|\^/| Maple 18 (X86 64 WINDOWS) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. #BEGIN OUTFILE1 # before write maple top matter # before write_ats library and user def block #BEGIN ATS LIBRARY BLOCK # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc # End Function number 2 # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc # End Function number 3 # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc # End Function number 4 # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 5 # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 6 # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc # End Function number 7 # Begin Function number 8 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := sec_temp mod int_trunc(glob_sec_in_minute); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," 0.0 Seconds"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " 0.0 Seconds") end if; fprintf(fd, "\n") end proc # End Function number 8 # Begin Function number 9 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year)); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour)); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod int_trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" 0.0 Seconds\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" 0.0 Seconds\n") end if end proc # End Function number 9 # Begin Function number 10 > zero_ats_ar := proc(arr_a) > global ATS_MAX_TERMS; > local iii; > iii := 1; > while (iii <= ATS_MAX_TERMS) do # do number 1 > arr_a [iii] := glob__0; > iii := iii + 1; > od;# end do number 1 > end; zero_ats_ar := proc(arr_a) local iii; global ATS_MAX_TERMS; iii := 1; while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1 end do end proc # End Function number 10 # Begin Function number 11 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > global ATS_MAX_TERMS; > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := glob__0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 7 > ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]); > fi;# end if 7; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; global ATS_MAX_TERMS; ret_ats := glob__0; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]) end if; iii_ats := iii_ats + 1 end do end if; ret_ats end proc # End Function number 11 # Begin Function number 12 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global ATS_MAX_TERMS; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := glob__0; > if (jjj_att < mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 7 > ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / c(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global ATS_MAX_TERMS; ret_att := glob__0; if jjj_att < mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/c(mmm_att) end if; ret_att end proc # End Function number 12 # Begin Function number 13 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc # End Function number 13 # Begin Function number 14 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc # End Function number 14 # Begin Function number 15 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc # End Function number 15 # Begin Function number 16 > logitem_good_digits := proc(file,rel_error) > global glob_small_float,glob_prec; > local good_digits; > fprintf(file,""); > fprintf(file,"%d",glob_min_good_digits); > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float, glob_prec; fprintf(file, ""); fprintf(file, "%d", glob_min_good_digits); fprintf(file, "") end proc # End Function number 16 # Begin Function number 17 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc # End Function number 17 # Begin Function number 18 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc # End Function number 18 # Begin Function number 19 > logitem_h_reason := proc(file) > global glob_h_reason; > fprintf(file,""); > if (glob_h_reason = 1) then # if number 6 > fprintf(file,"Max H"); > elif > (glob_h_reason = 2) then # if number 7 > fprintf(file,"Display Interval"); > elif > (glob_h_reason = 3) then # if number 8 > fprintf(file,"Optimal"); > elif > (glob_h_reason = 4) then # if number 9 > fprintf(file,"Pole Accuracy"); > elif > (glob_h_reason = 5) then # if number 10 > fprintf(file,"Min H (Pole)"); > elif > (glob_h_reason = 6) then # if number 11 > fprintf(file,"Pole"); > elif > (glob_h_reason = 7) then # if number 12 > fprintf(file,"Opt Iter"); > else > fprintf(file,"Impossible"); > fi;# end if 12 > fprintf(file,""); > end; logitem_h_reason := proc(file) global glob_h_reason; fprintf(file, ""); if glob_h_reason = 1 then fprintf(file, "Max H") elif glob_h_reason = 2 then fprintf(file, "Display Interval") elif glob_h_reason = 3 then fprintf(file, "Optimal") elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy") elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)") elif glob_h_reason = 6 then fprintf(file, "Pole") elif glob_h_reason = 7 then fprintf(file, "Opt Iter") else fprintf(file, "Impossible") end if; fprintf(file, "") end proc # End Function number 19 # Begin Function number 20 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc # End Function number 20 # Begin Function number 21 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc # End Function number 21 # Begin Function number 22 > chk_data := proc() > global glob_max_iter,ALWAYS, ATS_MAX_TERMS; > local errflag; > errflag := false; > if (glob_max_iter < 2) then # if number 12 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 12; > if (errflag) then # if number 12 > quit; > fi;# end if 12 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, ATS_MAX_TERMS; errflag := false; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc # End Function number 22 # Begin Function number 23 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := c(clock_sec2); > sub1 := c(t_end2-t_start2); > sub2 := c(t2-t_start2); > if (sub1 = glob__0) then # if number 12 > sec_left := glob__0; > else > if (sub2 > glob__0) then # if number 13 > rrr := (sub1/sub2); > sec_left := rrr * c(ms2) - c(ms2); > else > sec_left := glob__0; > fi;# end if 13 > fi;# end if 12; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := c(clock_sec2); sub1 := c(t_end2 - t_start2); sub2 := c(t2 - t_start2); if sub1 = glob__0 then sec_left := glob__0 else if glob__0 < sub2 then rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2) else sec_left := glob__0 end if end if; sec_left end proc # End Function number 23 # Begin Function number 24 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 12 > rrr := (glob__100*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 12; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := glob__100*sub2/sub1 else rrr := 0. end if; rrr end proc # End Function number 24 # Begin Function number 25 > comp_rad_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 12 > ret := float_abs(term1 * glob_h / term2); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM TWO TERM RADIUS ANALYSIS > end; comp_rad_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2) else ret := glob_larger_float end if; ret end proc # End Function number 25 # Begin Function number 26 > comp_ord_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM ORDER ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 12 > ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no)); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM TWO TERM ORDER ANALYSIS > end; comp_ord_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)* c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no)) else ret := glob_larger_float end if; ret end proc # End Function number 26 # Begin Function number 27 > c := proc(in_val) > #To Force Conversion when needed > local ret; > ret := evalf(in_val); > ret; > #End Conversion > end; c := proc(in_val) local ret; ret := evalf(in_val); ret end proc # End Function number 27 # Begin Function number 28 > comp_rad_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret,temp; > temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3); > if (float_abs(temp) > glob__0) then # if number 12 > ret := float_abs((term2*glob_h*term1)/(temp)); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM THREE TERM RADIUS ANALYSIS > end; comp_rad_from_three_terms := proc(term1, term2, term3, last_no) local ret, temp; global glob_h, glob_larger_float; temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2 - term1*term3*c(last_no) + term1*term3); if glob__0 < float_abs(temp) then ret := float_abs(term2*glob_h*term1/temp) else ret := glob_larger_float end if; ret end proc # End Function number 28 # Begin Function number 29 > comp_ord_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM ORDER ANALYSIS > local ret; > ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3)); > ret; > #TOP THREE TERM ORDER ANALYSIS > end; comp_ord_from_three_terms := proc(term1, term2, term3, last_no) local ret; ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3 - glob__4*term2*term2*c(last_no) + glob__4*term2*term2 + term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no)) /(term2*term2*c(last_no) - glob__2*term2*term2 - term1*term3*c(last_no) + term1*term3)); ret end proc # End Function number 29 # Begin Function number 30 > comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > #TOP SIX TERM RADIUS ANALYSIS > global glob_h,glob_larger_float,glob_six_term_ord_save; > local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs; > if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 12 > rm0 := term6/term5; > rm1 := term5/term4; > rm2 := term4/term3; > rm3 := term3/term2; > rm4 := term2/term1; > nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2; > nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3; > dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; > dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; > ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; > ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; > if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 13 > rad_c := glob_larger_float; > ord_no := glob_larger_float; > else > if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2; > if (float_abs(rcs) <> glob__0) then # if number 15 > if (rcs > glob__0) then # if number 16 > rad_c := sqrt(rcs) * float_abs(glob_h); > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 16 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 15 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 14 > fi;# end if 13 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 12; > glob_six_term_ord_save := ord_no; > rad_c; > #BOTTOM SIX TERM RADIUS ANALYSIS > end; comp_rad_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no, ds1, rcs; global glob_h, glob_larger_float, glob_six_term_ord_save; if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and term2 <> glob__0 and term1 <> glob__0 then rm0 := term6/term5; rm1 := term5/term4; rm2 := term4/term3; rm3 := term3/term2; rm4 := term2/term1; nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1 + c(last_no - 3)*rm2; nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2 + c(last_no - 4)*rm3; dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; if float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0 then rad_c := glob_larger_float; ord_no := glob_larger_float else if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2; if float_abs(rcs) <> glob__0 then if glob__0 < rcs then rad_c := sqrt(rcs)*float_abs(glob_h) else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if; glob_six_term_ord_save := ord_no; rad_c end proc # End Function number 30 # Begin Function number 31 > comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > global glob_six_term_ord_save; > #TOP SIX TERM ORDER ANALYSIS > #TOP SAVED FROM SIX TERM RADIUS ANALYSIS > glob_six_term_ord_save; > #BOTTOM SIX TERM ORDER ANALYSIS > end; comp_ord_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) global glob_six_term_ord_save; glob_six_term_ord_save end proc # End Function number 31 # Begin Function number 32 > factorial_2 := proc(nnn) > ret := nnn!; > ret;; > end; Warning, `ret` is implicitly declared local to procedure `factorial_2` factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc # End Function number 32 # Begin Function number 33 > factorial_1 := proc(nnn) > global ATS_MAX_TERMS,array_fact_1; > local ret; > if (nnn <= ATS_MAX_TERMS) then # if number 12 > if (array_fact_1[nnn] = 0) then # if number 13 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 13; > else > ret := factorial_2(nnn); > fi;# end if 12; > ret; > end; factorial_1 := proc(nnn) local ret; global ATS_MAX_TERMS, array_fact_1; if nnn <= ATS_MAX_TERMS then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc # End Function number 33 # Begin Function number 34 > factorial_3 := proc(mmm,nnn) > global ATS_MAX_TERMS,array_fact_2; > local ret; > if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 12 > if (array_fact_2[mmm,nnn] = 0) then # if number 13 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 13; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 12; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global ATS_MAX_TERMS, array_fact_2; if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc # End Function number 34 # Begin Function number 35 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc # End Function number 35 # Begin Function number 36 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc # End Function number 36 # Begin Function number 37 > float_abs := proc(x) > abs(x); > end; float_abs := proc(x) abs(x) end proc # End Function number 37 # Begin Function number 38 > expt := proc(x,y) > x^y; > end; expt := proc(x, y) x^y end proc # End Function number 38 # Begin Function number 39 > neg := proc(x) > -x; > end; neg := proc(x) -x end proc # End Function number 39 # Begin Function number 40 > int_trunc := proc(x) > trunc(x); > end; int_trunc := proc(x) trunc(x) end proc # End Function number 40 # Begin Function number 41 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer))); > omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,""); > omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,""); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS))); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(glob__10, c(-glob_desired_digits_correct))* c(float_abs(c(estimated_answer))); omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, ""); omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "") ; omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := c(float_abs(desired_abs_gbl_error)/( sqrt(c(estimated_steps))*c(ATS_MAX_TERMS))); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc # End Function number 41 #END ATS LIBRARY BLOCK #BEGIN USER FUNCTION BLOCK #BEGIN BLOCK 3 #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(c(0.5) * c(x) + c(0.25) * ln(c(2.0) * c(x) + c(3.0))); > end; exact_soln_y := proc(x) return c(0.5)*c(x) + c(0.25)*ln(c(2.0)*c(x) + c(3.0)) 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_0D1, > array_const_0D2, > array_const_0D3, #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_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_0D1, array_const_0D2, array_const_0D3, 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_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_0D1, > array_const_0D2, > array_const_0D3, #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_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_0D1, array_const_0D2, array_const_0D3, 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_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_0D1, > array_const_0D2, > array_const_0D3, #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_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_0D1, array_const_0D2, array_const_0D3, 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_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_0D1, > array_const_0D2, > array_const_0D3, #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_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_0D1, array_const_0D2, array_const_0D3, 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_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_0D1, > array_const_0D2, > array_const_0D3, #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_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)*28*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_0D1, array_const_0D2, array_const_0D3, 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_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)*28*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_0D1, > array_const_0D2, > array_const_0D3, #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_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_0D1, array_const_0D2, array_const_0D3, 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_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_0D1, > array_const_0D2, > array_const_0D3, #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_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_0D1, array_const_0D2, array_const_0D3, 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_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_0D1, > array_const_0D2, > array_const_0D3, #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_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > # before write maple main top matter > # before generate constants assign > # before generate globals assign > #END OUTFILE1 > #BEGIN OUTFILE2 > #END OUTFILE2 > #BEGIN ATOMHDR1 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D1[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp3[1] := array_const_0D2[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp4[1] := array_tmp3[1] + array_const_0D3[1]; > #emit pre div LINEAR - LINEAR $eq_no = 1 i = 1 > array_tmp5[1] := array_tmp2[1] / array_tmp4[1]; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp6[1] := array_const_0D0[1] + array_tmp5[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_tmp6[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1)); > if (2 <= ATS_MAX_TERMS) then # if number 3 > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(1); > array_y_higher[2,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_0D1[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp3[2] := array_const_0D2[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp4[2] := array_tmp3[2]; > #emit pre div LINEAR - LINEAR $eq_no = 1 i = 2 > array_tmp5[2] := (array_tmp2[2] - array_tmp5[1] * array_tmp4[2]) / array_tmp4[1]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp6[2] := array_tmp5[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_tmp6[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y_higher[2,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre div LINEAR - LINEAR $eq_no = 1 i = 3 > array_tmp5[3] := neg( array_tmp5[2]) * array_tmp4[2] / array_tmp4[1]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp6[3] := array_tmp5[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_tmp6[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y_higher[2,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre div LINEAR - LINEAR $eq_no = 