.6553774653238374871831996288689e-19 relative error = 1.5205515401977905629644157350959e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.085 y[1] (closed_form) = -0.0010872794205922848911289110244447 y[1] (numeric) = -0.0010872794205922847255593879466037 absolute error = 1.6556952307784104128243050050880e-19 relative error = 1.5227872425622537182307984247704e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.084 y[1] (closed_form) = -0.0010858918768469512134786090984545 y[1] (numeric) = -0.0010858918768469510478773986392503 absolute error = 1.6560121045920413127365341566681e-19 relative error = 1.5250248573555215171480226299919e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.083 y[1] (closed_form) = -0.0010845064574346632685385355874001 y[1] (numeric) = -0.00108450645743466310290572663806 absolute error = 1.6563280894934006563461983324237e-19 relative error = 1.5272643866144864512667848245128e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.082 y[1] (closed_form) = -0.0010831231585619698478281689556519 y[1] (numeric) = -0.0010831231585619696821638501354404 absolute error = 1.6566431882021148512701860973637e-19 relative error = 1.5295058323760617916707065347167e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.081 y[1] (closed_form) = -0.0010817419764431595040860696227115 y[1] (numeric) = -0.0010817419764431593383903292798317 absolute error = 1.6569574034287985171008637739654e-19 relative error = 1.5317491966771836750071419369471e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (closed_form) = -0.0010803629073002427904754232113271 y[1] (numeric) = -0.0010803629073002426247483494238184 absolute error = 1.6572707378750866358268759961901e-19 relative error = 1.5339944815548131847430770455869e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.079 y[1] (closed_form) = -0.0010789859473629345450630740322226 y[1] (numeric) = -0.0010789859473629343793047546088559 absolute error = 1.6575831942336665793927048033392e-19 relative error = 1.5362416890459384276595112115969e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.078 y[1] (closed_form) = -0.001077611092868636220445135384686 y[1] (numeric) = -0.001077611092868636054655657865855 absolute error = 1.6578947751883100148976683873913e-19 relative error = 1.5384908211875766055976706949294e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.077 y[1] (closed_form) = -0.0010762383400624182583926512677028 y[1] (numeric) = -0.0010762383400624180925721029263123 absolute error = 1.6582054834139046879328732734995e-19 relative error = 1.5407418800167760824703632536118e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.076 y[1] (closed_form) = -0.001074867685197002509391170826949 y[1] (numeric) = -0.0010748676851970023435396386693004 absolute error = 1.6585153215764860845524763106118e-19 relative error = 1.5429948675706184465517420068628e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.075 y[1] (closed_form) = -0.0010734991245327446969484823133438 y[1] (numeric) = -0.0010734991245327445310660530800169 absolute error = 1.6588242923332689723734653296781e-19 relative error = 1.5452497858862205680587062788766e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.074 y[1] (closed_form) = -0.0010721326543376169265451375035748 y[1] (numeric) = -0.0010721326543376167606318976703069 absolute error = 1.6591323983326788212960296428385e-19 relative error = 1.5475066370007366520371267134097e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.073 y[1] (closed_form) = -0.001070768270887190239102780436588 y[1] (numeric) = -0.0010707682708871900731588162151497 absolute error = 1.6594396422143831043344636608305e-19 relative error = 1.5497654229513602865660416665475e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.072 y[1] (closed_form) = -0.0010694059704646172088456759570184 y[1] (numeric) = -0.0010694059704646170428710732960862 absolute error = 1.6597460266093224790464287502939e-19 relative error = 1.5520261457753264862929317355483e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.071 y[1] (closed_form) = -0.0010680457493606145854312139314214 y[1] (numeric) = -0.0010680457493606144194260585174473 absolute error = 1.6600515541397418500462899906506e-19 relative error = 1.5542888075099137313131392649704e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (closed_form) = -0.0010666876038734459802255441204606 y[1] (numeric) = -0.0010666876038734458141899213785384 absolute error = 1.6603562274192213130861456749776e-19 relative error = 1.5565534101924460014064597869244e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.069 y[1] (closed_form) = -0.0010653315303089045966008745543769 y[1] (numeric) = -0.0010653315303089044305348696491062 absolute error = 1.6606600490527069811860781841892e-19 relative error = 1.5588199558602948056438925997802e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.068 