1 i = 4 > array_tmp5[4] := neg( array_tmp5[3]) * array_tmp4[2] / array_tmp4[1]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp6[4] := array_tmp5[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_tmp6[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y_higher[2,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre div LINEAR - LINEAR $eq_no = 1 i = 5 > array_tmp5[5] := neg( array_tmp5[4]) * array_tmp4[2] / array_tmp4[1]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp6[5] := array_tmp5[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_tmp6[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 LINEAR - LINEAR (NOP) $eq_no = 1 i = 1 > array_tmp5[kkk] := neg(array_tmp5[kkk-1]) * array_tmp4[2] / array_tmp4[1]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp6[kkk] := array_tmp5[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_tmp6[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_0D1, array_const_0D2, array_const_0D3, 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_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; array_tmp1[1] := array_const_0D1[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; array_tmp3[1] := array_const_0D2[1]*array_x[1]; array_tmp4[1] := array_tmp3[1] + array_const_0D3[1]; array_tmp5[1] := array_tmp2[1]/array_tmp4[1]; array_tmp6[1] := array_const_0D0[1] + array_tmp5[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp6[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_y[2] := temporary; array_y_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_y_higher[2, 1] := c(temporary) end if end if; kkk := 2; array_tmp1[2] := array_const_0D1[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_const_0D2[1]*array_x[2]; array_tmp4[2] := array_tmp3[2]; array_tmp5[2] := (-array_tmp4[2]*array_tmp5[1] + array_tmp2[2])/array_tmp4[1]; array_tmp6[2] := array_tmp5[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp6[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_tmp5[3] := neg(array_tmp5[2])*array_tmp4[2]/array_tmp4[1]; array_tmp6[3] := array_tmp5[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp6[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_tmp5[4] := neg(array_tmp5[3])*array_tmp4[2]/array_tmp4[1]; array_tmp6[4] := array_tmp5[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp6[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_tmp5[5] := neg(array_tmp5[4])*array_tmp4[2]/array_tmp4[1]; array_tmp6[5] := array_tmp5[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp6[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_tmp5[kkk] := neg(array_tmp5[kkk - 1])*array_tmp4[2]/array_tmp4[1]; array_tmp6[kkk] := array_tmp5[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_tmp6[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_0D1, > array_const_0D2, > array_const_0D3, > #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_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 30; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_y_init:= Array(0..(30),[]); > array_norms:= Array(0..(30),[]); > array_fact_1:= Array(0..(30),[]); > array_1st_rel_error:= Array(0..(2),[]); > array_last_rel_error:= Array(0..(2),[]); > array_est_rel_error:= Array(0..(2),[]); > array_max_est_error:= Array(0..(2),[]); > array_type_pole:= Array(0..(2),[]); > array_type_real_pole:= Array(0..(2),[]); > array_type_complex_pole:= Array(0..(2),[]); > array_est_digits:= Array(0..(2),[]); > array_y:= Array(0..(30),[]); > array_x:= Array(0..(30),[]); > array_tmp0:= Array(0..(30),[]); > array_tmp1:= Array(0..(30),[]); > array_tmp2:= Array(0..(30),[]); > array_tmp3:= Array(0..(30),[]); > array_tmp4:= Array(0..(30),[]); > array_tmp5:= Array(0..(30),[]); > array_tmp6:= 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_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_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_0D1); > array_const_0D1[1] := c(0.1); > zero_ats_ar(array_const_0D2); > array_const_0D2[1] := c(0.2); > zero_ats_ar(array_const_0D3); > array_const_0D3[1] := c(0.3); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_h := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 1000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 30; > glob_iolevel := INFO; > # set default block > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := (0.0); > glob_max_minutes := (15.0); > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/div_lin_linpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := c(0.1);"); > omniout_str(ALWAYS,"x_end := c(5.0) ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"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,""); > omniout_str(ALWAYS,"glob_type_given_pole := 1;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(-1.5);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(1.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=8;"); > omniout_str(ALWAYS,"glob_max_minutes:=(3.0);"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"glob_max_iter:=100000;"); > omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);"); > omniout_str(ALWAYS,"glob_look_poles:=false;"); > omniout_str(ALWAYS,"glob_h:=c(0.001);"); > omniout_str(ALWAYS,"glob_display_interval:=c(0.01);"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"return(c(0.5) * c(x) + c(0.25) * ln(c(2.0) * c(x) + c(3.0)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := glob__0; > glob_smallish_float := glob__0; > glob_large_float := c(1.0e100); > glob_larger_float := c( 1.1e100); > glob_almost_1 := c( 0.99); > # before second block > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN BLOCK 2 > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := c(0.1); > x_end := c(5.0) ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_type_given_pole := 1; > array_given_rad_poles[1,1] := c(-1.5); > array_given_rad_poles[1,2] := c(0.0); > array_given_ord_poles[1,1] := c(1.0); > array_given_ord_poles[1,2] := c(0.0); > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=8; > glob_max_minutes:=(3.0); > glob_subiter_method:=3; > glob_max_iter:=100000; > glob_upper_ratio_limit:=c(1.000001); > glob_lower_ratio_limit:=c(0.999999); > glob_look_poles:=false; > glob_h:=c(0.001); > glob_display_interval:=c(0.01); > #END OVERRIDE BLOCK > #END BLOCK 2 > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours); > # after second input block > glob_check_sign := c(my_check_sign(x_start,x_end)); > glob__pi := arccos(glob__m1); > glob_prec = expt(10.0,c(-Digits)); > if (glob_optimize) then # if number 9 > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > found_h := false; > glob_min_pole_est := glob_larger_float; > last_min_pole_est := glob_larger_float; > glob_least_given_sing := glob_larger_float; > glob_least_ratio_sing := glob_larger_float; > glob_least_3_sing := glob_larger_float; > glob_least_6_sing := glob_larger_float; > glob_min_h := float_abs(glob_min_h) * glob_check_sign; > glob_max_h := float_abs(glob_max_h) * glob_check_sign; > glob_h := float_abs(glob_min_h) * glob_check_sign; > glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign)); > display_max := c(x_end) - c(x_start)/glob__10; > if ((glob_display_interval) > (display_max)) then # if number 10 > glob_display_interval := c(display_max); > fi;# end if 10; > chk_data(); > min_value := glob_larger_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := glob_small_float; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := c(x_start); > array_x[2] := c(glob_h); > glob_next_display := c(x_start); > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 10 > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 10; > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > atomall(); > if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > glob_h := glob_check_sign * float_abs(glob_min_h); > glob_h_reason := 1; > found_h := true; > fi;# end if 10; > if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL"); > glob_h_reason := 2; > glob_h := glob_display_interval; > found_h := true; > fi;# end if 10; > if (glob_look_poles) then # if number 10 > check_for_pole(); > fi;# end if 10; > if ( not found_h) then # if number 10 > est_answer := est_size_answer(); > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (estimated_step_error < est_needed_step_err) then # if number 11 > omniout_str(ALWAYS,"Double H and LOOP"); > glob_h := glob_h*glob__2; > else > omniout_str(ALWAYS,"Found H for OPTIMAL"); > found_h := true; > glob_h_reason := 3; > glob_h := glob_h/glob__2; > fi;# end if 11; > fi;# end if 10; > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 10 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 10; > if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MAX H"); > glob_h := glob_check_sign * float_abs(glob_max_h); > glob_h_reason := 1; > found_h := true; > fi;# end if 10; > else > found_h := true; > glob_h := glob_h * glob_check_sign; > fi;# end if 9; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 9 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 9; > #BEGIN SOLUTION CODE > if (found_h) then # if number 9 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := c(x_start); > array_x[2] := c(glob_h); > glob_next_display := c(x_start); > glob_min_pole_est := glob_larger_float; > glob_least_given_sing := glob_larger_float; > glob_least_ratio_sing := glob_larger_float; > glob_least_3_sing := glob_larger_float; > glob_least_6_sing := glob_larger_float; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 10 > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 10; > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_iter < glob_max_iter) and (glob_check_sign * array_x[1] < glob_check_sign * x_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 10 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 10; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > track_estimated_error(); > atomall(); > track_estimated_error(); > display_alot(current_iter); > if (glob_look_poles) then # if number 10 > check_for_pole(); > fi;# end if 10; > if (reached_interval()) then # if number 10 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 10; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := ATS_MAX_TERMS; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 10 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 10; > if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 10; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; "); > 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,"2015-04-24T20:11:23-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"div_lin_lin") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; ") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_h_reason(html_log_file) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_float(html_log_file,glob_desired_digits_correct) > ; > if (array_est_digits[1] <> -16) then # if number 11 > logitem_integer(html_log_file,array_est_digits[1]) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_min_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_min_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > logitem_integer(html_log_file,ATS_MAX_TERMS) > ; > if (glob_type_given_pole = 0) then # if number 11 > logitem_str(html_log_file,"Not Given") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 4) then # if number 12 > logitem_str(html_log_file,"No Solution") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 5) then # if number 13 > logitem_str(html_log_file,"Some Pole") > ; > logitem_str(html_log_file,"????") > ; > elif > (glob_type_given_pole = 3) then # if number 14 > logitem_str(html_log_file,"No Pole") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 1) then # if number 15 > logitem_str(html_log_file,"Real Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > elif > (glob_type_given_pole = 2) then # if number 16 > logitem_str(html_log_file,"Complex Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > fi;# end if 16; > if (glob_least_ratio_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_ratio_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_3_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_3_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_6_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_6_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,(glob_clock_sec)) > ; > if (c(glob_percent_done) < glob__100) then # if number 16 > logitem_time(html_log_file,(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 16; > log_revs(html_log_file," 308.maple.seems.ok ") > ; > logitem_str(html_log_file,"div_lin_lin diffeq.mxt") > ; > logitem_str(html_log_file,"div_lin_lin 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_0D1, array_const_0D2, array_const_0D3, 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_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 30; Digits := 32; max_terms := 30; glob_html_log := true; array_y_init := Array(0 .. 30, []); array_norms := Array(0 .. 30, []); array_fact_1 := Array(0 .. 30, []); array_1st_rel_error := Array(0 .. 2, []); array_last_rel_error := Array(0 .. 2, []); array_est_rel_error := Array(0 .. 2, []); array_max_est_error := Array(0 .. 2, []); array_type_pole := Array(0 .. 2, []); array_type_real_pole := Array(0 .. 2, []); array_type_complex_pole := Array(0 .. 2, []); array_est_digits := Array(0 .. 2, []); array_y := Array(0 .. 30, []); array_x := Array(0 .. 30, []); array_tmp0 := Array(0 .. 30, []); array_tmp1 := Array(0 .. 30, []); array_tmp2 := Array(0 .. 30, []); array_tmp3 := Array(0 .. 30, []); array_tmp4 := Array(0 .. 30, []); array_tmp5 := Array(0 .. 30, []); array_tmp6 := 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_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_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_0D1); array_const_0D1[1] := c(0.1); zero_ats_ar(array_const_0D2); array_const_0D2[1] := c(0.2); zero_ats_ar(array_const_0D3); array_const_0D3[1] := c(0.3); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_h := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 1000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 30; glob_iolevel := INFO; glob_orig_start_sec := elapsed_time_seconds(); glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/div_lin_linpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = ( 0.1 * x + \ 0.2 ) / ( 0.2 * x + 0.3 ) ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := c(0.1);"); omniout_str(ALWAYS, "x_end := c(5.0) ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "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, ""); omniout_str(ALWAYS, "glob_type_given_pole := 1;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(-1.5);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(1.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=8;"); omniout_str(ALWAYS, "glob_max_minutes:=(3.0);"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "glob_max_iter:=100000;"); omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);"); omniout_str(ALWAYS, "glob_look_poles:=false;"); omniout_str(ALWAYS, "glob_h:=c(0.001);"); omniout_str(ALWAYS, "glob_display_interval:=c(0.01);"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "return(c(0.5) * c(x) + c(0.25) * ln(c(2.0) * c(x) + c(3.0)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := glob__0; glob_smallish_float := glob__0; glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := c(0.1); x_end := c(5.0); array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_type_given_pole := 1; array_given_rad_poles[1, 1] := c(-1.5); array_given_rad_poles[1, 2] := c(0.); array_given_ord_poles[1, 1] := c(1.0); array_given_ord_poles[1, 2] := c(0.); glob_desired_digits_correct := 8; glob_max_minutes := 3.0; glob_subiter_method := 3; glob_max_iter := 100000; glob_upper_ratio_limit := c(1.000001); glob_lower_ratio_limit := c(0.999999); glob_look_poles := false; glob_h := c(0.001); glob_display_interval := c(0.01); glob_last_good_h := glob_h; glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours; glob_check_sign := c(my_check_sign(x_start, x_end)); glob__pi := arccos(glob__m1); glob_prec = expt(10.0, c(-Digits)); if glob_optimize then omniout_str(ALWAYS, "START of Optimize"); found_h := false; glob_min_pole_est := glob_larger_float; last_min_pole_est := glob_larger_float; glob_least_given_sing := glob_larger_float; glob_least_ratio_sing := glob_larger_float; glob_least_3_sing := glob_larger_float; glob_least_6_sing := glob_larger_float; glob_min_h := float_abs(glob_min_h)*glob_check_sign; glob_max_h := float_abs(glob_max_h)*glob_check_sign; glob_h := float_abs(glob_min_h)*glob_check_sign; glob_display_interval := c(float_abs(c(glob_display_interval))*glob_check_sign); display_max := c(x_end) - c(x_start)/glob__10; if display_max < glob_display_interval then glob_display_interval := c(display_max) end if; chk_data(); min_value := glob_larger_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer) ; omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := glob_small_float; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y_higher[r_order, term_no] := array_y_init[it]*expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); glob_h := float_abs(glob_min_h)*glob_check_sign; glob_h_reason := 1; found_h := true end if; if glob_check_sign*glob_display_interval <= glob_check_sign*glob_h then omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL"); glob_h_reason := 2; glob_h := glob_display_interval; found_h := true end if; if glob_look_poles then check_for_pole() end if; if not found_h then est_answer := est_size_answer(); est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if estimated_step_error < est_needed_step_err then omniout_str(ALWAYS, "Double H and LOOP"); glob_h := glob_h*glob__2 else omniout_str(ALWAYS, "Found H for OPTIMAL"); found_h := true; glob_h_reason := 3; glob_h := glob_h/glob__2 end if end if; opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then omniout_str(ALWAYS, "SETTING H FOR MAX H"); glob_h := float_abs(glob_max_h)*glob_check_sign; glob_h_reason := 1; found_h := true end if else found_h := true; glob_h := glob_check_sign*glob_h end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); glob_min_pole_est := glob_larger_float; glob_least_given_sing := glob_larger_float; glob_least_ratio_sing := glob_larger_float; glob_least_3_sing := glob_larger_float; glob_least_6_sing := glob_larger_float; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and glob_clock_sec - glob_orig_start_sec < glob_max_sec do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); track_estimated_error(); atomall(); track_estimated_error(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); term_no := ATS_MAX_TERMS; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = ( 0.1 * x +\ 0.2 ) / ( 0.2 * x + 0.3 ) ; "); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2015-04-24T20:11:23-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "div_lin_lin"); logitem_str(html_log_file, "diff ( y , x , 1 ) = (\ 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; "); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_h_reason(html_log_file); logitem_integer(html_log_file, Digits); logitem_float(html_log_file, glob_desired_digits_correct); if array_est_digits[1] <> -16 then logitem_integer(html_log_file, array_est_digits[1]) else logitem_str(html_log_file, "Unknown") end if; if glob_min_good_digits <> -16 then logitem_integer(html_log_file, glob_min_good_digits) else logitem_str(html_log_file, "Unknown") end if; if glob_good_digits <> -16 then logitem_integer(html_log_file, glob_good_digits) else logitem_str(html_log_file, "Unknown") end if; logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); logitem_integer(html_log_file, ATS_MAX_TERMS); if glob_type_given_pole = 0 then logitem_str(html_log_file, "Not Given"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 4 then logitem_str(html_log_file, "No Solution"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 5 then logitem_str(html_log_file, "Some Pole"); logitem_str(html_log_file, "????") elif glob_type_given_pole = 3 then logitem_str(html_log_file, "No Pole"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 1 then logitem_str(html_log_file, "Real Sing"); logitem_float(html_log_file, glob_least_given_sing) elif glob_type_given_pole = 2 then logitem_str(html_log_file, "Complex Sing"); logitem_float(html_log_file, glob_least_given_sing) end if; if glob_least_ratio_sing < glob_large_float then logitem_float(html_log_file, glob_least_ratio_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_3_sing < glob_large_float then logitem_float(html_log_file, glob_least_3_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_6_sing < glob_large_float then logitem_float(html_log_file, glob_least_6_sing) else logitem_str(html_log_file, "NONE") end if; logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, glob_clock_sec); if c(glob_percent_done) < glob__100 then logitem_time(html_log_file, glob_total_exp_sec); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 308.maple.seems.ok "); logitem_str(html_log_file, "div_lin_lin diffeq.mxt"); logitem_str(html_log_file, "div_lin_lin maple results"); logitem_str(html_log_file, "OK"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc # End Function number 12 > main(); ##############ECHO OF PROBLEM################# ##############temp/div_lin_linpostode.ode################# diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := c(0.1); x_end := c(5.0) ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_type_given_pole := 1; array_given_rad_poles[1,1] := c(-1.5); array_given_rad_poles[1,2] := c(0.0); array_given_ord_poles[1,1] := c(1.0); array_given_ord_poles[1,2] := c(0.0); #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=8; glob_max_minutes:=(3.0); glob_subiter_method:=3; glob_max_iter:=100000; glob_upper_ratio_limit:=c(1.000001); glob_lower_ratio_limit:=c(0.999999); glob_look_poles:=false; glob_h:=c(0.001); glob_display_interval:=c(0.01); #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(c(0.5) * c(x) + c(0.25) * ln(c(2.0) * c(x) + c(3.0))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.34078770245142021576704228815162 y[1] (numeric) = 0.34078770245142021576704228815162 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 32 h = 0.001 memory used=4.2MB, alloc=40.3MB, time=0.09 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (closed_form) = 0.3473453398890792343233386968357 y[1] (numeric) = 0.3473453398890792343233386968357 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = 0.35389333245105950409486557030942 y[1] (numeric) = 0.35389333245105950409486557030942 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = 0.36043179884465406886154539455255 y[1] (numeric) = 0.36043179884465406886154539455253 absolute error = 2e-32 relative error = 5.5488999761144799368372389507983e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = 0.3669608555990130910206192070108 y[1] (numeric) = 0.36696085559901309102061920701078 absolute error = 2e-32 relative error = 5.4501725987510991193494552431563e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 0.37348061711810863785979934005082 y[1] (numeric) = 0.37348061711810863785979934005081 absolute error = 1e-32 relative error = 2.6775151217118245687315054392236e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (closed_form) = 0.37999119573209929356848838920975 y[1] (numeric) = 0.37999119573209929356848838920975 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (closed_form) = 0.38649270174715226216024999720855 y[1] (numeric) = 0.38649270174715226216024999720855 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (closed_form) = 0.39298524349377821653338588920742 y[1] (numeric) = 0.39298524349377821653338588920742 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (closed_form) = 0.39946892737373185337205602380502 y[1] (numeric) = 0.39946892737373185337205602380501 absolute error = 1e-32 relative error = 2.5033236166186919093485788124559e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (closed_form) = 0.40594385790552892641219382116172 y[1] (numeric) = 0.40594385790552892641219382116172 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (closed_form) = 0.4124101377686284460451917794556 y[1] (numeric) = 0.41241013776862844604519177945558 absolute error = 2e-32 relative error = 4.8495413105534420906762168276315e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (closed_form) = 0.4188678678463267459221389920879 y[1] (numeric) = 0.4188678678463267459221389920879 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (closed_form) = 0.4253171472674082220786874001326 y[1] (numeric) = 0.42531714726740822207868740013258 absolute error = 2e-32 relative error = 4.7023733062484469139585942688441e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (closed_form) = 0.43175807344659574234424965070802 y[1] (numeric) = 0.43175807344659574234424965070797 absolute error = 5e-32 relative error = 1.1580559362993477818589108157180e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (closed_form) = 0.43819074212384199892203015549625 y[1] (numeric) = 0.43819074212384199892203015549621 absolute error = 4e-32 relative error = 9.1284447969225126835283763310228e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (closed_form) = 0.44461524740250143077803031897182 y[1] (numeric) = 0.44461524740250143077803031897178 absolute error = 4e-32 relative error = 8.9965425688131625049674596617487e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (closed_form) = 0.45103168178642077084813620568292 y[1] (numeric) = 0.45103168178642077084813620568288 absolute error = 4e-32 relative error = 8.8685566037335254934820245117692e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (closed_form) = 0.45744013621598477227907421855438 y[1] (numeric) = 0.45744013621598477227907421855435 absolute error = 3e-32 relative error = 6.5582351929510642356442767897795e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=44.6MB, alloc=44.3MB, time=0.56 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (closed_form) = 0.4638407001031522343897634105277 y[1] (numeric) = 0.4638407001031522343897634105277 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (closed_form) = 0.47023346136551607940174081551925 y[1] (numeric) = 0.47023346136551607940174081551925 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (closed_form) = 0.47661850645941992205508406268062 y[1] (numeric) = 0.4766185064594199220550840626806 absolute error = 2e-32 relative error = 4.1962281633944133597028019383599e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (closed_form) = 0.48299592041216232298933037963902 y[1] (numeric) = 0.48299592041216232298933037963902 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (closed_form) = 0.4893657868533187203819708881094 y[1] (numeric) = 0.48936578685331872038197088810937 absolute error = 3e-32 relative error = 6.1303836120019001507308765003911e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (closed_form) = 0.49572818804520989010992460206855 y[1] (numeric) = 0.4957281880452098901099246020685 absolute error = 5e-32 relative error = 1.0086172464221472213847157327777e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.35 y[1] (closed_form) = 0.50208320491254469008752605408678 y[1] (numeric) = 0.50208320491254469008752605408674 absolute error = 4e-32 relative error = 7.9668070169699055691017889561757e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (closed_form) = 0.50843091707126379703072272375312 y[1] (numeric) = 0.50843091707126379703072272375311 absolute error = 1e-32 relative error = 1.9668355452503605930606054064859e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (closed_form) = 0.51477140285661014142318185198192 y[1] (numeric) = 0.51477140285661014142318185198191 absolute error = 1e-32 relative error = 1.9426098544921512516606577088354e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (closed_form) = 0.5211047393504507867591660311945 y[1] (numeric) = 0.52110473935045078675916603119447 absolute error = 3e-32 relative error = 5.7570000298585939556452842297696e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (closed_form) = 0.52743100240787408016808441657505 y[1] (numeric) = 0.52743100240787408016808441657503 absolute error = 2e-32 relative error = 3.7919651876158688280363539421421e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (closed_form) = 0.53375026668308502135206702466542 y[1] (numeric) = 0.53375026668308502135206702466538 absolute error = 4e-32 relative error = 7.4941414546870956021399990605526e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (closed_form) = 0.54006260565462095355779979107295 y[1] (numeric) = 0.54006260565462095355779979107291 absolute error = 4e-32 relative error = 7.4065487188314362463704829741108e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (closed_form) = 0.54636809164990887231997179444025 y[1] (numeric) = 0.54636809164990887231997179444023 absolute error = 2e-32 relative error = 3.6605358741950859240699500638765e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (closed_form) = 0.55266679586918487330904506636812 y[1] (numeric) = 0.55266679586918487330904506636811 absolute error = 1e-32 relative error = 1.8094085034135070466757859772017e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (closed_form) = 0.5589587884087955182288007388129 y[1] (numeric) = 0.55895878840879551822880073881288 absolute error = 2e-32 relative error = 3.5780813209744121459764458918722e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (closed_form) = 0.56524413828390018585768530595088 y[1] (numeric) = 0.56524413828390018585768530595084 absolute error = 4e-32 relative error = 7.0765882015939726460801759860451e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=85.0MB, alloc=44.3MB, time=1.02 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (closed_form) = 0.57152291345059279260660473547305 y[1] (numeric) = 0.57152291345059279260660473547302 absolute error = 3e-32 relative error = 5.2491333757510756763933776896717e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (closed_form) = 0.57779518082746061204026163531308 y[1] (numeric) = 0.57779518082746061204026163531305 absolute error = 3e-32 relative error = 5.1921513012685555917006440094453e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (closed_form) = 0.58406100631659729441272884633945 y[1] (numeric) = 0.58406100631659729441272884633944 absolute error = 1e-32 relative error = 1.7121499110281948364474088851210e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (closed_form) = 0.5903204548240865841978426259895 y[1] (numeric) = 0.59032045482408658419784262598949 absolute error = 1e-32 relative error = 1.6939951713141915045756633720947e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (closed_form) = 0.5965735902799726547086160607291 y[1] (numeric) = 0.59657359027997265470861606072908 absolute error = 2e-32 relative error = 3.3524782735712416600528720462830e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (closed_form) = 0.60282047565773242311164161134392 y[1] (numeric) = 0.60282047565773242311164161134392 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (closed_form) = 0.60906117299326467542066990011515 y[1] (numeric) = 0.60906117299326467542066990011515 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (closed_form) = 0.61529574340341031841746849697362 y[1] (numeric) = 0.61529574340341031841746849697363 absolute error = 1e-32 relative error = 1.6252347114716890663455855788701e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (closed_form) = 0.62152424710401758296512332745038 y[1] (numeric) = 0.62152424710401758296512332745037 absolute error = 1e-32 relative error = 1.6089476873339764497493446905842e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (closed_form) = 0.62774674342756552996219297958825 y[1] (numeric) = 0.62774674342756552996219297958825 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (closed_form) = 0.63396329084035875539177091215028 y[1] (numeric) = 0.63396329084035875539177091215026 absolute error = 2e-32 relative error = 3.1547567956953351440991746565250e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.57 y[1] (closed_form) = 0.64017394695930575374462312943618 y[1] (numeric) = 0.64017394695930575374462312943618 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (closed_form) = 0.64637876856829297877591628487188 y[1] (numeric) = 0.64637876856829297877591628487188 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (closed_form) = 0.6525778116341662363630550554856 y[1] (numeric) = 0.65257781163416623636305505548562 absolute error = 2e-32 relative error = 3.0647686212187610193784367730060e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (closed_form) = 0.65877113132233065547495966178488 y[1] (numeric) = 0.6587711313223306554749596617849 absolute error = 2e-32 relative error = 3.0359557438187411935966217021652e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (closed_form) = 0.66495878201198010928080136938592 y[1] (numeric) = 0.66495878201198010928080136938596 absolute error = 4e-32 relative error = 6.0154104407751617987513698675692e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (closed_form) = 0.67114081731096659859004564850872 y[1] (numeric) = 0.67114081731096659859004564850875 absolute error = 3e-32 relative error = 4.4700008144639175641606399747784e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (closed_form) = 0.67731729007031976352648724538125 y[1] (numeric) = 0.6773172900703197635264872453813 absolute error = 5e-32 relative error = 7.3820646147699772464868363780511e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=125.5MB, alloc=44.3MB, time=1.47 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (closed_form) = 0.68348825239842635602572003764272 y[1] (numeric) = 0.68348825239842635602572003764278 absolute error = 6e-32 relative error = 8.7784976244221022545403778257149e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (closed_form) = 0.68965375567487918486371276466538 y[1] (numeric) = 0.68965375567487918486371276466542 absolute error = 4e-32 relative error = 5.8000119147987422858892473598579e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (closed_form) = 0.6958138505640047359546703218079 y[1] (numeric) = 0.69581385056400473595467032180792 absolute error = 2e-32 relative error = 2.8743319759715377221164928910393e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (closed_form) = 0.70196858702807837310394157001875 y[1] (numeric) = 0.70196858702807837310394157001878 absolute error = 3e-32 relative error = 4.2736955120756729572562748155751e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (closed_form) = 0.7081180143402357377939494464392 y[1] (numeric) = 0.70811801434023573779394944643925 absolute error = 5e-32 relative error = 7.0609699213182362132075413210781e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (closed_form) = 0.71426218109708869046715082661262 y[1] (numeric) = 0.71426218109708869046715082661266 absolute error = 4e-32 relative error = 5.6001845062776541152345779376886e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (closed_form) = 0.72040113523105386971960409154928 y[1] (numeric) = 0.72040113523105386971960409154931 absolute error = 3e-32 relative error = 4.1643465748257206855079960431021e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (closed_form) = 0.72653492402240168942106781788198 y[1] (numeric) = 0.72653492402240168942106781788202 absolute error = 4e-32 relative error = 5.5055853032560697494498723481948e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (closed_form) = 0.7326635941110333466404555603754 y[1] (numeric) = 0.73266359411103334664045556037545 absolute error = 5e-32 relative error = 6.8244144245582133122611560246892e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (closed_form) = 0.73878719150799317500433860545315 y[1] (numeric) = 0.73878719150799317500433860545321 absolute error = 6e-32 relative error = 8.1214185478134187174302761934719e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (closed_form) = 0.74490576160672344839319064070588 y[1] (numeric) = 0.74490576160672344839319064070595 absolute error = 7e-32 relative error = 9.3971618435348918736333921413257e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (closed_form) = 0.75101934919406851834331458809672 y[1] (numeric) = 0.75101934919406851834331458809679 absolute error = 7e-32 relative error = 9.3206653164286880337975993834208e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (closed_form) = 0.7571279984610349548451532067909 y[1] (numeric) = 0.75712799846103495484515320679098 absolute error = 8e-32 relative error = 1.0566245094965556497304083454238e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (closed_form) = 0.76323175301331415409865769723072 y[1] (numeric) = 0.7632317530133141540986576972308 absolute error = 8e-32 relative error = 1.0481744199471801119502847748469e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (closed_form) = 0.76933065588157367790499653095405 y[1] (numeric) = 0.7693306558815736779049965309541 absolute error = 5e-32 relative error = 6.4991560673875852280896736283144e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (closed_form) = 0.77542474953152339745562120400552 y[1] (numeric) = 0.77542474953152339745562120400557 absolute error = 5e-32 relative error = 6.4480789438572525787398350556623e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (closed_form) = 0.781514075873762329051498374646 y[1] (numeric) = 0.78151407587376232905149837464605 absolute error = 5e-32 relative error = 6.3978374214307153377344680912011e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=165.9MB, alloc=44.3MB, time=1.92 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (closed_form) = 0.78759867627341187048594769260508 y[1] (numeric) = 0.78759867627341187048594769260511 absolute error = 3e-32 relative error = 3.8090465237889270717398623391812e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (closed_form) = 0.79367859155954097420405440220648 y[1] (numeric) = 0.79367859155954097420405440220652 absolute error = 4e-32 relative error = 5.0398234783430264671350784833908e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (closed_form) = 0.79975386203438862667086852168958 y[1] (numeric) = 0.79975386203438862667086852168962 absolute error = 4e-32 relative error = 5.0015388357424449026265567005295e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.84 