y[1] (closed_form) = -0.0010639775249802960041313428745753 y[1] (numeric) = -0.0010639775249802958380350407109211 absolute error = 1.6609630216365416932930752025725e-19 relative error = 1.5610884465508812073774980685263e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.067 y[1] (closed_form) = -0.0010626255842084209565647454754543 y[1] (numeric) = -0.0010626255842084207904382306996047 absolute error = 1.6612651477584956059460000891604e-19 relative error = 1.5633588843016778446262697397645e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.066 y[1] (closed_form) = -0.0010612757043215582534477834121056 y[1] (numeric) = -0.001061275704321558087291140412326 absolute error = 1.6615664299977966684219295277234e-19 relative error = 1.5656312711502109458708900045569e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.065 y[1] (closed_form) = -0.0010599278816554476452828569356228 y[1] (numeric) = -0.0010599278816554474790961698431067 absolute error = 1.6618668709251609818371253026596e-19 relative error = 1.5679056091340623412701988125600e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.064 y[1] (closed_form) = -0.001058582112553272782094812182879 y[1] (numeric) = -0.0010585821125532726158781648725966 absolute error = 1.6621664731028230426738651433785e-19 relative error = 1.5701819002908714693121658406260e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.063 y[1] (closed_form) = -0.0010572383933656442052864139861423 y[1] (numeric) = -0.0010572383933656440390398900776857 absolute error = 1.6624652390845658712023250007087e-19 relative error = 1.5724601466583373789121175478540e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.062 y[1] (closed_form) = -0.0010558967204505823826616879841383 y[1] (numeric) = -0.0010558967204505822163853708425632 absolute error = 1.6627631714157510252646818204882e-19 relative error = 1.5747403502742207269709317064851e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.061 y[1] (closed_form) = -0.0010545570901735007864966432145015 y[1] (numeric) = -0.0010545570901735006201906159511667 absolute error = 1.6630602726333484998865918170854e-19 relative error = 1.5770225131763457714058732835920e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (closed_form) = -0.0010532194989071890145372531522954 y[1] (numeric) = -0.0010532194989071888482015986256988 absolute error = 1.6633565452659665131791943786648e-19 relative error = 1.5793066374026023596667069617611e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.059 y[1] (closed_form) = -0.0010518839430317959538049387347344 y[1] (numeric) = -0.0010518839430317957874397395513463 absolute error = 1.6636519918338811789927960122868e-19 relative error = 1.5815927249909479127496831274552e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.058 y[1] (closed_form) = -0.0010505504189348129870901612827095 y[1] (numeric) = -0.0010505504189348128206954997978029 absolute error = 1.6639466148490660667814021163737e-19 relative error = 1.5838807779794094047219558230171e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.057 y[1] (closed_form) = -0.0010492189230110572420150963994692 y[1] (numeric) = -0.0010492189230110570755910547179471 absolute error = 1.6642404168152216491352868068670e-19 relative error = 1.5861707984060853377689529518859e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.056 y[1] (closed_form) = -0.0010478894516626548825467219001088 y[1] (numeric) = -0.0010478894516626547160933818773283 absolute error = 1.6645334002278046374368224779435e-19 relative error = 1.5884627883091477127771809460997e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.055 y[1] (closed_form) = -0.0010465620012990244428420136066079 y[1] (numeric) = -0.0010465620012990242763594568492022 absolute error = 1.6648255675740572060928312050841e-19 relative error = 1.5907567497268439954649081500961e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop memory used=794.3MB, alloc=44.3MB, time=11.67 x[1] = 2.054 y[1] (closed_form) = -0.0010452365683368602033073024362657 y[1] (numeric) = -0.0010452365683368600367956103029621 absolute error = 1.6651169213330361057947694544295e-19 relative error = 1.5930526846974990780731333447668e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.053 y[1] (closed_form) = -0.001043913149200115608754204620719 y[1] (numeric) = -0.0010439131492001154422134582231549 absolute error = 1.6654074639756416662561158047880e-19 relative error = 1.5953505952595172366292081302081e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.052 y[1] (closed_form) = -0.0010425917403199867285348941224911 y[1] (numeric) = -0.0010425917403199865619651743260265 absolute error = 1.6656971979646466888743984746499e-19 relative error = 1.5976504834513840837954443042218e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.051 y[1] (closed_form) = -0.001041272338134895758539842370386 