y[1] (closed_form) = 0.8058245274823888424106148122395 y[1] (numeric) = 0.80582452748238884241061481223954 absolute error = 4e-32 relative error = 4.9638598275198558257760037690398e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (closed_form) = 0.81189062717900322570073980377195 y[1] (numeric) = 0.81189062717900322570073980377199 absolute error = 4e-32 relative error = 4.9267719888557007835770719685926e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (closed_form) = 0.81795219989936600270794095718138 y[1] (numeric) = 0.8179521998993660027079409571814 absolute error = 2e-32 relative error = 2.4451306570800387503369062001845e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (closed_form) = 0.82400928392674628173735999762335 y[1] (numeric) = 0.82400928392674628173735999762337 absolute error = 2e-32 relative error = 2.4271571194794915487985102997064e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (closed_form) = 0.83006191706083215903834217371598 y[1] (numeric) = 0.83006191706083215903834217371601 absolute error = 3e-32 relative error = 3.6141882169738683814240610526873e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (closed_form) = 0.83611013662584115208610320158785 y[1] (numeric) = 0.83611013662584115208610320158787 absolute error = 2e-32 relative error = 2.3920293659769358253219447766002e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (closed_form) = 0.84215397947846131126154556701772 y[1] (numeric) = 0.84215397947846131126154556701776 absolute error = 4e-32 relative error = 4.7497252254001880581543698255129e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (closed_form) = 0.84819348201562723421191513270008 y[1] (numeric) = 0.84819348201562723421191513270011 absolute error = 3e-32 relative error = 3.5369288536276768799945574176821e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (closed_form) = 0.85422868018213508473059212236948 y[1] (numeric) = 0.8542286801821350847305921223695 absolute error = 2e-32 relative error = 2.3412934339474159566134075528369e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (closed_form) = 0.86025960947810059958936884917552 y[1] (numeric) = 0.86025960947810059958936884917554 absolute error = 2e-32 relative error = 2.3248795804947221212525776444570e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (closed_form) = 0.86628630496626395224177563960785 y[1] (numeric) = 0.86628630496626395224177563960786 absolute error = 1e-32 relative error = 1.1543527749049932173913723201890e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (closed_form) = 0.8723088012791452315481785080505 y[1] (numeric) = 0.87230880127914523154817850805051 absolute error = 1e-32 relative error = 1.1463830223122931047828947128783e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (closed_form) = 0.8783271326260541865151224858769 y[1] (numeric) = 0.8783271326260541865151224858769 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (closed_form) = 0.88434133279995778436094102138565 y[1] (numeric) = 0.88434133279995778436094102138567 absolute error = 2e-32 relative error = 2.2615701944719681133861804866640e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (closed_form) = 0.89035143518420902889052747525158 y[1] (numeric) = 0.8903514351842090288905274752516 absolute error = 2e-32 relative error = 2.2463040109394674245141682726475e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=206.4MB, alloc=44.3MB, time=2.38 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (closed_form) = 0.89635747275914038906299166807582 y[1] (numeric) = 0.89635747275914038906299166807585 absolute error = 3e-32 relative error = 3.3468789976899405771304854119383e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = 0.90235947810852509365018983330655 y[1] (numeric) = 0.90235947810852509365018983330655 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = 0.90835748342590945689995861277442 y[1] (numeric) = 0.90835748342590945689995861277444 absolute error = 2e-32 relative error = 2.2017763231904180195703648003241e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (closed_form) = 0.9143515205208193120278891680735 y[1] (numeric) = 0.91435152052081931202788916807352 absolute error = 2e-32 relative error = 2.1873425647728892606266627244246e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (closed_form) = 0.9203416208248435440624864054662 y[1] (numeric) = 0.92034162082484354406248640546619 absolute error = 1e-32 relative error = 1.0865530552706762594074716735526e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (closed_form) = 0.92632781539759763096148053531598 y[1] (numeric) = 0.92632781539759763096148053531599 absolute error = 1e-32 relative error = 1.0795314394945388281453412879012e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (closed_form) = 0.93231013493257002190669710002782 y[1] (numeric) = 0.93231013493257002190669710002782 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (closed_form) = 0.93828860976285410417977654593872 y[1] (numeric) = 0.93828860976285410417977654593872 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (closed_form) = 0.94426326986676843493326088171268 y[1] (numeric) = 0.94426326986676843493326088171268 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (closed_form) = 0.950234144873367841416642270954 y[1] (numeric) = 0.95023414487336784141664227095402 absolute error = 2e-32 relative error = 2.1047444051450375184000163668647e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.09 y[1] (closed_form) = 0.95620126406784792271367440664102 y[1] (numeric) = 0.95620126406784792271367440664105 absolute error = 3e-32 relative error = 3.1374148024417722616221019537706e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (closed_form) = 0.96216465639684541771749005744932 y[1] (numeric) = 0.96216465639684541771749005744936 absolute error = 4e-32 relative error = 4.1572925937431207035131246513119e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (closed_form) = 0.9681243504736368378387529295741 y[1] (numeric) = 0.96812435047363683783875292957413 absolute error = 3e-32 relative error = 3.0987754811996060009360973465050e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (closed_form) = 0.9740803745832376987369763361793 y[1] (numeric) = 0.97408037458323769873697633617931 absolute error = 1e-32 relative error = 1.0266093292638731855798870520207e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (closed_form) = 0.98003275668740462311679386907362 y[1] (numeric) = 0.98003275668740462311679386907365 absolute error = 3e-32 relative error = 3.0611221712019699753693212986263e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (closed_form) = 0.9859815244295425262725335978379 y[1] (numeric) = 0.98598152442954252627253359783794 absolute error = 4e-32 relative error = 4.0568711490960973806798290716580e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (closed_form) = 0.99192670513951903753161942108618 y[1] (numeric) = 0.99192670513951903753161942108621 absolute error = 3e-32 relative error = 3.0244170103052485613117491624933e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop memory used=246.9MB, alloc=44.3MB, time=2.83 x[1] = 1.16 y[1] (closed_form) = 0.99786832583838825397821537721968 y[1] (numeric) = 0.99786832583838825397821537721968 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (closed_form) = 1.0038064132430258677735774974204 y[1] (numeric) = 1.0038064132430258677735774974204 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (closed_form) = 1.0097409937706776549714463628424 y[1] (numeric) = 1.0097409937706776549714463628424 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (closed_form) = 1.0156720935434232619003005981462 y[1] (numeric) = 1.0156720935434232619003005981461 absolute error = 1e-31 relative error = 9.8456973107457615769221698246558e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (closed_form) = 1.0215997383925571748962440943854 y[1] (numeric) = 1.0215997383925571748962440943852 absolute error = 2e-31 relative error = 1.9577138920835210367571203268701e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (closed_form) = 1.0275239538628887103695298213238 y[1] (numeric) = 1.0275239538628887103695298213237 absolute error = 1e-31 relative error = 9.7321332144188488046522967114178e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (closed_form) = 1.0334447652169628148249280789488 y[1] (numeric) = 1.0334447652169628148249280789487 absolute error = 1e-31 relative error = 9.6763758805247673315731629999004e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (closed_form) = 1.0393621974392034184838336585051 y[1] (numeric) = 1.0393621974392034184838336585051 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (closed_form) = 1.0452762752399810415284178653819 y[1] (numeric) = 1.0452762752399810415284178653818 absolute error = 1e-31 relative error = 9.5668487239932214849813665290801e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (closed_form) = 1.0511870230596063086611778641268 y[1] (numeric) = 1.0511870230596063086611778641268 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (closed_form) = 1.0570944650722509856044278809346 y[1] (numeric) = 1.0570944650722509856044278809346 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (closed_form) = 1.0629986251897981103126616904035 y[1] (numeric) = 1.0629986251897981103126616904034 absolute error = 1e-31 relative error = 9.4073498902357496161231905163831e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (closed_form) = 1.0688995270656227519968165631058 y[1] (numeric) = 1.0688995270656227519968165631056 absolute error = 2e-31 relative error = 1.8710832490406877764319613021822e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (closed_form) = 1.0747971940983048925252260026192 y[1] (numeric) = 1.0747971940983048925252260026188 absolute error = 4e-31 relative error = 3.7216323432587462937473429416765e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (closed_form) = 1.0806916494352758873347644132833 y[1] (numeric) = 1.0806916494352758873347644132828 absolute error = 5e-31 relative error = 4.6266666376230354065653396655178e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (closed_form) = 1.0865829159763999266219718841956 y[1] (numeric) = 1.0865829159763999266219718841952 absolute error = 4e-31 relative error = 3.6812653145808139427328314115469e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (closed_form) = 1.0924710163774918822536693100606 y[1] (numeric) = 1.0924710163774918822536693100601 absolute error = 5e-31 relative error = 4.5767804592010361671639880828864e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (closed_form) = 1.0983559730537728915068090897212 y[1] (numeric) = 1.0983559730537728915068090897206 absolute error = 6e-31 relative error = 5.4627098565487150089460380271683e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=287.4MB, alloc=44.3MB, time=3.28 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (closed_form) = 1.1042378081832649953862919968797 y[1] (numeric) = 1.1042378081832649953862919968792 absolute error = 5e-31 relative error = 4.5280101468597552687008373140746e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (closed_form) = 1.1101165437101261168465703035315 y[1] (numeric) = 1.1101165437101261168465703035309 absolute error = 6e-31 relative error = 5.4048379280497610150189073170030e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (closed_form) = 1.1159922013479266327284780882695 y[1] (numeric) = 1.1159922013479266327284780882688 absolute error = 7e-31 relative error = 6.2724452657869866598656005894511e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (closed_form) = 1.1218648025828687625883413321425 y[1] (numeric) = 1.1218648025828687625883413321418 absolute error = 7e-31 relative error = 6.2396110332402831174862675328267e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (closed_form) = 1.1277343686769499678144750733064 y[1] (numeric) = 1.1277343686769499678144750733056 absolute error = 8e-31 relative error = 7.0938691080112631059335388127823e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (closed_form) = 1.1336009206710715254700796119589 y[1] (numeric) = 1.1336009206710715254700796119581 absolute error = 8e-31 relative error = 7.0571572888844715234229047609328e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (closed_form) = 1.1394644793880934131456281747839 y[1] (numeric) = 1.1394644793880934131456281747831 absolute error = 8e-31 relative error = 7.0208419347096273023905163610276e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (closed_form) = 1.145325065435836613723304017679 y[1] (numeric) = 1.1453250654358366137233040176781 absolute error = 9e-31 relative error = 7.8580311141406674171411499070347e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (closed_form) = 1.1511826992100339223269555781111 y[1] (numeric) = 1.1511826992100339223269555781102 absolute error = 9e-31 relative error = 7.8180466108255376112053180955754e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (closed_form) = 1.1570374008972303118302723687255 y[1] (numeric) = 1.1570374008972303118302723687246 absolute error = 9e-31 relative error = 7.7784866703711617093581119686991e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (closed_form) = 1.1628891904776338881011080143391 y[1] (numeric) = 1.1628891904776338881011080143381 absolute error = 1.0e-30 relative error = 8.5992716089249195502382474619026e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (closed_form) = 1.1687380877279184416495147297588 y[1] (numeric) = 1.1687380877279184416495147297578 absolute error = 1.0e-30 relative error = 8.5562369405111697535352911329841e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (closed_form) = 1.1745841122239785785002603118738 y[1] (numeric) = 1.1745841122239785785002603118728 absolute error = 1.0e-30 relative error = 8.5136516797131037635996097370882e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (closed_form) = 1.1804272833436383899072321252056 y[1] (numeric) = 1.1804272833436383899072321252045 absolute error = 1.1e-30 relative error = 9.3186595694753616004416477377786e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.48 y[1] (closed_form) = 1.1862676202693145979477274021629 y[1] (numeric) = 1.1862676202693145979477274021618 absolute error = 1.1e-30 relative error = 9.2727811263218199271993651873644e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (closed_form) = 1.1921051419906350920603723713662 y[1] (numeric) = 1.1921051419906350920603723713652 absolute error = 1.0e-30 relative error = 8.3885218239236130521032530539099e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (closed_form) = 1.1979398673070137502031193395952 y[1] (numeric) = 1.197939867307013750203119339594 absolute error = 1.2e-30 relative error = 1.0017197296368618719254396836305e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.51 y[1] (closed_form) = 1.2037718148301824174898611172196 y[1] (numeric) = 1.2037718148301824174898611172185 absolute error = 1.1e-30 relative error = 9.1379444712715620769233793040335e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=327.9MB, alloc=44.3MB, time=3.75 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (closed_form) = 1.209601002986680894898679408258 y[1] (numeric) = 1.2096010029866808948986794082567 absolute error = 1.3e-30 relative error = 1.0747345585776721636380103164016e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.53 y[1] (closed_form) = 1.2154274500203057709151731789812 y[1] (numeric) = 1.2154274500203057709151731789798 absolute error = 1.4e-30 relative error = 1.1518581384488318348527344760012e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (closed_form) = 1.2212511739945189097648012824525 y[1] (numeric) = 1.2212511739945189097648012824511 absolute error = 1.4e-30 relative error = 1.1463653258328686214989816110911e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (closed_form) = 1.2270721927948163911833494121853 y[1] (numeric) = 1.2270721927948163911833494121839 absolute error = 1.4e-30 relative error = 1.1409271664866906110524946959829e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.56 y[1] (closed_form) = 1.2328905241310586784596266063164 y[1] (numeric) = 1.232890524131058678459626606315 absolute error = 1.4e-30 relative error = 1.1355428341755810727754846670565e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (closed_form) = 1.238706185539762773744927944843 y[1] (numeric) = 1.2387061855397627737449279448414 absolute error = 1.6e-30 relative error = 1.2916703078404379258638159425732e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (closed_form) = 1.2445191943863571023457524441035 y[1] (numeric) = 1.244519194386357102345752444102 absolute error = 1.5e-30 relative error = 1.2052847451176632301701574551323e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.59 y[1] (closed_form) = 1.2503295678673998508862741910164 y[1] (numeric) = 1.2503295678673998508862741910148 absolute error = 1.6e-30 relative error = 1.2796626114577204440665946914547e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (closed_form) = 1.256137323012761467832101247829 y[1] (numeric) = 1.2561373230127614678321012478276 absolute error = 1.4e-30 relative error = 1.1145278261792217991426022853878e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (closed_form) = 1.2619424766877720188943111943805 y[1] (numeric) = 1.2619424766877720188943111943791 absolute error = 1.4e-30 relative error = 1.1094008053953365528131050340862e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (closed_form) = 1.267745045595334074270419563738 y[1] (numeric) = 1.2677450455953340742704195637367 absolute error = 1.3e-30 relative error = 1.0254427769343156641377532159000e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (closed_form) = 1.2735450462780017895150036303367 y[1] (numeric) = 1.2735450462780017895150036303354 absolute error = 1.3e-30 relative error = 1.0207726878600125826149036588330e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.64 y[1] (closed_form) = 1.2793424951200268270557316424878 y[1] (numeric) = 1.2793424951200268270557316424864 absolute error = 1.4e-30 relative error = 1.0943121215313442615255006872239e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.65 y[1] (closed_form) = 1.285137408349371750969462940651 y[1] (numeric) = 1.2851374083493717509694629406495 absolute error = 1.5e-30 relative error = 1.1671903644347240561086794640607e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (closed_form) = 1.2909298020396915135971647491218 y[1] (numeric) = 1.2909298020396915135971647491202 absolute error = 1.6e-30 relative error = 1.2394167347225017226933678675994e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.67 y[1] (closed_form) = 1.296719692112283638895252845347 y[1] (numeric) = 1.2967196921122836388952528453456 absolute error = 1.4e-30 relative error = 1.0796473659773597893540643792844e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.68 y[1] (closed_form) = 1.3025070943380076940845489273748 y[1] (numeric) = 1.3025070943380076940845489273734 absolute error = 1.4e-30 relative error = 1.0748501916694300670177236685045e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=368.3MB, alloc=44.3MB, time=4.20 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (closed_form) = 1.3082920243391746281566162056041 y[1] (numeric) = 1.3082920243391746281566162056028 absolute error = 1.3e-30 relative error = 9.9366194688577806284297648769449e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (closed_form) = 1.3140744975914065431213503185162 y[1] (numeric) = 1.3140744975914065431213503185147 absolute error = 1.5e-30 relative error = 1.1414877944510604481113248865216e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (closed_form) = 1.3198545294254674515202233165088 y[1] (numeric) = 1.3198545294254674515202233165073 absolute error = 1.5e-30 relative error = 1.1364888830990714213981176450769e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (closed_form) = 1.3256321350290655616776467272002 y[1] (numeric) = 1.3256321350290655616776467271987 absolute error = 1.5e-30 relative error = 1.1315356352364762802039187359654e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.73 y[1] (closed_form) = 1.3314073294486276204099528154626 y[1] (numeric) = 1.331407329448627620409952815461 absolute error = 1.6e-30 relative error = 1.2017359110247680466807551500255e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (closed_form) = 1.337180127591045831449173600674 y[1] (numeric) = 1.3371801275910458314491736006724 absolute error = 1.6e-30 relative error = 1.1965478449656808159425647160837e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (closed_form) = 1.3429505442253978566590638300268 y[1] (numeric) = 1.3429505442253978566590638300251 absolute error = 1.7e-30 relative error = 1.2658694002619025338960453893889e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.76 y[1] (closed_form) = 1.3487185939846403962158534249171 y[1] (numeric) = 1.3487185939846403962158534249154 absolute error = 1.7e-30 relative error = 1.2604556707248599700775049658830e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (closed_form) = 1.3544842913672768332884527253053 y[1] (numeric) = 1.3544842913672768332884527253035 absolute error = 1.8e-30 relative error = 1.3289190664463149640020081628796e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (closed_form) = 1.3602476507389994183749272373754 y[1] (numeric) = 1.3602476507389994183749272373735 absolute error = 1.9e-30 relative error = 1.3968044708386464100612431049977e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.79 y[1] (closed_form) = 1.3660086863343064583268881563262 y[1] (numeric) = 1.3660086863343064583268881563243 absolute error = 1.9e-30 relative error = 1.3909135564127800978834970098271e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (closed_form) = 1.3717674122580949652141073704154 y[1] (numeric) = 1.3717674122580949652141073704135 absolute error = 1.9e-30 relative error = 1.3850744543292294341884750805410e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.81 y[1] (closed_form) = 1.3775238424872292105414665129165 y[1] (numeric) = 1.3775238424872292105414665129147 absolute error = 1.8e-30 relative error = 1.3066924466076437396564932618036e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.82 y[1] (closed_form) = 1.3832779908720856209227964195743 y[1] (numeric) = 1.3832779908720856209227964195724 absolute error = 1.9e-30 relative error = 1.3735489269240434680780287896857e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (closed_form) = 1.3890298711380744421349588392415 y[1] (numeric) = 1.3890298711380744421349588392398 absolute error = 1.7e-30 relative error = 1.2238757677739055880405350554020e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (closed_form) = 1.3947794968871385895145580275731 y[1] (numeric) = 1.3947794968871385895145580275714 absolute error = 1.7e-30 relative error = 1.2188306494281360562882913409339e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.85 y[1] (closed_form) = 1.4005268815992300939130201354198 y[1] (numeric) = 1.4005268815992300939130201354181 absolute error = 1.7e-30 relative error = 1.2138288970639451767995265495984e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (closed_form) = 1.406272038633764543887693919572 y[1] (numeric) = 1.4062720386337645438876939195703 absolute error = 1.7e-30 relative error = 1.2088699435790538641059708285077e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=408.7MB, alloc=44.3MB, time=4.66 TOP MAIN SOLVE Loop x[1] = 1.87 y[1] (closed_form) = 1.4120149812310539164715289416845 y[1] (numeric) = 1.4120149812310539164715289416827 absolute error = 1.8e-30 relative error = 1.2747740101388191095554030111483e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (closed_form) = 1.4177557225137181807263640541696 y[1] (numeric) = 1.4177557225137181807263640541679 absolute error = 1.7e-30 relative error = 1.1990782142539021409958153716819e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (closed_form) = 1.423494275488076050339656485657 y[1] (numeric) = 1.4234942754880760503396564856553 absolute error = 1.7e-30 relative error = 1.1942443529793036456415835637526e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (closed_form) = 1.4292306530455152537665018515263 y[1] (numeric) = 1.4292306530455152537665018515244 absolute error = 1.9e-30 relative error = 1.3293865450977650099742872416723e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (closed_form) = 1.4349648679638426828430892786492 y[1] (numeric) = 1.4349648679638426828430892786474 absolute error = 1.8e-30 relative error = 1.2543861108977026442775266736316e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.92 y[1] (closed_form) = 1.4406969329086147733994998098201 y[1] (numeric) = 1.4406969329086147733994998098185 absolute error = 1.6e-30 relative error = 1.1105736143754878260757986013478e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.93 y[1] (closed_form) = 1.4464268604344484641743268606048 y[1] (numeric) = 1.4464268604344484641743268606031 absolute error = 1.7e-30 relative error = 1.1753100322607313594519716712175e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (closed_form) = 1.4521546629863130732764470224524 y[1] (numeric) = 1.4521546629863130732764470224509 absolute error = 1.5e-30 relative error = 1.0329478245211804145020845178731e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (closed_form) = 1.4578803529008034245460016535121 y[1] (numeric) = 1.4578803529008034245460016535107 absolute error = 1.4e-30 relative error = 9.6029828319886707541608628185484e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (closed_form) = 1.4636039424073945494329954304972 y[1] (numeric) = 1.4636039424073945494329954304957 absolute error = 1.5e-30 relative error = 1.0248674224891330595954928556635e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.97 y[1] (closed_form) = 1.4693254436296782834337315146188 y[1] (numeric) = 1.4693254436296782834337315146175 absolute error = 1.3e-30 relative error = 8.8475974171427044742604822995613e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (closed_form) = 1.4750448685865820696985576810726 y[1] (numeric) = 1.4750448685865820696985576810712 absolute error = 1.4e-30 relative error = 9.4912367061858153110001553203176e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (closed_form) = 1.480762229193570276145182683647 y[1] (numeric) = 1.4807622291935702761451826836457 absolute error = 1.3e-30 relative error = 8.7792622905298294004979997885485e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = 1.4864775372638283262763381858608 y[1] (numeric) = 1.4864775372638283262763381858595 absolute error = 1.3e-30 relative error = 8.7455071967849639115229716357701e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (closed_form) = 1.4921908045094299379051180911056 y[1] (numeric) = 1.4921908045094299379051180911044 absolute error = 1.2e-30 relative error = 8.0418670077149411179581024394062e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (closed_form) = 1.4979020425424877581323383493364 y[1] (numeric) = 1.4979020425424877581323383493352 absolute error = 1.2e-30 relative error = 8.0112047778715956113993737838765e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (closed_form) = 1.5036112628762876771942423323194 y[1] (numeric) = 1.5036112628762876771942423323183 absolute error = 1.1e-30 relative error = 7.3157206730135040212561917652489e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=449.1MB, alloc=44.3MB, time=5.11 TOP MAIN SOLVE Loop x[1] = 2.04 y[1] (closed_form) = 1.5093184769264070982024442360474 y[1] (numeric) = 1.5093184769264070982024442360464 absolute error = 1.0e-30 relative error = 6.6255069111484747824174266217889e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (closed_form) = 1.5150236960118174343278657694572 y[1] (numeric) = 1.5150236960118174343278657694562 absolute error = 1.0e-30 relative error = 6.6005568271468133876421207351880e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (closed_form) = 1.5207269313559710996333822489189 y[1] (numeric) = 1.520726931355971099633382248918 absolute error = 9e-31 relative error = 5.9182222754318302453603050931717e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (closed_form) = 1.5264281940878732545328454525821 y[1] (numeric) = 1.5264281940878732545328454525812 absolute error = 9e-31 relative error = 5.8961175080875694081003423585120e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (closed_form) = 1.5321274952431385617440714408922 y[1] (numeric) = 1.5321274952431385617440714408914 absolute error = 8e-31 relative error = 5.2214975743454382623839619823618e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (closed_form) = 1.5378248457650332036073355244235 y[1] (numeric) = 1.5378248457650332036073355244226 absolute error = 9e-31 relative error = 5.8524220263346719621577265896784e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (closed_form) = 1.5435202565055024067560488458838 y[1] (numeric) = 1.5435202565055024067560488458828 absolute error = 1.0e-30 relative error = 6.4786969641977948178963888485869e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (closed_form) = 1.5492137382261837153498260189663 y[1] (numeric) = 1.5492137382261837153498260189653 absolute error = 1.0e-30 relative error = 6.4548872458682067409896174641568e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (closed_form) = 1.5549053015994062494093920930452 y[1] (numeric) = 1.5549053015994062494093920930442 absolute error = 1.0e-30 relative error = 6.4312598263790102471924489851353e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (closed_form) = 1.5605949572091761802250954012356 y[1] (numeric) = 1.5605949572091761802250954012347 absolute error = 9e-31 relative error = 5.7670313225250761954856966628896e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (closed_form) = 1.5662827155521486503436384100036 y[1] (numeric) = 1.5662827155521486503436384100027 absolute error = 9e-31 relative error = 5.7460890748751604990758991415370e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (closed_form) = 1.5719685870385863612685293506886 y[1] (numeric) = 1.5719685870385863612685293506877 absolute error = 9e-31 relative error = 5.7253052473236739706899511547064e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (closed_form) = 1.577652581993305047736278918474 y[1] (numeric) = 1.577652581993305047736278918473 absolute error = 1.0e-30 relative error = 6.3385311279149772679949259685808e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (closed_form) = 1.583334710656606053250170287812 y[1] (numeric) = 1.5833347106566060532501702878109 absolute error = 1.1e-30 relative error = 6.9473623776228083882089394831107e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (closed_form) = 1.5890149831851962174642326324331 y[1] (numeric) = 1.589014983185196217464232632432 absolute error = 1.1e-30 relative error = 6.9225275509677016571396569240762e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (closed_form) = 1.594693409653095282009625764743 y[1] (numeric) = 1.5946934096530952820096257647417 absolute error = 1.3e-30 relative error = 8.1520372011996839983989248735146e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (closed_form) = 1.6003700000525310174418340844513 y[1] (numeric) = 1.60037000005253101744183408445 absolute error = 1.3e-30 relative error = 8.1231215278799803553783180232287e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (closed_form) = 1.6060447642948222701577677736404 y[1] (numeric) = 1.6060447642948222701577677736392 absolute error = 1.2e-30 relative error = 7.4717718128292190441342329328885e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=489.6MB, alloc=44.3MB, time=5.56 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (closed_form) = 1.6117177122112501243850307541177 y[1] (numeric) = 1.6117177122112501243850307541164 absolute error = 1.3e-30 relative error = 8.0659286061727362704972443236039e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (closed_form) = 1.6173888535539173706792459542978 y[1] (numeric) = 1.6173888535539173706792459542965 absolute error = 1.3e-30 relative error = 8.0376465878535444163885008578211e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (closed_form) = 1.6230581979965964687774898823465 y[1] (numeric) = 1.6230581979965964687774898823452 absolute error = 1.3e-30 relative error = 8.0095710776399780245228530461392e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (closed_form) = 1.6287257551355661891446931121726 y[1] (numeric) = 1.6287257551355661891446931121712 absolute error = 1.4e-30 relative error = 8.5956766851978201011918323886044e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (closed_form) = 1.634391534490437114113474061559 y[1] (numeric) = 1.6343915344904371141134740615576 absolute error = 1.4e-30 relative error = 8.5658789247001661600167234595774e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (closed_form) = 1.6400555455049661761545021715042 y[1] (numeric) = 1.6400555455049661761545021715028 absolute error = 1.4e-30 relative error = 8.5362962482404576882815228344613e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (closed_form) = 1.6457177975478604075223924469396 y[1] (numeric) = 1.6457177975478604075223924469383 absolute error = 1.3e-30 relative error = 7.8992886990528744182984994201230e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (closed_form) = 1.6513782999135700722996214489358 y[1] (numeric) = 1.6513782999135700722996214489345 absolute error = 1.3e-30 relative error = 7.8722119581445358161630728046720e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (closed_form) = 1.65703706182307134870637505503 y[1] (numeric) = 1.6570370618230713487063750550286 absolute error = 1.4e-30 relative error = 8.4488152513602845941970753466887e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (closed_form) = 1.6626940924246387264559838141821 y[1] (numeric) = 1.6626940924246387264559838141807 absolute error = 1.4e-30 relative error = 8.4200696109916245277172642452506e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (closed_form) = 1.6683494007946072809121078214375 y[1] (numeric) = 1.6683494007946072809121078214362 absolute error = 1.3e-30 relative error = 7.7921327473779261017505288662461e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (closed_form) = 1.6740029959381249828435759373105 y[1] (numeric) = 1.6740029959381249828435759373092 absolute error = 1.3e-30 relative error = 7.7658164480850845657380799477744e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (closed_form) = 1.6796548867898951996742798248048 y[1] (numeric) = 1.6796548867898951996742798248035 absolute error = 1.3e-30 relative error = 7.7396851592800712072553741874848e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (closed_form) = 1.685305082214909541287326216681 y[1] (numeric) = 1.6853050822149095412873262166796 absolute error = 1.4e-30 relative error = 8.3071012766427560533573133165182e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (closed_form) = 1.6909535910091712006633530967327 y[1] (numeric) = 1.6909535910091712006633530967313 absolute error = 1.4e-30 relative error = 8.2793520025849534988342321008245e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (closed_form) = 1.6966004219004089369111455498201 y[1] (numeric) = 1.6966004219004089369111455498186 absolute error = 1.5e-30 relative error = 8.8412096368560878895772917544120e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (closed_form) = 1.7022455835487818455831087691774 y[1] (numeric) = 1.7022455835487818455831087691757 absolute error = 1.7e-30 relative error = 9.9868081105894231088666463959060e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (closed_form) = 1.7078890845475750585574673614304 y[1] (numeric) = 1.7078890845475750585574673614287 absolute error = 1.7e-30 relative error = 9.9538079807468006582052635656152e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=530.1MB, alloc=44.3MB, time=6.01 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (closed_form) = 1.7135309334238865132119933363154 y[1] (numeric) = 1.7135309334238865132119933363137 absolute error = 1.7e-30 relative error = 9.9210347875258387042265218739160e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (closed_form) = 1.7191711386393049281093841654432 y[1] (numeric) = 1.7191711386393049281093841654415 absolute error = 1.7e-30 relative error = 9.8884861535397891669936843344437e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.42 y[1] (closed_form) = 1.7248097085905791199609127658376 y[1] (numeric) = 1.724809708590579119960912765836 absolute error = 1.6e-30 relative error = 9.2763856327515292119352721991805e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (closed_form) = 1.7304466516102787942314796150454 y[1] (numeric) = 1.7304466516102787942314796150438 absolute error = 1.6e-30 relative error = 9.2461677365847090205701318392021e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (closed_form) = 1.7360819759674469393945696656776 y[1] (numeric) = 1.7360819759674469393945696656761 absolute error = 1.5e-30 relative error = 8.6401449975546910255723451993839e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (closed_form) = 1.7417156898682439525387385216992 y[1] (numeric) = 1.7417156898682439525387385216977 absolute error = 1.5e-30 relative error = 8.6121977813352012346075676545458e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (closed_form) = 1.747347801456583621767036876704 y[1] (numeric) = 1.7473478014565836217670368767025 absolute error = 1.5e-30 relative error = 8.5844386489604686953909414097494e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (closed_form) = 1.7529783188147610886161703105666 y[1] (numeric) = 1.7529783188147610886161703105651 absolute error = 1.5e-30 relative error = 8.5568656719849964567280897701647e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (closed_form) = 1.758607249964072911552150656354 y[1] (numeric) = 1.7586072499640729115521506563528 absolute error = 1.2e-30 relative error = 6.8235815587847436761070859804119e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (closed_form) = 1.7642346028654293494727186560858 y[1] (numeric) = 1.7642346028654293494727186560846 absolute error = 1.2e-30 relative error = 6.8018164820652964308504220052776e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (closed_form) = 1.7698603854199589820629240910936 y[1] (numeric) = 1.7698603854199589820629240910925 