y[1] (numeric) = -0.0010412723381348955919412297949135 absolute error = 1.6659861257547252297633753336159e-19 relative error = 1.5999523513116685173149999158925e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (closed_form) = -0.0010399549390904745649415053181806 y[1] (numeric) = -0.0010399549390904743983140803389324 absolute error = 1.6662742497924812735989637234684e-19 relative error = 1.6022562008790246640673003390836e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.049 y[1] (closed_form) = -0.0010386395396395482695677915471189 y[1] (numeric) = -0.0010386395396395481029116342954712 absolute error = 1.6665615725164772987206107766317e-19 relative error = 1.6045620341921938197452134990009e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.048 y[1] (closed_form) = -0.0010373261362421188767894976858155 y[1] (numeric) = -0.0010373261362421187101046880500893 absolute error = 1.6668480963572627339278969571153e-19 relative error = 1.6068698532900063841661612956496e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.047 y[1] (closed_form) = -0.0010360147253653489418062488154433 y[1] (numeric) = -0.001036014725365348775092866441703 absolute error = 1.6671338237374023074102762195701e-19 relative error = 1.6091796602113837922293123006082e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.046 y[1] (closed_form) = -0.0010347053034835452802158317676165 y[1] (numeric) = -0.0010347053034835451134739560604661 absolute error = 1.6674187570715042882459754443544e-19 relative error = 1.6114914569953404405309639576481e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.045 y[1] (closed_form) = -0.0010333978670781427187521583112677 y[1] (numeric) = -0.0010333978670781425519818684346429 absolute error = 1.6677028987662486209042036192936e-19 relative error = 1.6138052456809856096501857928939e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.044 y[1] (closed_form) = -0.0010320924126376878870774431671257 y[1] (numeric) = -0.0010320924126376877202788180450842 absolute error = 1.6679862512204149531829575610848e-19 relative error = 1.6161210283075253821167585360305e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.043 y[1] (closed_form) = -0.0010307889366578230505145285881905 y[1] (numeric) = -0.0010307889366578228836876469056994 absolute error = 1.6682688168249105580128557602384e-19 relative error = 1.6184388069142645560734075700838e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.042 y[1] (closed_form) = -0.0010294874356412699836056329059029 y[1] (numeric) = -0.0010294874356412698167505731096231 absolute error = 1.6685505979627981495555851524498e-19 relative error = 1.6207585835406085546442927631134e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.041 y[1] (closed_form) = -0.0010281879060978138843841449685515 y[1] (numeric) = -0.0010281879060978137175009852676192 absolute error = 1.6688315970093235940237072259557e-19 relative error = 1.6230803602260653310216804903316e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.04 y[1] (closed_form) = -0.0010268903445442873292464297948487 y[1] (numeric) = -0.0010268903445442871623352481616543 absolute error = 1.6691118163319435156467398285373e-19 relative error = 1.6254041390102472692826875292805e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.039 y[1] (closed_form) = -0.0010255947475045542683109530355453 y[1] (numeric) = -0.00102559474750455410137182720651 absolute error = 1.6693912582903527982066092994093e-19 relative error = 1.6277299219328730809479505033402e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.038 y[1] (closed_form) = -0.0010243011115094940611523729834066 y[1] (numeric) = -0.0010243011115094938941853804597554 absolute error = 1.6696699252365119825637540804601e-19 relative error = 1.6300577110337696972940386595870e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.037 y[1] (closed_form) = -0.0010230094330969855527985889008112 y[1] (numeric) = -0.0010230094330969853858038069493437 absolute error = 1.6699478195146745605933557186068e-19 relative error = 1.6323875083528741574313919954523e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.036 y[1] (closed_form) = -0.0010217197088118911898790733486079 y[1] (numeric) = -0.0010217197088118910228565790024664 absolute error = 1.6702249434614141659493761169901e-19 relative error = 1.6347193159302354921595310943361e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.035 y[1] (closed_form) = -0.0010204319352060411768131540036012 y[1] (numeric) = -0.001020431935206041009763024063036 absolute error = 1.6705012994056516620722909881695e-19 relative error = 1.6370531358060166036112494928899e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.034 y[1] (closed_form) = -0.0010191461088382176719272471490593 y[1] (numeric) = -0.0010191461088382175048495581821911 absolute error = 1.6707768896686821278546286683828e-19 relative error = 1.6393889700204961406974639816925e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.033 y[1] (closed_form) = -0.0010178622262741390233903806168481 y[1] (numeric) = -0.0010178622262741388562852089604279 absolute error = 1.6710517165642017413766507295017e-19 relative error = 1.6417268206140703703643629360792e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.032 y[1] (closed_form) = -0.0010165802840864440448576784550824 y[1] (numeric) = -0.0010165802840864438777251002152489 absolute error = 1.6713257823983345621227461359445e-19 relative error = 1.6440666896272550446744575845537e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.031 y[1] (closed_form) = -0.0010153002788546763307118129954249 y[1] (numeric) = -0.001015300278854676163551904048459 absolute error = 1.6715990894696592120873539990736e-19 relative error = 1.6464085791006872637231060480947e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (closed_form) = -0.0010140222071652686107927623032123 y[1] (numeric) = -0.0010140222071652684436055982962887 absolute error = 1.6718716400692354561774812432986e-19 relative error = 1.6487524910751273344020450243624e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.029 y[1] (closed_form) = -0.0010127460656115271445065422152959 y[1] (numeric) = -0.0010127460656115269772921985672328 absolute error = 1.6721434364806306823171406781910e-19 relative error = 1.6510984275914606250214291459128e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.028 y[1] (closed_form) = -0.0010114718507936161542039123086774 y[1] (numeric) = -0.0010114718507936159869624642106828 absolute error = 1.6724144809799462816573020315548e-19 relative error = 1.6534463906906994158018433106329e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.027 y[1] (closed_form) = -0.0010101995593185422977203842015157 y[1] (numeric) = -0.0010101995593185421304519066179313 absolute error = 1.6726847758358439292932234019486e-19 relative error = 1.6557963824139847452477186653143e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.026 y[1] (closed_form) = -0.0010089291878001391799691885706836 y[1] (numeric) = -0.0010089291878001390126737562397264 absolute error = 1.6729543233095717658893132981549e-19 relative error = 1.6581484048025882524135484191933e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.025 y[1] (closed_form) = -0.0010076607328590519034791841805464 y[1] (numeric) = -0.0010076607328590517361568716150473 absolute error = 1.6732231256549904806099639102721e-19 relative error = 1.6605024598979140150742652729973e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.024 y[1] (closed_form) = -0.0010063941911227216577700180597924 y[1] (numeric) = -0.0010063941911227214904208995479324 absolute error = 1.6734911851185992957530944653868e-19 relative error = 1.6628585497415003838111079701555e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.023 y[1] (closed_form) = -0.00100512955922537034745717074073 y[1] (numeric) = -0.0010051295592253701800813203467739 absolute error = 1.6737585039395618534814494232685e-19 relative error = 1.6652166763750218120242703099588e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.022 y[1] (closed_form) = -0.0010038668338079852589798441922182 y[1] (numeric) = -0.001003866833807985091577335757245 absolute error = 1.6740250843497320050450098275007e-19 relative error = 1.6675768418402906818835919072039e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.021 y[1] (closed_form) = -0.0010026060115183037658449727370467 y[1] (numeric) = -0.0010026060115183035984158798796787 absolute error = 1.6742909285736795028861973084084e-19 relative error = 1.6699390481792591262285160388215e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (closed_form) = -0.0010013470890107980722809588508551 y[1] (numeric) = -0.0010013470890107979048253549679835 absolute error = 1.6745560388287155960178789997049e-19 relative error = 1.6723032974340208464285060847941e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.019 y[1] (closed_form) = -0.0010000900629466599951950562962618 y[1] (numeric) = -0.00100009006294665982771301456377 absolute error = 1.6748204173249185290625179448060e-19 relative error = 1.6746695916468129262150783479142e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.018 y[1] (closed_form) = -0.00099883492999378578432864255647147 y[1] (numeric) = -0.00099883492999378561682023592995558 absolute error = 1.6750840662651589453391573952717e-19 relative error = 1.6770379328600176414965754242346e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.017 y[1] (closed_form) = -0.0009975816868267609805049410009049 y[1] (numeric) = -0.00099758168682676081297024221639238 absolute error = 1.6753469878451251943832787070289e-19 relative error = 1.6794083231161642661667707930332e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.016 y[1] (closed_form) = -0.00099633033012684531186407064501566 