absolute error = 1.1e-30 relative error = 6.2151795082920506977499952962322e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (closed_form) = 1.7754846054696057818079820748597 y[1] (numeric) = 1.7754846054696057818079820748586 absolute error = 1.1e-30 relative error = 6.1954916230268081162459260041199e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (closed_form) = 1.7811072707977187504659496417085 y[1] (numeric) = 1.7811072707977187504659496417075 absolute error = 1.0e-30 relative error = 5.6144849689604714633785064754455e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (closed_form) = 1.7867283891296342308409752445493 y[1] (numeric) = 1.7867283891296342308409752445482 absolute error = 1.1e-30 relative error = 6.1565037343803610285189295984017e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (closed_form) = 1.7923479681332510027749779304797 y[1] (numeric) = 1.7923479681332510027749779304788 absolute error = 9e-31 relative error = 5.0213463903293250243515781957370e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (closed_form) = 1.7979660154195982703907473732514 y[1] (numeric) = 1.7979660154195982703907473732507 absolute error = 7e-31 relative error = 3.8932882712838056481488791131049e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (closed_form) = 1.8035825385433966457717765273382 y[1] (numeric) = 1.8035825385433966457717765273375 absolute error = 7e-31 relative error = 3.8811642109006648555759719007062e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=570.6MB, alloc=44.3MB, time=6.48 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (closed_form) = 1.8091975450036122324528221152715 y[1] (numeric) = 1.8091975450036122324528221152709 absolute error = 6e-31 relative error = 3.3163874318589241937604485322179e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (closed_form) = 1.8148110422440039103194313578149 y[1] (numeric) = 1.8148110422440039103194313578144 absolute error = 5e-31 relative error = 2.7551077680338154627826582287200e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (closed_form) = 1.8204230376536639217736928553044 y[1] (numeric) = 1.8204230376536639217736928553039 absolute error = 5e-31 relative error = 2.7466143289663485543596957042390e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (closed_form) = 1.8260335385675518573165010099528 y[1] (numeric) = 1.8260335385675518573165010099523 absolute error = 5e-31 relative error = 2.7381753370873429717794385140996e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (closed_form) = 1.831642552267022137022921144248 y[1] (numeric) = 1.8316425522670221370229211442473 absolute error = 7e-31 relative error = 3.8217063647795838057175994868272e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (closed_form) = 1.8372500859803450827460789425148 y[1] (numeric) = 1.8372500859803450827460789425142 absolute error = 6e-31 relative error = 3.2657502894051779359722003130009e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (closed_form) = 1.8428561468832216742756630823131 y[1] (numeric) = 1.8428561468832216742756630823124 absolute error = 7e-31 relative error = 3.7984516652799687168508080918688e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (closed_form) = 1.8484607420992920810989311598007 y[1] (numeric) = 1.8484607420992920810989311598 absolute error = 7e-31 relative error = 3.7869346319198091897648033929411e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (closed_form) = 1.8540638787006380598643701921518 y[1] (numeric) = 1.8540638787006380598643701921512 absolute error = 6e-31 relative error = 3.2361344551973635041339598395855e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (closed_form) = 1.8596655637082793061302243152364 y[1] (numeric) = 1.8596655637082793061302243152359 absolute error = 5e-31 relative error = 2.6886554752509986472046071781670e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (closed_form) = 1.8652658040926638474913198419719 y[1] (numeric) = 1.8652658040926638474913198419714 absolute error = 5e-31 relative error = 2.6805831045791299222303604929858e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (closed_form) = 1.8708646067741525637173630858502 y[1] (numeric) = 1.8708646067741525637173630858496 absolute error = 6e-31 relative error = 3.2070733383243212379777227780084e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (closed_form) = 1.8764619786234979181035457834437 y[1] (numeric) = 1.8764619786234979181035457834432 absolute error = 5e-31 relative error = 2.6645890281602254177625277324634e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (closed_form) = 1.8820579264623169828292676921494 y[1] (numeric) = 1.882057926462316982829267692149 absolute error = 4e-31 relative error = 2.1253330961596675189030694323253e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (closed_form) = 1.8876524570635588397424913601216 y[1] (numeric) = 1.8876524570635588397424913601211 absolute error = 5e-31 relative error = 2.6487926743559690187713001562259e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (closed_form) = 1.8932455771519664366351093997505 y[1] (numeric) = 1.8932455771519664366351093997499 absolute error = 6e-31 relative error = 3.1691609754218345121965634402149e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (closed_form) = 1.8988372934045329777481725889267 y[1] (numeric) = 1.8988372934045329777481725889261 absolute error = 6e-31 relative error = 3.1598283964827023278806116782630e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (closed_form) = 1.9044276124509529259443536788732 y[1] (numeric) = 1.9044276124509529259443536788725 absolute error = 7e-31 relative error = 3.6756450884426984944564920840523e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=611.0MB, alloc=44.3MB, time=6.94 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (closed_form) = 1.9100165408740676927080756241038 y[1] (numeric) = 1.9100165408740676927080756241029 absolute error = 9e-31 relative error = 4.7120010782112871596022386485852e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (closed_form) = 1.9156040852103060908807952757458 y[1] (numeric) = 1.915604085210306090880795275745 absolute error = 8e-31 relative error = 4.1762283040452556514309735042448e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (closed_form) = 1.9211902519501196238094977647396 y[1] (numeric) = 1.9211902519501196238094977647388 absolute error = 8e-31 relative error = 4.1640852548983816825048384999758e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (closed_form) = 1.9267750475384126833800280680073 y[1] (numeric) = 1.9267750475384126833800280680066 absolute error = 7e-31 relative error = 3.6330136249911375281643444717548e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (closed_form) = 1.9323584783749677282229813671356 y[1] (numeric) = 1.932358478374967728222981367135 absolute error = 6e-31 relative error = 3.1050139335666888507991401237566e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (closed_form) = 1.9379405508148655122180207950299 y[1] (numeric) = 1.9379405508148655122180207950293 absolute error = 6e-31 relative error = 3.0960702058053943738797530468251e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (closed_form) = 1.9435212711689004322822290046036 y[1] (numeric) = 1.943521271168900432282229004603 absolute error = 6e-31 relative error = 3.0871800010665146783910930869108e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (closed_form) = 1.9491006457039910633089783521724 y[1] (numeric) = 1.9491006457039910633089783521716 absolute error = 8e-31 relative error = 4.1044571082733897900077508995142e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (closed_form) = 1.9546786806435859470253834465155 y[1] (numeric) = 1.9546786806435859470253834465148 absolute error = 7e-31 relative error = 3.5811512497262319254967305287620e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (closed_form) = 1.9602553821680647004582496003833 y[1] (numeric) = 1.9602553821680647004582496003826 absolute error = 7e-31 relative error = 3.5709632855377856705553915495041e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (closed_form) = 1.96583075641513450864013145365 y[1] (numeric) = 1.9658307564151345086401314536493 absolute error = 7e-31 relative error = 3.5608355282654730693536824087869e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (closed_form) = 1.9714048094802220651482574768038 y[1] (numeric) = 1.9714048094802220651482574768029 absolute error = 9e-31 relative error = 4.5652724172733087067419415298581e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (closed_form) = 1.9769775474168610230492573689469 y[1] (numeric) = 1.976977547416861023049257368946 absolute error = 9e-31 relative error = 4.5524037497337749559948356677499e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (closed_form) = 1.9825489762370750178214588569772 y[1] (numeric) = 1.9825489762370750178214588569764 absolute error = 8e-31 relative error = 4.0352092663981445526999903783265e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (closed_form) = 1.988119101911756322843615335458 y[1] (numeric) = 1.9881191019117563228436153354574 absolute error = 6e-31 relative error = 3.0179278465915132334842808017132e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (closed_form) = 1.9936879303710401970739121219138 y[1] (numeric) = 1.9936879303710401970739121219131 absolute error = 7e-31 relative error = 3.5110810941696616375045224558868e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (closed_form) = 1.9992554675046749835956112932052 y[1] (numeric) = 1.9992554675046749835956112932044 absolute error = 8e-31 relative error = 4.0014896195257213178889097512213e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=651.5MB, alloc=44.3MB, time=7.39 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (closed_form) = 2.0048217191623880167753758482465 y[1] (numeric) = 2.0048217191623880167753758482457 absolute error = 8e-31 relative error = 3.9903797547356928576090810722675e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (closed_form) = 2.0103866911542473948668141174837 y[1] (numeric) = 2.0103866911542473948668141174829 absolute error = 8e-31 relative error = 3.9793339436637755307766196168212e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (closed_form) = 2.01595038925101967399476359074 y[1] (numeric) = 2.0159503892510196739947635907392 absolute error = 8e-31 relative error = 3.9683516234604450224803464901884e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (closed_form) = 2.0215128191845235385749560214964 y[1] (numeric) = 2.0215128191845235385749560214955 absolute error = 9e-31 relative error = 4.4521112676547814039673950694909e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (closed_form) = 2.0270739866479795023586466358177 y[1] (numeric) = 2.0270739866479795023586466358168 absolute error = 9e-31 relative error = 4.4398971420291502174032506178482e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (closed_form) = 2.032633897296355693442230681029 y[1] (numeric) = 2.0326338972963556934422306810281 absolute error = 9e-31 relative error = 4.4277525883884294542380718711967e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (closed_form) = 2.0381925567467097757474986710704 y[1] (numeric) = 2.0381925567467097757474986710695 absolute error = 9e-31 relative error = 4.4156770027486896657590083292923e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (closed_form) = 2.0437499705785270586586927507289 y[1] (numeric) = 2.0437499705785270586586927507279 absolute error = 1.0e-30 relative error = 4.8929664312945709902016200131433e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3 y[1] (closed_form) = 2.0493061443340548456976226184613 y[1] (numeric) = 2.0493061443340548456976226184602 absolute error = 1.1e-30 relative error = 5.3676704334356905541990846984151e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (closed_form) = 2.054861083518633072327489040773 y[1] (numeric) = 2.0548610835186330723274890407718 absolute error = 1.2e-30 relative error = 5.8398108252903639082001774563863e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (closed_form) = 2.0604147936010212821994612371554 y[1] (numeric) = 2.0604147936010212821994612371543 absolute error = 1.1e-30 relative error = 5.3387308391312395055918902093067e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (closed_form) = 2.0659672800137219903931826871241 y[1] (numeric) = 2.0659672800137219903931826871229 absolute error = 1.2e-30 relative error = 5.8084172562114812167841639351243e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (closed_form) = 2.0715185481533004814529657275953 y[1] (numeric) = 2.0715185481533004814529657275941 absolute error = 1.2e-30 relative error = 5.7928518239422266695552493764407e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (closed_form) = 2.077068603380701089285212182581 y[1] (numeric) = 2.0770686033807010892852121825798 absolute error = 1.2e-30 relative error = 5.7773729671077926443506714575167e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (closed_form) = 2.0826174510215600052593045613186 y[1] (numeric) = 2.0826174510215600052593045613175 absolute error = 1.1e-30 relative error = 5.2818149557924375818429851218487e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (closed_form) = 2.0881650963665146601435951483107 y[1] (numeric) = 2.0881650963665146601435951483097 absolute error = 1.0e-30 relative error = 4.7888933769654391213316202245270e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (closed_form) = 2.09371154467150972480992923437 y[1] (numeric) = 2.0937115446715097248099292343691 absolute error = 9e-31 relative error = 4.2985864136370532522157606881691e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (closed_form) = 2.0992568011580997739541298851826 y[1] (numeric) = 2.0992568011580997739541298851816 absolute error = 1.0e-30 relative error = 4.7635906166807637748807069676723e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=692.0MB, alloc=44.3MB, time=7.86 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (closed_form) = 2.1048008710137486564058064050106 y[1] (numeric) = 2.1048008710137486564058064050097 absolute error = 9e-31 relative error = 4.2759389374754832020099637562151e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (closed_form) = 2.110343759392125614938493601341 y[1] (numeric) = 2.1103437593921256149384936013402 absolute error = 8e-31 relative error = 3.7908515920194734436811706718707e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (closed_form) = 2.1158854714133981978402557229696 y[1] (numeric) = 2.1158854714133981978402557229689 absolute error = 7e-31 relative error = 3.3083076067080530548648402538505e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (closed_form) = 2.121426012164522003865274098337 y[1] (numeric) = 2.1214260121645220038652740983363 absolute error = 7e-31 relative error = 3.2996672803393211749446087822506e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (closed_form) = 2.126965386699527301558362432571 y[1] (numeric) = 2.1269653866995273015583624325702 absolute error = 8e-31 relative error = 3.7612271690108824873531903271192e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (closed_form) = 2.1325036000398025633266045266951 y[1] (numeric) = 2.1325036000398025633266045266942 absolute error = 9e-31 relative error = 4.2203914684280099697439350930993e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.16 y[1] (closed_form) = 2.1380406571743749540251765520541 y[1] (numeric) = 2.1380406571743749540251765520532 absolute error = 9e-31 relative error = 4.2094615786653748983172297748116e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (closed_form) = 2.1435765630601878132276951252059 y[1] (numeric) = 2.1435765630601878132276951252051 absolute error = 8e-31 relative error = 3.7320803641271078051496540930432e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (closed_form) = 2.149111322622375169764922842604 y[1] (numeric) = 2.1491113226223751697649228426032 absolute error = 8e-31 relative error = 3.7224688715698031226099989880016e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (closed_form) = 2.1546449407545333265391684879741 y[1] (numeric) = 2.154644940754533326539168487973 absolute error = 1.1e-30 relative error = 5.1052494969996862286815618339830e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (closed_form) = 2.1601774223189895530550478341365 y[1] (numeric) = 2.1601774223189895530550478341354 absolute error = 1.1e-30 relative error = 5.0921743215847987828285308396404e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (closed_form) = 2.1657087721470679225502349213538 y[1] (numeric) = 2.1657087721470679225502349213529 absolute error = 9e-31 relative error = 4.1556834029339344039716598763164e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (closed_form) = 2.1712389950393523300622489875459 y[1] (numeric) = 2.1712389950393523300622489875449 absolute error = 1.0e-30 relative error = 4.6056652551133627464739535790646e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.23 y[1] (closed_form) = 2.1767680957659467272290088258501 y[1] (numeric) = 2.1767680957659467272290088258491 absolute error = 1.0e-30 relative error = 4.5939666331250901085807069149946e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.24 y[1] (closed_form) = 2.1822960790667326090916680279879 y[1] (numeric) = 2.1822960790667326090916680279868 absolute error = 1.1e-30 relative error = 5.0405626007925527260039718264368e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (closed_form) = 2.1878229496516237876479488276074 y[1] (numeric) = 2.1878229496516237876479488276061 absolute error = 1.3e-30 relative error = 5.9419799038446161526797187146000e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (closed_form) = 2.1933487122008184863926502040805 y[1] (numeric) = 2.1933487122008184863926502040793 absolute error = 1.2e-30 relative error = 5.4710862587641762723005400310070e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (closed_form) = 2.1988733713650487895790522062409 y[1] (numeric) = 2.1988733713650487895790522062397 absolute error = 1.2e-30 relative error = 5.4573401798715059217554095871104e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=732.5MB, alloc=44.3MB, time=8.33 TOP MAIN SOLVE Loop x[1] = 3.28 y[1] (closed_form) = 2.2043969317658274794404112319524 y[1] (numeric) = 2.2043969317658274794404112319513 absolute error = 1.1e-30 relative error = 4.9900269055394090786778178984782e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (closed_form) = 2.2099193979956922941244817608723 y[1] (numeric) = 2.2099193979956922941244817608711 absolute error = 1.2e-30 relative error = 5.4300622958844180937210866397811e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (closed_form) = 2.2154407746184476386158535973822 y[1] (numeric) = 2.2154407746184476386158535973812 absolute error = 1.0e-30 relative error = 4.5137744662672110051597833570381e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (closed_form) = 2.2209610661694037804507080811716 y[1] (numeric) = 2.2209610661694037804507080811706 absolute error = 1.0e-30 relative error = 4.5025552911863832339619626362142e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (closed_form) = 2.2264802771556135615662231630646 y[1] (numeric) = 2.2264802771556135615662231630638 absolute error = 8e-31 relative error = 3.5931151432521144922053169040584e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.33 y[1] (closed_form) = 2.2319984120561066571721500060664 y[1] (numeric) = 2.2319984120561066571721500060655 absolute error = 9e-31 relative error = 4.0322609332455758567043894628545e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (closed_form) = 2.237515475322121412084900152734 y[1] (numeric) = 2.2375154753221214120849001527332 absolute error = 8e-31 relative error = 3.5753942657528609719919070778340e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (closed_form) = 2.2430314713773342845246825417549 y[1] (numeric) = 2.2430314713773342845246825417543 absolute error = 6e-31 relative error = 2.6749513221567496931101370445298e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (closed_form) = 2.2485464046180869269436768795401 y[1] (numeric) = 2.2485464046180869269436768795394 absolute error = 7e-31 relative error = 3.1131223201012576443002526076578e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (closed_form) = 2.254060279413610933027790010835 y[1] (numeric) = 2.2540602794136109330277900108344 absolute error = 6e-31 relative error = 2.6618631519299419313080237111629e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (closed_form) = 2.2595731001062502795960836699724 y[1] (numeric) = 2.2595731001062502795960836699719 absolute error = 5e-31 relative error = 2.2128073660307288127420890279616e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (closed_form) = 2.2650848710116814917103567037832 y[1] (numeric) = 2.2650848710116814917103567037827 absolute error = 5e-31 relative error = 2.2074228052067608414129595245216e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (closed_form) = 2.270595596419131558902486538415 y[1] (numeric) = 2.2705955964191315589024865384146 absolute error = 4e-31 relative error = 1.7616523199059511947162416491377e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (closed_form) = 2.2761052805915936300288598842761 y[1] (numeric) = 2.2761052805915936300288598842758 absolute error = 3e-31 relative error = 1.3180409647923910448956599563161e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.42 y[1] (closed_form) = 2.2816139277660405138694305162414 y[1] (numeric) = 2.281613927766040513869430516241 absolute error = 4e-31 relative error = 1.7531449783515543556269516334759e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (closed_form) = 2.2871215421536360122035139655811 y[1] (numeric) = 2.2871215421536360122035139655808 absolute error = 3e-31 relative error = 1.3116924241704671096630724219853e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (closed_form) = 2.2926281279399441117152490517502 y[1] (numeric) = 2.2926281279399441117152490517499 absolute error = 3e-31 relative error = 1.3085419145998481124101093616447e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=773.0MB, alloc=44.3MB, time=8.78 TOP MAIN SOLVE Loop x[1] = 3.45 y[1] (closed_form) = 2.2981336892851360607086106492814 y[1] (numeric) = 2.2981336892851360607086106492811 absolute error = 3e-31 relative error = 1.3054070848825111001605833297537e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.46 y[1] (closed_form) = 2.3036382303241953562448355056161 y[1] (numeric) = 2.3036382303241953562448355056158 absolute error = 3e-31 relative error = 1.3022878160768343984001610586879e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.47 y[1] (closed_form) = 2.3091417551671206669540141220114 y[1] (numeric) = 2.3091417551671206669540141220111 absolute error = 3e-31 relative error = 1.2991839904531454393190741199874e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (closed_form) = 2.3146442678991267164172996984404 y[1] (numeric) = 2.3146442678991267164172996984401 absolute error = 3e-31 relative error = 1.2960954914782358288768991109788e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (closed_form) = 2.3201457725808431516665850875184 y[1] (numeric) = 2.3201457725808431516665850875182 absolute error = 2e-31 relative error = 8.6201480253340935567441816517393e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.5 y[1] (closed_form) = 2.3256462732485114210044978636711 y[1] (numeric) = 2.3256462732485114210044978636707 absolute error = 4e-31 relative error = 1.7199520176439885791848187982725e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.51 y[1] (closed_form) = 2.3311457739141796850090613064392 y[1] (numeric) = 2.3311457739141796850090613064387 absolute error = 5e-31 relative error = 2.1448680112374959732305398666640e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.52 y[1] (closed_form) = 2.336644278565895784254266643139 y[1] (numeric) = 2.3366442785658957842542666431385 absolute error = 5e-31 relative error = 2.1398207873852009738210864017507e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (closed_form) = 2.3421417911678982869500025819313 y[1] (numeric) = 2.3421417911678982869500025819308 absolute error = 5e-31 relative error = 2.1347981658731143169145119631343e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (closed_form) = 2.347638315660805639382197198438 y[1] (numeric) = 2.3476383156608056393821971984377 absolute error = 3e-31 relative error = 1.2778799783541485196155433216839e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (closed_form) = 2.3531338559618034417165517030572 y[1] (numeric) = 2.3531338559618034417165517030567 absolute error = 5e-31 relative error = 2.1248260005830968929688709580391e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.56 y[1] (closed_form) = 2.3586284159648298714167944358308 y[1] (numeric) = 2.3586284159648298714167944358303 absolute error = 5e-31 relative error = 2.1198760966994795652039598800399e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (closed_form) = 2.3641219995407592762208673330356 y[1] (numeric) = 2.3641219995407592762208673330352 absolute error = 4e-31 relative error = 1.6919600599195037153424474548764e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (closed_form) = 2.3696146105375839583157885656805 y[1] (numeric) = 2.36961461053758395831578856568 absolute error = 5e-31 relative error = 2.1100477595661313774466801484877e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (closed_form) = 2.3751062527805941710540282670373 y[1] (numeric) = 2.3751062527805941710540282670368 absolute error = 5e-31 relative error = 2.1051689768179336877987167217484e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (closed_form) = 2.3805969300725563492610051303924 y[1] (numeric) = 2.3805969300725563492610051303919 absolute error = 5e-31 relative error = 2.1003135544863568803237366021887e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (closed_form) = 2.3860866461938895938946777032428 y[1] (numeric) = 2.3860866461938895938946777032425 absolute error = 3e-31 relative error = 1.2572887932571015220656204081798e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.62 y[1] (closed_form) = 2.3915754049028404315340845763032 y[1] (numeric) = 2.3915754049028404315340845763031 absolute error = 1e-31 relative error = 4.1813442216789554248596967438860e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=813.4MB, alloc=44.3MB, time=9.23 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (closed_form) = 2.3970632099356558688940030886862 y[1] (numeric) = 2.3970632099356558688940030886862 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (closed_form) = 2.4025500650067547622875689120772 y[1] (numeric) = 2.4025500650067547622875689120772 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (closed_form) = 2.4080359738088975216876527150923 y[1] (numeric) = 2.4080359738088975216876527150923 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (closed_form) = 2.4135209400133541687709503013186 y[1] (numeric) = 2.4135209400133541687709503013186 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (closed_form) = 2.4190049672700707680660358649567 y[1] (numeric) = 2.4190049672700707680660358649566 absolute error = 1e-31 relative error = 4.1339311557038014290472347955288e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.68 y[1] (closed_form) = 2.4244880592078342500679824370056 y[1] (numeric) = 2.4244880592078342500679824370054 absolute error = 2e-31 relative error = 8.2491641581995274135078433838248e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (closed_form) = 2.4299702194344356449274987093632 y[1] (numeric) = 2.429970219434435644927498709363 absolute error = 2e-31 relative error = 8.2305535434318646533374934832190e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (closed_form) = 2.4354514515368317450717980878139 y[1] (numeric) = 2.4354514515368317450717980878138 absolute error = 1e-31 relative error = 4.1060149212540229136073882144230e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (closed_form) = 2.4409317590813052148675362296518 y[1] (numeric) = 2.4409317590813052148675362296517 absolute error = 1e-31 relative error = 4.0967962184095246159619096981442e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (closed_form) = 2.4464111456136231651930609599386 y[1] (numeric) = 2.4464111456136231651930609599384 absolute error = 2e-31 relative error = 8.1752407136714065766986084043914e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (closed_form) = 2.4518896146591942105478480972506 y[1] (numeric) = 2.4518896146591942105478480972503 absolute error = 3e-31 relative error = 1.2235461099324373939756801671737e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.74 y[1] (closed_form) = 2.4573671697232240260912843665438 y[1] (numeric) = 2.4573671697232240260912843665434 absolute error = 4e-31 relative error = 1.6277583786758754535432681663414e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (closed_form) = 2.4628438142908694217708414647269 y[1] (numeric) = 2.4628438142908694217708414647265 absolute error = 4e-31 relative error = 1.6241387199584665622040319188472e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (closed_form) = 2.4683195518273909504711018994382 y[1] (numeric) = 2.4683195518273909504711018994379 absolute error = 3e-31 relative error = 1.2154017893586694514247894073834e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (closed_form) = 2.4737943857783040668899870386262 y[1] (numeric) = 2.473794385778304066889987038626 absolute error = 2e-31 relative error = 8.0847462970159539258792197386664e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (closed_form) = 2.4792683195695288536268416282024 y[1] (numeric) = 2.4792683195695288536268416282022 absolute error = 2e-31 relative error = 8.0668961250118204320083545569536e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (closed_form) = 2.4847413566075383307486887189274 y[1] (numeric) = 2.4847413566075383307486887189273 absolute error = 1e-31 relative error = 4.0245637532484178829596373666118e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=853.9MB, alloc=44.3MB, time=9.69 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (closed_form) = 2.4902135002795053648859274514507 y[1] (numeric) = 2.4902135002795053648859274514506 absolute error = 1e-31 relative error = 4.0157199368156926037790078274436e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (closed_form) = 2.4956847539534481936969475149136 y[1] (numeric) = 2.4956847539534481936969475149134 absolute error = 2e-31 relative error = 8.0138326638882285634679963772492e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (closed_form) = 2.5011551209783745813325234075842 y[1] (numeric) = 2.5011551209783745813325234075842 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.83 y[1] (closed_form) = 2.506624604684424620325375006673 y[1] (numeric) = 2.5066246046844246203253750066729 absolute error = 1e-31 relative error = 3.9894286449242627853749959211586e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (closed_form) = 2.512093208383012195127885527785 y[1] (numeric) = 2.5120932083830121951278855277848 absolute error = 2e-31 relative error = 7.9614880265026587319545188657327e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (closed_form) = 2.5175609353669651223216018405847 y[1] (numeric) = 2.5175609353669651223216018405846 absolute error = 1e-31 relative error = 3.9720984940300475349824305833517e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (closed_form) = 2.5230277889106639823257543932069 y[1] (numeric) = 2.5230277889106639823257543932069 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (closed_form) = 2.5284937722701796572385747197584 y[1] (numeric) = 2.5284937722701796572385747197582 absolute error = 2e-31 relative error = 7.9098474433034593723171151092541e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (closed_form) = 2.5339588886834095892546086285107 y[1] (numeric) = 2.5339588886834095892546086285107 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (closed_form) = 2.5394231413702127739134745692352 y[1] (numeric) = 2.5394231413702127739134745692352 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (closed_form) = 2.5448865335325435022505521247499 y[1] (numeric) = 2.54488653353254350225055212475 absolute error = 1e-31 relative error = 3.9294482752907073729893068725914e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (closed_form) = 2.5503490683545838657378587061685 y[1] (numeric) = 2.5503490683545838657378587061687 absolute error = 2e-31 relative error = 7.8420637583166049633537213110678e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (closed_form) = 2.5558107490028750377238378516884 y[1] (numeric) = 2.5558107490028750377238378516886 absolute error = 2e-31 relative error = 7.8253055347712296327723816068731e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (closed_form) = 2.5612715786264473449038953719112 y[1] (numeric) = 2.5612715786264473449038953719114 absolute error = 2e-31 relative error = 7.8086213765451427155545059995484e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (closed_form) = 2.5667315603569491421792361093134 y[1] (numeric) = 2.5667315603569491421792361093135 absolute error = 1e-31 relative error = 3.8960053924023610078088177912497e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (closed_form) = 2.5721906973087745040898312493812 y[1] (numeric) = 2.5721906973087745040898312493813 absolute error = 1e-31 relative error = 3.8877366326154495259930154824371e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (closed_form) = 2.5776489925791897458381416888696 y[1] (numeric) = 2.5776489925791897458381416888699 absolute error = 3e-31 relative error = 1.1638512491951849473480356333653e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (closed_form) = 2.5831064492484587867534954584218 y[1] (numeric) = 2.5831064492484587867534954584219 absolute error = 1e-31 relative error = 3.8713077437863419521931725207353e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=894.4MB, alloc=44.3MB, time=10.16 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (closed_form) = 2.5885630703799673688827258957464 y[1] (numeric) = 2.5885630703799673688827258957466 absolute error = 2e-31 relative error = 7.7262942629650744023352928307613e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (closed_form) = 2.59401885902034614323078219734 y[1] (numeric) = 2.59401885902034614323078219734 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4 y[1] (closed_form) = 2.5994738181995926360154858944913 y[1] (numeric) = 2.5994738181995926360154858944914 absolute error = 1e-31 relative error = 3.8469323791558883190378613794305e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.01 y[1] (closed_form) = 2.6049279509311921071433871690848 y[1] (numeric) = 2.6049279509311921071433871690847 absolute error = 1e-31 relative error = 3.8388777687403090444251277926395e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (closed_form) = 2.6103812602122373129587359112992 y[1] (numeric) = 2.6103812602122373129587359112991 absolute error = 1e-31 relative error = 3.8308580253855136036204035838820e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.03 y[1] (closed_form) = 2.6158337490235471851648868742535 y[1] (numeric) = 2.6158337490235471851648868742534 absolute error = 1e-31 relative error = 3.8228729190961983048840196837066e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (closed_form) = 2.621285420329784437666969720768 y[1] (numeric) = 2.6212854203297844376669697207679 absolute error = 1e-31 relative error = 3.8149222219158026752776392981378e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (closed_form) = 2.6267362770795721129363373633174 y[1] (numeric) = 2.6267362770795721129363373633172 absolute error = 2e-31 relative error = 7.6140114158076696116390485171868e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.06 y[1] (closed_form) = 2.6321863222056090793511245934703 y[1] (numeric) = 2.6321863222056090793511245934703 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.07 y[1] (closed_form) = 2.6376355586247844908231690372336 y[1] (numeric) = 2.6376355586247844908231690372334 absolute error = 2e-31 relative error = 7.5825486711392526614400324282944e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (closed_form) = 2.6430839892382912198795340329838 y[1] (numeric) = 2.6430839892382912198795340329835 absolute error = 3e-31 relative error = 1.1350377105740662406691429095386e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (closed_form) = 2.6485316169317382752268947917502 y[1] (numeric) = 2.64853161693173827522689479175 absolute error = 2e-31 relative error = 7.5513540680966197629728653614849e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (closed_form) = 2.6539784445752622146890724436479 y[1] (numeric) = 2.6539784445752622146890724436476 absolute error = 3e-31 relative error = 1.1303784347352204787528598078337e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (closed_form) = 2.6594244750236375642719931612126 y[1] (numeric) = 2.6594244750236375642719931612123 absolute error = 3e-31 relative error = 1.1280636198451679375790555521507e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (closed_form) = 2.6648697111163862539762799145602 y[1] (numeric) = 2.66486971111638625397627991456 absolute error = 2e-31 relative error = 7.5050573454195091377544122923171e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (closed_form) = 2.6703141556778860808455215501768 y[1] (numeric) = 2.6703141556778860808455215501766 absolute error = 2e-31 relative error = 7.4897554497376354699681272612237e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (closed_form) = 2.6757578115174782096079773404251 y[1] (numeric) = 2.675757811517478209607977340425 absolute error = 1e-31 relative error = 3.7372590138599991165891256683244e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (closed_form) = 2.6812006814295737211410350097329 y[1] (numeric) = 2.6812006814295737211410350097328 absolute error = 1e-31 relative error = 3.7296723327207862876849565467523e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=935.0MB, alloc=44.3MB, time=10.61 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (closed_form) = 2.6866427681937592188611171200857 y[1] (numeric) = 2.6866427681937592188611171200856 absolute error = 1e-31 relative error = 