y[1] (numeric) = -0.00099633033012684514430315221968081 absolute error = 1.6756091842533485442829312842860e-19 relative error = 1.6817807644579308739183619013658e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.015 y[1] (closed_form) = -0.00099508085658195762798061776106625 y[1] (numeric) = -0.00099508085658195746039355199394342 absolute error = 1.6758706576712282992128991709361e-19 relative error = 1.6841552589281461360723757334350e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.014 y[1] (closed_form) = -0.00099383326288666087175923895987176 y[1] (numeric) = -0.00099383326288666070414609793256608 absolute error = 1.6761314102730568225470424094886e-19 relative error = 1.6865318085697911154344776786714e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.013 y[1] (closed_form) = -0.00099258754574214708900411969899509 y[1] (numeric) = -0.00099258754574214692136497527639065 absolute error = 1.6763914442260444659273321430888e-19 relative error = 1.6889104154260010561891414442299e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.012 y[1] (closed_form) = -0.00099134370185622247555842548420477 y[1] (numeric) = -0.00099134370185622230789334931517033 absolute error = 1.6766507616903444046664865920707e-19 relative error = 1.6912910815400671698426047971647e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.011 y[1] (closed_form) = -0.00099010172794329246191019532177521 y[1] (numeric) = -0.00099010172794329229421925883986747 absolute error = 1.6769093648190773798595104579995e-19 relative error = 1.6936738089554384172255030684907e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (closed_form) = -0.00098886162072434683516143825299956 y[1] (numeric) = -0.00098886162072434666744471267716393 absolute error = 1.6771672557583563475778429607431e-19 relative error = 1.6960585997157232865660396052788e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.009 y[1] (closed_form) = -0.00098762337692694489825750406266258 y[1] (numeric) = -0.00098762337692694473051506039793148 absolute error = 1.6774244366473110355182295633677e-19 relative error = 1.6984454558646915676445197175041e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.008 y[1] (closed_form) = -0.0009863869932852006663741085037373 y[1] (numeric) = -0.00098638699328520049860601754192606 absolute error = 1.6776809096181124074768494513760e-19 relative error = 1.7008343794462761220400421331901e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.007 y[1] (closed_form) = -0.00098515246653976810035970162476421 y[1] (numeric) = -0.00098515246653976793256603394516451 absolute error = 1.6779366767959970360176549729406e-19 relative error = 1.7032253725045746494801095480921e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.006 y[1] (closed_form) = -0.00098391979343782637713117502777023 y[1] (numeric) = -0.00098391979343782620931200099784109 absolute error = 1.6781917402992913837023104814655e-19 relative error = 1.7056184370838514503038875343805e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.005 y[1] (closed_form) = -0.00098268897073306519692121012669949 y[1] (numeric) = -0.00098268897073306502907659990275589 absolute error = 1.6784461022394359932475563173201e-19 relative error = 1.7080135752285391840498088561330e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.004 y[1] (closed_form) = -0.00098145999518567012727587472265856 y[1] (numeric) = -0.0009814599951856699594058982505576 absolute error = 1.6786997647210095869742689884038e-19 relative error = 1.7104107889832406241781881275743e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.003 y[1] (closed_form) = -0.00098023286356230798370137946631065 y[1] (numeric) = -0.00098023286356230781580610648213535 absolute error = 1.6789527298417530759109409259386e-19 relative error = 1.7128100803927304089394797425270e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.002 y[1] (closed_form) = -0.00097900757263611224685920904296017 y[1] (numeric) = -0.00097900757263611207893870907370082 absolute error = 1.6792049996925934789127624693532e-19 relative error = 1.7152114515019567883987801001099e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 TOP MAIN SOLVE Loop x[1] = 2.001 y[1] (closed_form) = -0.00097778411918666851620914519571034 y[1] (numeric) = -0.00097778411918666834826348755994357 absolute error = 1.6794565763576677521559549392797e-19 relative error = 1.7176149043560433676271433519637e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = -0.001 Finished! diff ( y , x , 1 ) = neg ( 5.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; Iterations = 1000 Total Elapsed Time = 12 Seconds Elapsed Time(since restart) = 12 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Expected Total Time = 12 Seconds Time to Timeout = 2 Minutes 47 Seconds Percent Done = 0 % > quit memory used=839.3MB, alloc=44.3MB, time=12.30