3.7221174762743170272080533252101e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (closed_form) = 2.6920840745749015030168957258057 y[1] (numeric) = 2.6920840745749015030168957258056 absolute error = 1e-31 relative error = 3.7145942411100472145536449922087e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (closed_form) = 2.6975246033232513227406000272442 y[1] (numeric) = 2.6975246033232513227406000272443 absolute error = 1e-31 relative error = 3.7071024255646702761143763993991e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (closed_form) = 2.7029643571745462155908585053684 y[1] (numeric) = 2.7029643571745462155908585053684 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (closed_form) = 2.708403338850112444200878333896 y[1] (numeric) = 2.708403338850112444200878333896 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (closed_form) = 2.7138415510569660395278038520073 y[1] (numeric) = 2.7138415510569660395278038520072 absolute error = 1e-31 relative error = 3.6848135058236090689786431073601e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (closed_form) = 2.719278996487912960082786118634 y[1] (numeric) = 2.719278996487912960082786118634 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (closed_form) = 2.7247156778216483764066111003036 y[1] (numeric) = 2.7247156778216483764066111003034 absolute error = 2e-31 relative error = 7.3402154077190065390345267020941e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (closed_form) = 2.730151597722855089942649362507 y[1] (numeric) = 2.7301515977228550899426493625068 absolute error = 2e-31 relative error = 7.3256005332016925240684978794459e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (closed_form) = 2.735586758842301095347380177588 y[1] (numeric) = 2.7355867588423010953473801775878 absolute error = 2e-31 relative error = 7.3110457693778243315791882916669e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (closed_form) = 2.7410211638169362951687831036709 y[1] (numeric) = 2.7410211638169362951687831036709 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (closed_form) = 2.74645481526998837571445612984 y[1] (numeric) = 2.74645481526998837571445612984 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (closed_form) = 2.7518877158110578528243876423235 y[1] (numeric) = 2.7518877158110578528243876423234 absolute error = 1e-31 relative error = 3.6338691955142951219001647763581e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.29 y[1] (closed_form) = 2.7573198680362122961578563755988 y[1] (numeric) = 2.7573198680362122961578563755987 absolute error = 1e-31 relative error = 3.6267101673343719936310917946897e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (closed_form) = 2.7627512745280797404999362051485 y[1] (numeric) = 2.7627512745280797404999362051486 absolute error = 1e-31 relative error = 3.6195802684800691150101540711149e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (closed_form) = 2.768181937855941292490518544706 y[1] (numeric) = 2.7681819378559412924905185447062 absolute error = 2e-31 relative error = 7.2249586367472419376140271601027e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (closed_form) = 2.7736118605758229410776120480435 y[1] (numeric) = 2.7736118605758229410776120480438 absolute error = 3e-31 relative error = 1.0816221413825282523180614991071e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=975.5MB, alloc=44.3MB, time=11.06 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (closed_form) = 2.7790410452305865798969154822709 y[1] (numeric) = 2.7790410452305865798969154822712 absolute error = 3e-31 relative error = 1.0795090648799970123368955314772e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (closed_form) = 2.7844694943500202496812636084756 y[1] (numeric) = 2.784469494350020249681263608476 absolute error = 4e-31 relative error = 1.4365393508948179332155525753081e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (closed_form) = 2.7898972104509276087064966151815 y[1] (numeric) = 2.7898972104509276087064966151819 absolute error = 4e-31 relative error = 1.4337445784798232712416631737860e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (closed_form) = 2.79532419603721663918458039909 y[1] (numeric) = 2.7953241960372166391845803990903 absolute error = 3e-31 relative error = 1.0732207749830740311210969046810e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (closed_form) = 2.8007504535999875974203874274148 y[1] (numeric) = 2.800750453599987597420387427415 absolute error = 2e-31 relative error = 7.1409432333725744562410737887699e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (closed_form) = 2.8061759856176202154554160447037 y[1] (numeric) = 2.8061759856176202154554160447038 absolute error = 1e-31 relative error = 3.5635683760578786835384545207608e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (closed_form) = 2.8116007945558601618298602421299 y[1] (numeric) = 2.8116007945558601618298602421302 absolute error = 3e-31 relative error = 1.0670078077260967181686062209382e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (closed_form) = 2.8170248828679047690038227601234 y[1] (numeric) = 2.8170248828679047690038227601238 absolute error = 4e-31 relative error = 1.4199377592745129494518423460537e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (closed_form) = 2.8224482529944880348890729445437 y[1] (numeric) = 2.8224482529944880348890729445441 absolute error = 4e-31 relative error = 1.4172093308552897704397894005664e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (closed_form) = 2.8278709073639649058545683422384 y[1] (numeric) = 2.8278709073639649058545683422387 absolute error = 3e-31 relative error = 1.0608687943243092988720023420600e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (closed_form) = 2.8332928483923948484819672389349 y[1] (numeric) = 2.8332928483923948484819672389352 absolute error = 3e-31 relative error = 1.0588386589484367924593295553522e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (closed_form) = 2.8387140784836247172615401555701 y[1] (numeric) = 2.8387140784836247172615401555703 absolute error = 2e-31 relative error = 7.0454436223755005875398090161447e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (closed_form) = 2.844134600029370925334223976658 y[1] (numeric) = 2.8441346000293709253342239766582 absolute error = 2e-31 relative error = 7.0320159952322450503063269309394e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (closed_form) = 2.8495544154093009253020354325275 y[1] (numeric) = 2.8495544154093009253020354325276 absolute error = 1e-31 relative error = 3.5093205962040320724291903089954e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (closed_form) = 2.8549735269911140070466539352201 y[1] (numeric) = 2.8549735269911140070466539352202 absolute error = 1e-31 relative error = 3.5026594486636459123912556580130e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.48 y[1] (closed_form) = 2.8603919371306214194146804017308 y[1] (numeric) = 2.8603919371306214194146804017308 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (closed_form) = 2.8658096481718258225478620962427 y[1] (numeric) = 2.8658096481718258225478620962428 absolute error = 1e-31 relative error = 3.4894152884087255846443033818264e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (closed_form) = 2.8712266624470000775574273699597 y[1] (numeric) = 2.8712266624470000775574273699599 absolute error = 2e-31 relative error = 6.9656639308841677518024533487170e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1016.0MB, alloc=44.3MB, time=11.52 TOP MAIN SOLVE Loop x[1] = 4.51 y[1] (closed_form) = 2.8766429822767653801635824296672 y[1] (numeric) = 2.8766429822767653801635824296673 absolute error = 1e-31 relative error = 3.4762742758176195632261655188814e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.52 y[1] (closed_form) = 2.8820586099701687448441691475842 y[1] (numeric) = 2.8820586099701687448441691475843 absolute error = 1e-31 relative error = 3.4697420674951182762172789222332e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (closed_form) = 2.8874735478247598459604529205746 y[1] (numeric) = 2.8874735478247598459604529205749 absolute error = 3e-31 relative error = 1.0389705568939360411528339184120e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (closed_form) = 2.8928877981266672222529874386226 y[1] (numeric) = 2.8928877981266672222529874386229 absolute error = 3e-31 relative error = 1.0370260477930374232654778389842e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (closed_form) = 2.8983013631506738510264739253115 y[1] (numeric) = 2.8983013631506738510264739253117 absolute error = 2e-31 relative error = 6.9005936560918841135250780371361e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (closed_form) = 2.9037142451602920982694812093458 y[1] (numeric) = 2.9037142451602920982694812093459 absolute error = 1e-31 relative error = 3.4438650485898538012663857956739e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.57 y[1] (closed_form) = 2.909126446407838050882805361734 y[1] (numeric) = 2.9091264464078380508828053617343 absolute error = 3e-31 relative error = 1.0312374024526750143834256342752e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (closed_form) = 2.914537969134505237119109312817 y[1] (numeric) = 2.9145379691345052371191093128173 absolute error = 3e-31 relative error = 1.0293226685569216924460238123075e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (closed_form) = 2.9199488155704377412662798062043 y[1] (numeric) = 2.9199488155704377412662798062047 absolute error = 4e-31 relative error = 1.3698870263308244801920829947694e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (closed_form) = 2.9253589879348027185376574425498 y[1] (numeric) = 2.9253589879348027185376574425504 absolute error = 6e-31 relative error = 2.0510303264474840588286790313286e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.61 y[1] (closed_form) = 2.9307684884358623160639218308567 y[1] (numeric) = 2.9307684884358623160639218308572 absolute error = 5e-31 relative error = 1.7060371775282997667168035581251e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.62 y[1] (closed_form) = 2.936177319271045005813934636681 y[1] (numeric) = 2.9361773192710450058139346366815 absolute error = 5e-31 relative error = 1.7028944291557069171505900166520e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (closed_form) = 2.9415854826270163352052454514164 y[1] (numeric) = 2.9415854826270163352052454514168 absolute error = 4e-31 relative error = 1.3598108991304085969292601753016e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (closed_form) = 2.9469929806797491010992359752075 y[1] (numeric) = 2.946992980679749101099235975208 absolute error = 5e-31 relative error = 1.6966446926679503984682621247612e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (closed_form) = 2.9523998155945929528110042888189 y[1] (numeric) = 2.9523998155945929528110042888194 absolute error = 5e-31 relative error = 1.6935375668261361469582954189605e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.66 y[1] (closed_form) = 2.9578059895263434297000604744681 y[1] (numeric) = 2.9578059895263434297000604744685 absolute error = 4e-31 relative error = 1.3523537426606371960119414147925e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.67 y[1] (closed_form) = 2.9632115046193104388447052226749 y[1] (numeric) = 2.9632115046193104388447052226754 absolute error = 5e-31 relative error = 1.6873584596325869595694633708535e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1056.4MB, alloc=44.3MB, time=11.97 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (closed_form) = 2.9686163630073861782405822213809 y[1] (numeric) = 2.9686163630073861782405822213814 absolute error = 5e-31 relative error = 1.6842863437344596893798765152139e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.69 y[1] (closed_form) = 2.9740205668141125109023211505598 y[1] (numeric) = 2.9740205668141125109023211505601 absolute error = 3e-31 relative error = 1.0087354584819558517669816249350e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (closed_form) = 2.9794241181527477951864092781936 y[1] (numeric) = 2.9794241181527477951864092781939 absolute error = 3e-31 relative error = 1.0069059929138283660837407750099e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (closed_form) = 2.9848270191263331765934344386668 y[1] (numeric) = 2.9848270191263331765934344386671 absolute error = 3e-31 relative error = 1.0050833702510867766621973226028e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (closed_form) = 2.9902292718277583462486192247451 y[1] (numeric) = 2.9902292718277583462486192247455 absolute error = 4e-31 relative error = 1.3376900686799262761133951706468e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (closed_form) = 2.9956308783398267712011043740506 y[1] (numeric) = 2.995630878339826771201104374051 absolute error = 4e-31 relative error = 1.3352779973401772331137023139153e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (closed_form) = 3.0010318407353204016247275941025 y[1] (numeric) = 3.0010318407353204016247275941029 absolute error = 4e-31 relative error = 1.3328748951293732014512557201514e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (closed_form) = 3.0064321610770638599460716362486 y[1] (numeric) = 3.006432161077063859946071636249 absolute error = 4e-31 relative error = 1.3304807112517673804937533135968e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (closed_form) = 3.0118318414179881168693116607012 y[1] (numeric) = 3.0118318414179881168693116607015 absolute error = 3e-31 relative error = 9.9607154647371759757630762348752e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (closed_form) = 3.0172308838011936592118663647162 y[1] (numeric) = 3.0172308838011936592118663647165 absolute error = 3e-31 relative error = 9.9428917293214044674875422989685e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (closed_form) = 3.0226292902600131544100396728523 y[1] (numeric) = 3.0226292902600131544100396728526 absolute error = 3e-31 relative error = 9.9251337557902559278830422487848e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (closed_form) = 3.0280270628180736164997198752485 y[1] (numeric) = 3.0280270628180736164997198752487 absolute error = 2e-31 relative error = 6.6049607830739578262566616213101e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (closed_form) = 3.0334242034893580783237709710155 y[1] (numeric) = 3.0334242034893580783237709710158 absolute error = 3e-31 relative error = 9.8898136190417742943041516211671e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (closed_form) = 3.0388207142782667746649968114388 y[1] (numeric) = 3.038820714278266774664996811439 absolute error = 2e-31 relative error = 6.5815004834038350207280762446479e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (closed_form) = 3.0442165971796778409514727794864 y[1] (numeric) = 3.0442165971796778409514727794866 absolute error = 2e-31 relative error = 6.5698347543762328012581060796378e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (closed_form) = 3.0496118541790075321296126786166 y[1] (numeric) = 3.0496118541790075321296126786167 absolute error = 1e-31 relative error = 3.2791058266305569516529792563701e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (closed_form) = 3.0550064872522699662495608757116 y[1] (numeric) = 3.0550064872522699662495608757117 absolute error = 1e-31 relative error = 3.2733154714162938589209110575735e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (closed_form) = 3.060400498366136397257362338258 y[1] (numeric) = 3.0604004983661363972573623382581 absolute error = 1e-31 relative error = 3.2675461938196405327871796139940e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1096.9MB, alloc=44.3MB, time=12.44 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (closed_form) = 3.0657938894779940214388569577394 y[1] (numeric) = 3.0657938894779940214388569577393 absolute error = 1e-31 relative error = 3.2617978769938373099989532984927e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (closed_form) = 3.0711866625360043219113605351353 y[1] (numeric) = 3.0711866625360043219113605351352 absolute error = 1e-31 relative error = 3.2560704049628137485354375766567e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (closed_form) = 3.0765788194791609555109242359687 y[1] (numeric) = 3.0765788194791609555109242359686 absolute error = 1e-31 relative error = 3.2503636626130437653722748921345e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (closed_form) = 3.0819703622373471863752985546119 y[1] (numeric) = 3.081970362237347186375298554612 absolute error = 1e-31 relative error = 3.2446775356854923954683737512161e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (closed_form) = 3.0873612927313928704756583488807 y[1] (numeric) = 3.0873612927313928704756583488808 absolute error = 1e-31 relative error = 3.2390119107676529686434895338511e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (closed_form) = 3.0927516128731309953036639375228 y[1] (numeric) = 3.0927516128731309953036639375229 absolute error = 1e-31 relative error = 3.2333666752856735190753886882049e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (closed_form) = 3.0981413245654537788745313468734 y[1] (numeric) = 3.0981413245654537788745313468736 absolute error = 2e-31 relative error = 6.4554834349931425198023624873743e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.93 y[1] (closed_form) = 3.1035304297023683321614544289094 y[1] (numeric) = 3.1035304297023683321614544289095 absolute error = 1e-31 relative error = 3.2221369264805339728641121841816e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (closed_form) = 3.1089189301690518890319547575648 y[1] (numeric) = 3.1089189301690518890319547575649 absolute error = 1e-31 relative error = 3.2165521921333071801103508787509e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (closed_form) = 3.114306827841906607712524073896 y[1] (numeric) = 3.1143068278419066077125240738961 absolute error = 1e-31 relative error = 3.2109874051586659821155853630341e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (closed_form) = 3.1196941245886139477642608458272 y[1] (numeric) = 3.1196941245886139477642608458272 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (closed_form) = 3.1250808222681886265090796069368 y[1] (numeric) = 3.1250808222681886265090796069369 absolute error = 1e-31 relative error = 3.1999172401378035753165291408384e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (closed_form) = 3.1304669227310321588034816310385 y[1] (numeric) = 3.1304669227310321588034816310388 absolute error = 3e-31 relative error = 9.5832349424180713549552587532595e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (closed_form) = 3.1358524278189859840148107909436 y[1] (numeric) = 3.1358524278189859840148107909438 absolute error = 2e-31 relative error = 6.3778511458557961354637758468419e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Finished! diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; Iterations = 4900 Total Elapsed Time = 12 Seconds Elapsed Time(since restart) = 12 Seconds Time to Timeout = 2 Minutes 47 Seconds Percent Done = 100 % > quit memory used=1130.5MB, alloc=44.3MB, time=12.80